statistical research methodology

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• Indian J Anaesth
• v.60(9); 2016 Sep

Basic statistical tools in research and data analysis

Zulfiqar ali.

Department of Anaesthesiology, Division of Neuroanaesthesiology, Sheri Kashmir Institute of Medical Sciences, Soura, Srinagar, Jammu and Kashmir, India

S Bala Bhaskar

1 Department of Anaesthesiology and Critical Care, Vijayanagar Institute of Medical Sciences, Bellary, Karnataka, India

Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings. The statistical analysis gives meaning to the meaningless numbers, thereby breathing life into a lifeless data. The results and inferences are precise only if proper statistical tests are used. This article will try to acquaint the reader with the basic research tools that are utilised while conducting various studies. The article covers a brief outline of the variables, an understanding of quantitative and qualitative variables and the measures of central tendency. An idea of the sample size estimation, power analysis and the statistical errors is given. Finally, there is a summary of parametric and non-parametric tests used for data analysis.

INTRODUCTION

Statistics is a branch of science that deals with the collection, organisation, analysis of data and drawing of inferences from the samples to the whole population.[ 1 ] This requires a proper design of the study, an appropriate selection of the study sample and choice of a suitable statistical test. An adequate knowledge of statistics is necessary for proper designing of an epidemiological study or a clinical trial. Improper statistical methods may result in erroneous conclusions which may lead to unethical practice.[ 2 ]

Variable is a characteristic that varies from one individual member of population to another individual.[ 3 ] Variables such as height and weight are measured by some type of scale, convey quantitative information and are called as quantitative variables. Sex and eye colour give qualitative information and are called as qualitative variables[ 3 ] [ Figure 1 ].

Classification of variables

Quantitative variables

Quantitative or numerical data are subdivided into discrete and continuous measurements. Discrete numerical data are recorded as a whole number such as 0, 1, 2, 3,… (integer), whereas continuous data can assume any value. Observations that can be counted constitute the discrete data and observations that can be measured constitute the continuous data. Examples of discrete data are number of episodes of respiratory arrests or the number of re-intubations in an intensive care unit. Similarly, examples of continuous data are the serial serum glucose levels, partial pressure of oxygen in arterial blood and the oesophageal temperature.

A hierarchical scale of increasing precision can be used for observing and recording the data which is based on categorical, ordinal, interval and ratio scales [ Figure 1 ].

Categorical or nominal variables are unordered. The data are merely classified into categories and cannot be arranged in any particular order. If only two categories exist (as in gender male and female), it is called as a dichotomous (or binary) data. The various causes of re-intubation in an intensive care unit due to upper airway obstruction, impaired clearance of secretions, hypoxemia, hypercapnia, pulmonary oedema and neurological impairment are examples of categorical variables.

Ordinal variables have a clear ordering between the variables. However, the ordered data may not have equal intervals. Examples are the American Society of Anesthesiologists status or Richmond agitation-sedation scale.

Interval variables are similar to an ordinal variable, except that the intervals between the values of the interval variable are equally spaced. A good example of an interval scale is the Fahrenheit degree scale used to measure temperature. With the Fahrenheit scale, the difference between 70° and 75° is equal to the difference between 80° and 85°: The units of measurement are equal throughout the full range of the scale.

Ratio scales are similar to interval scales, in that equal differences between scale values have equal quantitative meaning. However, ratio scales also have a true zero point, which gives them an additional property. For example, the system of centimetres is an example of a ratio scale. There is a true zero point and the value of 0 cm means a complete absence of length. The thyromental distance of 6 cm in an adult may be twice that of a child in whom it may be 3 cm.

STATISTICS: DESCRIPTIVE AND INFERENTIAL STATISTICS

Descriptive statistics[ 4 ] try to describe the relationship between variables in a sample or population. Descriptive statistics provide a summary of data in the form of mean, median and mode. Inferential statistics[ 4 ] use a random sample of data taken from a population to describe and make inferences about the whole population. It is valuable when it is not possible to examine each member of an entire population. The examples if descriptive and inferential statistics are illustrated in Table 1 .

Example of descriptive and inferential statistics

Descriptive statistics

The extent to which the observations cluster around a central location is described by the central tendency and the spread towards the extremes is described by the degree of dispersion.

Measures of central tendency

The measures of central tendency are mean, median and mode.[ 6 ] Mean (or the arithmetic average) is the sum of all the scores divided by the number of scores. Mean may be influenced profoundly by the extreme variables. For example, the average stay of organophosphorus poisoning patients in ICU may be influenced by a single patient who stays in ICU for around 5 months because of septicaemia. The extreme values are called outliers. The formula for the mean is

where x = each observation and n = number of observations. Median[ 6 ] is defined as the middle of a distribution in a ranked data (with half of the variables in the sample above and half below the median value) while mode is the most frequently occurring variable in a distribution. Range defines the spread, or variability, of a sample.[ 7 ] It is described by the minimum and maximum values of the variables. If we rank the data and after ranking, group the observations into percentiles, we can get better information of the pattern of spread of the variables. In percentiles, we rank the observations into 100 equal parts. We can then describe 25%, 50%, 75% or any other percentile amount. The median is the 50 th percentile. The interquartile range will be the observations in the middle 50% of the observations about the median (25 th -75 th percentile). Variance[ 7 ] is a measure of how spread out is the distribution. It gives an indication of how close an individual observation clusters about the mean value. The variance of a population is defined by the following formula:

where σ 2 is the population variance, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The variance of a sample is defined by slightly different formula:

where s 2 is the sample variance, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. The formula for the variance of a population has the value ‘ n ’ as the denominator. The expression ‘ n −1’ is known as the degrees of freedom and is one less than the number of parameters. Each observation is free to vary, except the last one which must be a defined value. The variance is measured in squared units. To make the interpretation of the data simple and to retain the basic unit of observation, the square root of variance is used. The square root of the variance is the standard deviation (SD).[ 8 ] The SD of a population is defined by the following formula:

where σ is the population SD, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The SD of a sample is defined by slightly different formula:

where s is the sample SD, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. An example for calculation of variation and SD is illustrated in Table 2 .

Example of mean, variance, standard deviation

Normal distribution or Gaussian distribution

Most of the biological variables usually cluster around a central value, with symmetrical positive and negative deviations about this point.[ 1 ] The standard normal distribution curve is a symmetrical bell-shaped. In a normal distribution curve, about 68% of the scores are within 1 SD of the mean. Around 95% of the scores are within 2 SDs of the mean and 99% within 3 SDs of the mean [ Figure 2 ].

Normal distribution curve

Skewed distribution

It is a distribution with an asymmetry of the variables about its mean. In a negatively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the right of Figure 1 . In a positively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the left of the figure leading to a longer right tail.

Curves showing negatively skewed and positively skewed distribution

Inferential statistics

In inferential statistics, data are analysed from a sample to make inferences in the larger collection of the population. The purpose is to answer or test the hypotheses. A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. Hypothesis tests are thus procedures for making rational decisions about the reality of observed effects.

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty).

In inferential statistics, the term ‘null hypothesis’ ( H 0 ‘ H-naught ,’ ‘ H-null ’) denotes that there is no relationship (difference) between the population variables in question.[ 9 ]

Alternative hypothesis ( H 1 and H a ) denotes that a statement between the variables is expected to be true.[ 9 ]

The P value (or the calculated probability) is the probability of the event occurring by chance if the null hypothesis is true. The P value is a numerical between 0 and 1 and is interpreted by researchers in deciding whether to reject or retain the null hypothesis [ Table 3 ].

P values with interpretation

If P value is less than the arbitrarily chosen value (known as α or the significance level), the null hypothesis (H0) is rejected [ Table 4 ]. However, if null hypotheses (H0) is incorrectly rejected, this is known as a Type I error.[ 11 ] Further details regarding alpha error, beta error and sample size calculation and factors influencing them are dealt with in another section of this issue by Das S et al .[ 12 ]

Illustration for null hypothesis

PARAMETRIC AND NON-PARAMETRIC TESTS

Numerical data (quantitative variables) that are normally distributed are analysed with parametric tests.[ 13 ]

Two most basic prerequisites for parametric statistical analysis are:

• The assumption of normality which specifies that the means of the sample group are normally distributed
• The assumption of equal variance which specifies that the variances of the samples and of their corresponding population are equal.

However, if the distribution of the sample is skewed towards one side or the distribution is unknown due to the small sample size, non-parametric[ 14 ] statistical techniques are used. Non-parametric tests are used to analyse ordinal and categorical data.

Parametric tests

The parametric tests assume that the data are on a quantitative (numerical) scale, with a normal distribution of the underlying population. The samples have the same variance (homogeneity of variances). The samples are randomly drawn from the population, and the observations within a group are independent of each other. The commonly used parametric tests are the Student's t -test, analysis of variance (ANOVA) and repeated measures ANOVA.

Student's t -test

Student's t -test is used to test the null hypothesis that there is no difference between the means of the two groups. It is used in three circumstances:

where X = sample mean, u = population mean and SE = standard error of mean

where X 1 − X 2 is the difference between the means of the two groups and SE denotes the standard error of the difference.

• To test if the population means estimated by two dependent samples differ significantly (the paired t -test). A usual setting for paired t -test is when measurements are made on the same subjects before and after a treatment.

The formula for paired t -test is:

where d is the mean difference and SE denotes the standard error of this difference.

The group variances can be compared using the F -test. The F -test is the ratio of variances (var l/var 2). If F differs significantly from 1.0, then it is concluded that the group variances differ significantly.

Analysis of variance

The Student's t -test cannot be used for comparison of three or more groups. The purpose of ANOVA is to test if there is any significant difference between the means of two or more groups.

In ANOVA, we study two variances – (a) between-group variability and (b) within-group variability. The within-group variability (error variance) is the variation that cannot be accounted for in the study design. It is based on random differences present in our samples.

However, the between-group (or effect variance) is the result of our treatment. These two estimates of variances are compared using the F-test.

A simplified formula for the F statistic is:

where MS b is the mean squares between the groups and MS w is the mean squares within groups.

Repeated measures analysis of variance

As with ANOVA, repeated measures ANOVA analyses the equality of means of three or more groups. However, a repeated measure ANOVA is used when all variables of a sample are measured under different conditions or at different points in time.

As the variables are measured from a sample at different points of time, the measurement of the dependent variable is repeated. Using a standard ANOVA in this case is not appropriate because it fails to model the correlation between the repeated measures: The data violate the ANOVA assumption of independence. Hence, in the measurement of repeated dependent variables, repeated measures ANOVA should be used.

Non-parametric tests

When the assumptions of normality are not met, and the sample means are not normally, distributed parametric tests can lead to erroneous results. Non-parametric tests (distribution-free test) are used in such situation as they do not require the normality assumption.[ 15 ] Non-parametric tests may fail to detect a significant difference when compared with a parametric test. That is, they usually have less power.

As is done for the parametric tests, the test statistic is compared with known values for the sampling distribution of that statistic and the null hypothesis is accepted or rejected. The types of non-parametric analysis techniques and the corresponding parametric analysis techniques are delineated in Table 5 .

Analogue of parametric and non-parametric tests

Median test for one sample: The sign test and Wilcoxon's signed rank test

The sign test and Wilcoxon's signed rank test are used for median tests of one sample. These tests examine whether one instance of sample data is greater or smaller than the median reference value.

This test examines the hypothesis about the median θ0 of a population. It tests the null hypothesis H0 = θ0. When the observed value (Xi) is greater than the reference value (θ0), it is marked as+. If the observed value is smaller than the reference value, it is marked as − sign. If the observed value is equal to the reference value (θ0), it is eliminated from the sample.

If the null hypothesis is true, there will be an equal number of + signs and − signs.

The sign test ignores the actual values of the data and only uses + or − signs. Therefore, it is useful when it is difficult to measure the values.

Wilcoxon's signed rank test

There is a major limitation of sign test as we lose the quantitative information of the given data and merely use the + or – signs. Wilcoxon's signed rank test not only examines the observed values in comparison with θ0 but also takes into consideration the relative sizes, adding more statistical power to the test. As in the sign test, if there is an observed value that is equal to the reference value θ0, this observed value is eliminated from the sample.

Wilcoxon's rank sum test ranks all data points in order, calculates the rank sum of each sample and compares the difference in the rank sums.

Mann-Whitney test

It is used to test the null hypothesis that two samples have the same median or, alternatively, whether observations in one sample tend to be larger than observations in the other.

Mann–Whitney test compares all data (xi) belonging to the X group and all data (yi) belonging to the Y group and calculates the probability of xi being greater than yi: P (xi > yi). The null hypothesis states that P (xi > yi) = P (xi < yi) =1/2 while the alternative hypothesis states that P (xi > yi) ≠1/2.

Kolmogorov-Smirnov test

The two-sample Kolmogorov-Smirnov (KS) test was designed as a generic method to test whether two random samples are drawn from the same distribution. The null hypothesis of the KS test is that both distributions are identical. The statistic of the KS test is a distance between the two empirical distributions, computed as the maximum absolute difference between their cumulative curves.

Kruskal-Wallis test

The Kruskal–Wallis test is a non-parametric test to analyse the variance.[ 14 ] It analyses if there is any difference in the median values of three or more independent samples. The data values are ranked in an increasing order, and the rank sums calculated followed by calculation of the test statistic.

Jonckheere test

In contrast to Kruskal–Wallis test, in Jonckheere test, there is an a priori ordering that gives it a more statistical power than the Kruskal–Wallis test.[ 14 ]

Friedman test

The Friedman test is a non-parametric test for testing the difference between several related samples. The Friedman test is an alternative for repeated measures ANOVAs which is used when the same parameter has been measured under different conditions on the same subjects.[ 13 ]

Tests to analyse the categorical data

Chi-square test, Fischer's exact test and McNemar's test are used to analyse the categorical or nominal variables. The Chi-square test compares the frequencies and tests whether the observed data differ significantly from that of the expected data if there were no differences between groups (i.e., the null hypothesis). It is calculated by the sum of the squared difference between observed ( O ) and the expected ( E ) data (or the deviation, d ) divided by the expected data by the following formula:

A Yates correction factor is used when the sample size is small. Fischer's exact test is used to determine if there are non-random associations between two categorical variables. It does not assume random sampling, and instead of referring a calculated statistic to a sampling distribution, it calculates an exact probability. McNemar's test is used for paired nominal data. It is applied to 2 × 2 table with paired-dependent samples. It is used to determine whether the row and column frequencies are equal (that is, whether there is ‘marginal homogeneity’). The null hypothesis is that the paired proportions are equal. The Mantel-Haenszel Chi-square test is a multivariate test as it analyses multiple grouping variables. It stratifies according to the nominated confounding variables and identifies any that affects the primary outcome variable. If the outcome variable is dichotomous, then logistic regression is used.

SOFTWARES AVAILABLE FOR STATISTICS, SAMPLE SIZE CALCULATION AND POWER ANALYSIS

Numerous statistical software systems are available currently. The commonly used software systems are Statistical Package for the Social Sciences (SPSS – manufactured by IBM corporation), Statistical Analysis System ((SAS – developed by SAS Institute North Carolina, United States of America), R (designed by Ross Ihaka and Robert Gentleman from R core team), Minitab (developed by Minitab Inc), Stata (developed by StataCorp) and the MS Excel (developed by Microsoft).

There are a number of web resources which are related to statistical power analyses. A few are:

• StatPages.net – provides links to a number of online power calculators
• G-Power – provides a downloadable power analysis program that runs under DOS
• Power analysis for ANOVA designs an interactive site that calculates power or sample size needed to attain a given power for one effect in a factorial ANOVA design
• SPSS makes a program called SamplePower. It gives an output of a complete report on the computer screen which can be cut and paste into another document.

It is important that a researcher knows the concepts of the basic statistical methods used for conduct of a research study. This will help to conduct an appropriately well-designed study leading to valid and reliable results. Inappropriate use of statistical techniques may lead to faulty conclusions, inducing errors and undermining the significance of the article. Bad statistics may lead to bad research, and bad research may lead to unethical practice. Hence, an adequate knowledge of statistics and the appropriate use of statistical tests are important. An appropriate knowledge about the basic statistical methods will go a long way in improving the research designs and producing quality medical research which can be utilised for formulating the evidence-based guidelines.

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Conflicts of interest.

There are no conflicts of interest.

What Is Statistical Analysis?

Statistical analysis helps you pull meaningful insights from data. The process involves working with data and deducing numbers to tell quantitative stories.

Statistical analysis is a technique we use to find patterns in data and make inferences about those patterns to describe variability in the results of a data set or an experiment. 

In its simplest form, statistical analysis answers questions about:

• Quantification — how big/small/tall/wide is it?
• Variability — growth, increase, decline
• The confidence level of these variabilities

What Are the 2 Types of Statistical Analysis?

• Descriptive Statistics:  Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 
• Inferential Statistics:  Inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests.

What’s the Purpose of Statistical Analysis?

Using statistical analysis, you can determine trends in the data by calculating your data set’s mean or median. You can also analyze the variation between different data points from the mean to get the standard deviation . Furthermore, to test the validity of your statistical analysis conclusions, you can use hypothesis testing techniques, like P-value, to determine the likelihood that the observed variability could have occurred by chance.

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Statistical Analysis Methods

There are two major types of statistical data analysis: descriptive and inferential. 

Descriptive Statistical Analysis

Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 

Within the descriptive analysis branch, there are two main types: measures of central tendency (i.e. mean, median and mode) and measures of dispersion or variation (i.e. variance , standard deviation and range). 

For example, you can calculate the average exam results in a class using central tendency or, in particular, the mean. In that case, you’d sum all student results and divide by the number of tests. You can also calculate the data set’s spread by calculating the variance. To calculate the variance, subtract each exam result in the data set from the mean, square the answer, add everything together and divide by the number of tests.

Inferential Statistics

On the other hand, inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests. 

There are two main types of inferential statistical analysis: hypothesis testing and regression analysis. We use hypothesis testing to test and validate assumptions in order to draw conclusions about a population from the sample data. Popular tests include Z-test, F-Test, ANOVA test and confidence intervals . On the other hand, regression analysis primarily estimates the relationship between a dependent variable and one or more independent variables. There are numerous types of regression analysis but the most popular ones include linear and logistic regression .  

Statistical Analysis Steps  

In the era of big data and data science, there is a rising demand for a more problem-driven approach. As a result, we must approach statistical analysis holistically. We may divide the entire process into five different and significant stages by using the well-known PPDAC model of statistics: Problem, Plan, Data, Analysis and Conclusion.

In the first stage, you define the problem you want to tackle and explore questions about the problem. 

2. Plan

Next is the planning phase. You can check whether data is available or if you need to collect data for your problem. You also determine what to measure and how to measure it. 

The third stage involves data collection, understanding the data and checking its quality. 

4. Analysis

Statistical data analysis is the fourth stage. Here you process and explore the data with the help of tables, graphs and other data visualizations.  You also develop and scrutinize your hypothesis in this stage of analysis. 

5. Conclusion

The final step involves interpretations and conclusions from your analysis. It also covers generating new ideas for the next iteration. Thus, statistical analysis is not a one-time event but an iterative process.

Statistical Analysis Uses

Statistical analysis is useful for research and decision making because it allows us to understand the world around us and draw conclusions by testing our assumptions. Statistical analysis is important for various applications, including:

• Statistical quality control and analysis in product development 
• Clinical trials
• Customer satisfaction surveys and customer experience research 
• Marketing operations management
• Process improvement and optimization
• Training needs 

More on Statistical Analysis From Built In Experts Intro to Descriptive Statistics for Machine Learning

Benefits of Statistical Analysis

Here are some of the reasons why statistical analysis is widespread in many applications and why it’s necessary:

Understand Data

Statistical analysis gives you a better understanding of the data and what they mean. These types of analyses provide information that would otherwise be difficult to obtain by merely looking at the numbers without considering their relationship.

Find Causal Relationships

Statistical analysis can help you investigate causation or establish the precise meaning of an experiment, like when you’re looking for a relationship between two variables.

Make Data-Informed Decisions

Businesses are constantly looking to find ways to improve their services and products . Statistical analysis allows you to make data-informed decisions about your business or future actions by helping you identify trends in your data, whether positive or negative. 

Determine Probability

Statistical analysis is an approach to understanding how the probability of certain events affects the outcome of an experiment. It helps scientists and engineers decide how much confidence they can have in the results of their research, how to interpret their data and what questions they can feasibly answer.

You’ve Got Questions. Our Experts Have Answers. Confidence Intervals, Explained!

What Are the Risks of Statistical Analysis?

Statistical analysis can be valuable and effective, but it’s an imperfect approach. Even if the analyst or researcher performs a thorough statistical analysis, there may still be known or unknown problems that can affect the results. Therefore, statistical analysis is not a one-size-fits-all process. If you want to get good results, you need to know what you’re doing. It can take a lot of time to figure out which type of statistical analysis will work best for your situation .

Thus, you should remember that our conclusions drawn from statistical analysis don’t always guarantee correct results. This can be dangerous when making business decisions. In marketing , for example, we may come to the wrong conclusion about a product . Therefore, the conclusions we draw from statistical data analysis are often approximated; testing for all factors affecting an observation is impossible.

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Statistics for Research Students

(2 reviews)

Erich C Fein, Toowoomba, Australia

John Gilmour, Toowoomba, Australia

Tayna Machin, Toowoomba, Australia

Liam Hendry, Toowoomba, Australia

Copyright Year: 2022

ISBN 13: 9780645326109

Publisher: University of Southern Queensland

Language: English

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Reviewed by Sojib Bin Zaman, Assistant Professor, James Madison University on 3/18/24

From exploring data in Chapter One to learning advanced methodologies such as moderation and mediation in Chapter Seven, the reader is guided through the entire process of statistical methodology. With each chapter covering a different statistical... read more

Comprehensiveness rating: 5 see less

From exploring data in Chapter One to learning advanced methodologies such as moderation and mediation in Chapter Seven, the reader is guided through the entire process of statistical methodology. With each chapter covering a different statistical technique and methodology, students gain a comprehensive understanding of statistical research techniques.

Content Accuracy rating: 5

During my review of the textbook, I did not find any notable errors or omissions. In my opinion, the material was comprehensive, resulting in an enjoyable learning experience.

Relevance/Longevity rating: 5

A majority of the textbook's content is aligned with current trends, advancements, and enduring principles in the field of statistics. Several emerging methodologies and technologies are incorporated into this textbook to enhance students' statistical knowledge. It will be a valuable resource in the long run if students and researchers can properly utilize this textbook.

Clarity rating: 5

A clear explanation of complex statistical concepts such as moderation and mediation is provided in the writing style. Examples and problem sets are provided in the textbook in a comprehensive and well-explained manner.

Consistency rating: 5

Each chapter maintains consistent formatting and language, with resources organized consistently. Headings and subheadings worked well.

Modularity rating: 5

The textbook is well-structured, featuring cohesive chapters that flow smoothly from one to another. It is carefully crafted with a focus on defining terms clearly, facilitating understanding, and ensuring logical flow.

Organization/Structure/Flow rating: 5

From basic to advanced concepts, this book provides clarity of progression, logical arranging of sections and chapters, and effective headings and subheadings that guide readers. Further, the organization provides students with a lot of information on complex statistical methodologies.

Interface rating: 5

The available formats included PDFs, online access, and e-books. The e-book interface was particularly appealing to me, as it provided seamless navigation and viewing of content without compromising usability.

Grammatical Errors rating: 5

I found no significant errors in this document, and the overall quality of the writing was commendable. There was a high level of clarity and coherence in the text, which contributed to a positive reading experience.

Cultural Relevance rating: 5

The content of the book, as well as its accompanying examples, demonstrates a dedication to inclusivity by taking into account cultural diversity and a variety of perspectives. Furthermore, the material actively promotes cultural diversity, which enables readers to develop a deeper understanding of various cultural contexts and experiences.

In summary, this textbook provides a comprehensive resource tailored for advanced statistics courses, characterized by meticulous organization and practical supplementary materials. This book also provides valuable insights into the interpretation of computer output that enhance a greater understanding of each concept presented.

Reviewed by Zhuanzhuan Ma, Assistant Professor, University of Texas Rio Grande Valley on 3/7/24

The textbook covers all necessary areas and topics for students who want to conduct research in statistics. It includes foundational concepts, application methods, and advanced statistical techniques relevant to research methodologies. read more

The textbook covers all necessary areas and topics for students who want to conduct research in statistics. It includes foundational concepts, application methods, and advanced statistical techniques relevant to research methodologies.

The textbook presents statistical methods and data accurately, with up-to-date statistical practices and examples.

Relevance/Longevity rating: 4

The textbook's content is relevant to current research practices. The book includes contemporary examples and case studies that are currently prevalent in research communities. One small drawback is that the textbook did not include the example code for conduct data analysis.

The textbook break down complex statistical methods into understandable segments. All the concepts are clearly explained. Authors used diagrams, examples, and all kinds of explanations to facilitate learning for students with varying levels of background knowledge.

The terminology, framework, and presentation style (e.g. concepts, methodologies, and examples) seem consistent throughout the book.

The textbook is well organized that each chapter and section can be used independently without losing the context necessary for understanding. Also, the modular structure allows instructors and students to adapt the materials for different study plans.

The textbook is well-organized and progresses from basic concepts to more complex methods, making it easier for students to follow along. There is a logical flow of the content.

The digital format of the textbook has an interface that includes the design, layout, and navigational features. It is easier to use for readers.

The quality of writing is very high. The well-written texts help both instructors and students to follow the ideas clearly.

The textbook does not perpetuate stereotypes or biases and are inclusive in their examples, language, and perspectives.

Table of Contents

• Acknowledgement of Country
• Accessibility Information
• About the Authors
• Introduction
• I. Chapter One - Exploring Your Data
• II. Chapter Two - Test Statistics, p Values, Confidence Intervals and Effect Sizes
• III. Chapter Three- Comparing Two Group Means
• IV. Chapter Four - Comparing Associations Between Two Variables
• V. Chapter Five- Comparing Associations Between Multiple Variables
• VI. Chapter Six- Comparing Three or More Group Means
• VII. Chapter Seven- Moderation and Mediation Analyses
• VIII. Chapter Eight- Factor Analysis and Scale Reliability
• IX. Chapter Nine- Nonparametric Statistics

Ancillary Material

About the book.

This book aims to help you understand and navigate statistical concepts and the main types of statistical analyses essential for research students. 

About the Contributors

Dr Erich C. Fein  is an Associate Professor at the University of Southern Queensland. He received substantial training in research methods and statistics during his PhD program at Ohio State University.  He currently teaches four courses in research methods and statistics.  His research involves leadership, occupational health, and motivation, as well as issues related to research methods such as the following article: “ Safeguarding Access and Safeguarding Meaning as Strategies for Achieving Confidentiality .”  Click here to link to his  Google Scholar  profile.

Dr John Gilmour  is a Lecturer at the University of Southern Queensland and a Postdoctoral Research Fellow at the University of Queensland, His research focuses on the locational and temporal analyses of crime, and the evaluation of police training and procedures. John has worked across many different sectors including PTSD, social media, criminology, and medicine.

Dr Tanya Machin  is a Senior Lecturer and Associate Dean at the University of Southern Queensland. Her research focuses on social media and technology across the lifespan. Tanya has co-taught Honours research methods with Erich, and is also interested in ethics and qualitative research methods. Tanya has worked across many different sectors including primary schools, financial services, and mental health.

Dr Liam Hendry  is a Lecturer at the University of Southern Queensland. His research interests focus on long-term and short-term memory, measurement of human memory, attention, learning & diverse aspects of cognitive psychology.

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Choosing the Right Research Methodology: A Guide for Researchers

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Table of Contents

Choosing an optimal research methodology is crucial for the success of any research project. The methodology you select will determine the type of data you collect, how you collect it, and how you analyse it. Understanding the different types of research methods available along with their strengths and weaknesses, is thus imperative to make an informed decision.

Understanding different research methods:

There are several research methods available depending on the type of study you are conducting, i.e., whether it is laboratory-based, clinical, epidemiological, or survey based . Some common methodologies include qualitative research, quantitative research, experimental research, survey-based research, and action research. Each method can be opted for and modified, depending on the type of research hypotheses and objectives.

Qualitative vs quantitative research:

When deciding on a research methodology, one of the key factors to consider is whether your research will be qualitative or quantitative. Qualitative research is used to understand people’s experiences, concepts, thoughts, or behaviours . Quantitative research, on the contrary, deals with numbers, graphs, and charts, and is used to test or confirm hypotheses, assumptions, and theories. 

Qualitative research methodology:

Qualitative research is often used to examine issues that are not well understood, and to gather additional insights on these topics. Qualitative research methods include open-ended survey questions, observations of behaviours described through words, and reviews of literature that has explored similar theories and ideas. These methods are used to understand how language is used in real-world situations, identify common themes or overarching ideas, and describe and interpret various texts. Data analysis for qualitative research typically includes discourse analysis, thematic analysis, and textual analysis. 

Quantitative research methodology:

The goal of quantitative research is to test hypotheses, confirm assumptions and theories, and determine cause-and-effect relationships. Quantitative research methods include experiments, close-ended survey questions, and countable and numbered observations. Data analysis for quantitative research relies heavily on statistical methods.

Analysing qualitative vs quantitative data:

The methods used for data analysis also differ for qualitative and quantitative research. As mentioned earlier, quantitative data is generally analysed using statistical methods and does not leave much room for speculation. It is more structured and follows a predetermined plan. In quantitative research, the researcher starts with a hypothesis and uses statistical methods to test it. Contrarily, methods used for qualitative data analysis can identify patterns and themes within the data, rather than provide statistical measures of the data. It is an iterative process, where the researcher goes back and forth trying to gauge the larger implications of the data through different perspectives and revising the analysis if required.

When to use qualitative vs quantitative research:

The choice between qualitative and quantitative research will depend on the gap that the research project aims to address, and specific objectives of the study. If the goal is to establish facts about a subject or topic, quantitative research is an appropriate choice. However, if the goal is to understand people’s experiences or perspectives, qualitative research may be more suitable. 

Conclusion:

In conclusion, an understanding of the different research methods available, their applicability, advantages, and disadvantages is essential for making an informed decision on the best methodology for your project. If you need any additional guidance on which research methodology to opt for, you can head over to Elsevier Author Services (EAS). EAS experts will guide you throughout the process and help you choose the perfect methodology for your research goals.

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Statistical Analysis in Research: Meaning, Methods and Types

Home » Videos » Statistical Analysis in Research: Meaning, Methods and Types

The scientific method is an empirical approach to acquiring new knowledge by making skeptical observations and analyses to develop a meaningful interpretation. It is the basis of research and the primary pillar of modern science. Researchers seek to understand the relationships between factors associated with the phenomena of interest. In some cases, research works with vast chunks of data, making it difficult to observe or manipulate each data point. As a result, statistical analysis in research becomes a means of evaluating relationships and interconnections between variables with tools and analytical techniques for working with large data. Since researchers use statistical power analysis to assess the probability of finding an effect in such an investigation, the method is relatively accurate. Hence, statistical analysis in research eases analytical methods by focusing on the quantifiable aspects of phenomena.

What is Statistical Analysis in Research? A Simplified Definition

Statistical analysis uses quantitative data to investigate patterns, relationships, and patterns to understand real-life and simulated phenomena. The approach is a key analytical tool in various fields, including academia, business, government, and science in general. This statistical analysis in research definition implies that the primary focus of the scientific method is quantitative research. Notably, the investigator targets the constructs developed from general concepts as the researchers can quantify their hypotheses and present their findings in simple statistics.

When a business needs to learn how to improve its product, they collect statistical data about the production line and customer satisfaction. Qualitative data is valuable and often identifies the most common themes in the stakeholders’ responses. On the other hand, the quantitative data creates a level of importance, comparing the themes based on their criticality to the affected persons. For instance, descriptive statistics highlight tendency, frequency, variation, and position information. While the mean shows the average number of respondents who value a certain aspect, the variance indicates the accuracy of the data. In any case, statistical analysis creates simplified concepts used to understand the phenomenon under investigation. It is also a key component in academia as the primary approach to data representation, especially in research projects, term papers and dissertations. 

Most Useful Statistical Analysis Methods in Research

Using statistical analysis methods in research is inevitable, especially in academic assignments, projects, and term papers. It’s always advisable to seek assistance from your professor or you can try research paper writing by CustomWritings before you start your academic project or write statistical analysis in research paper. Consulting an expert when developing a topic for your thesis or short mid-term assignment increases your chances of getting a better grade. Most importantly, it improves your understanding of research methods with insights on how to enhance the originality and quality of personalized essays. Professional writers can also help select the most suitable statistical analysis method for your thesis, influencing the choice of data and type of study.

Descriptive Statistics

Descriptive statistics is a statistical method summarizing quantitative figures to understand critical details about the sample and population. A description statistic is a figure that quantifies a specific aspect of the data. For instance, instead of analyzing the behavior of a thousand students, research can identify the most common actions among them. By doing this, the person utilizes statistical analysis in research, particularly descriptive statistics.

• Measures of central tendency . Central tendency measures are the mean, mode, and media or the averages denoting specific data points. They assess the centrality of the probability distribution, hence the name. These measures describe the data in relation to the center.
• Measures of frequency . These statistics document the number of times an event happens. They include frequency, count, ratios, rates, and proportions. Measures of frequency can also show how often a score occurs.
• Measures of dispersion/variation . These descriptive statistics assess the intervals between the data points. The objective is to view the spread or disparity between the specific inputs. Measures of variation include the standard deviation, variance, and range. They indicate how the spread may affect other statistics, such as the mean.
• Measures of position . Sometimes researchers can investigate relationships between scores. Measures of position, such as percentiles, quartiles, and ranks, demonstrate this association. They are often useful when comparing the data to normalized information.

Inferential Statistics

Inferential statistics is critical in statistical analysis in quantitative research. This approach uses statistical tests to draw conclusions about the population. Examples of inferential statistics include t-tests, F-tests, ANOVA, p-value, Mann-Whitney U test, and Wilcoxon W test. This

Common Statistical Analysis in Research Types

Although inferential and descriptive statistics can be classified as types of statistical analysis in research, they are mostly considered analytical methods. Types of research are distinguishable by the differences in the methodology employed in analyzing, assembling, classifying, manipulating, and interpreting data. The categories may also depend on the type of data used.

Predictive Analysis

Predictive research analyzes past and present data to assess trends and predict future events. An excellent example of predictive analysis is a market survey that seeks to understand customers’ spending habits to weigh the possibility of a repeat or future purchase. Such studies assess the likelihood of an action based on trends.

Prescriptive Analysis

On the other hand, a prescriptive analysis targets likely courses of action. It’s decision-making research designed to identify optimal solutions to a problem. Its primary objective is to test or assess alternative measures.

Causal Analysis

Causal research investigates the explanation behind the events. It explores the relationship between factors for causation. Thus, researchers use causal analyses to analyze root causes, possible problems, and unknown outcomes.

Mechanistic Analysis

This type of research investigates the mechanism of action. Instead of focusing only on the causes or possible outcomes, researchers may seek an understanding of the processes involved. In such cases, they use mechanistic analyses to document, observe, or learn the mechanisms involved.

Exploratory Data Analysis

Similarly, an exploratory study is extensive with a wider scope and minimal limitations. This type of research seeks insight into the topic of interest. An exploratory researcher does not try to generalize or predict relationships. Instead, they look for information about the subject before conducting an in-depth analysis.

The Importance of Statistical Analysis in Research

As a matter of fact, statistical analysis provides critical information for decision-making. Decision-makers require past trends and predictive assumptions to inform their actions. In most cases, the data is too complex or lacks meaningful inferences. Statistical tools for analyzing such details help save time and money, deriving only valuable information for assessment. An excellent statistical analysis in research example is a randomized control trial (RCT) for the Covid-19 vaccine. You can download a sample of such a document online to understand the significance such analyses have to the stakeholders. A vaccine RCT assesses the effectiveness, side effects, duration of protection, and other benefits. Hence, statistical analysis in research is a helpful tool for understanding data.

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Research Methodology

Research Methodology is a critical component of any research exercise as it can make the difference between a completely irrelevant and a completely relevant exercise. Frequently, the research methodology underlying a multimillion dollar research project can make the difference between completely accurate and completely inaccurate results, although the underlying methods or processes may have been done accurately.

Research methodology is thus the foundation or general rules that determine the accuracy and validity of any research activity. It’s important to understand the difference between the terms ‘methodology’ and ‘method’, as the former refers to the general rules and guidelines pertaining to a set of methods, and explains why a specific strategy to address a specific research question is to be applied. Research methodology can cover the following three key areas of research:

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• Survey design
• Data collection
• Data analysis

Research methodology will determine how a specific survey is to be designed and how large the sample population should be, in addition to other practical questions such as which scaling method to use, what kind of target population to which to address the survey, how the survey is to be disseminated and so on. Each of these components will constitute a larger body of knowledge and have its own impact on the outcome and validity of the survey. For instance, using a Likert scale as opposed to a True-False type of question can lead to substantial variations in the accuracy of the survey.

In the same fashion, telephone interviews versus mail-response interviews each has its own set of pros and cons. Data collection is thus another important aspect of the research methodology. Data analysis is an extremely important aspect to consider when conducting research. There are a number of different methods that can be applied to similar problems based on the type of response (multiple choice, true false, numerical, etc.), sample size and expected outcome. Furthermore, each type of test will have its’ own pros and cons. For instance, in testing significance of variables, parametric (t-test, z-test, ANOVA, etc.) or non-parametric (chi-square, Kruskal-Wallis, Wilcoxon signed-rank, etc.) tests may be used. Based on the specific features of a dataset, a specific set of methods will have to be adopted in order to produce the most accurate possible result.

Types of research methodologies

Research is typically categorized in two forms:

• Qualitative: where variables are not quantified and judgment, inference and interpretation are required along specific qualitative analysis expertise, to generate results

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• Quantitative: where variables are quantified and scientific methods can be applied to generating a precise result which can be applied to building quantifiable results

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Given the nature of each type of research, different research methodologies are applied to each type; for instance, while a qualitative research project uses techniques such as case study, ethnography , and discourse analysis, quantitative methodologies use experiments, interviews, surveys and the like. Each research methodology, in addition to prescribing specific methods for design, data collection and analysis, provides general guidelines as to applicability and validity.

In general, qualitative research methodologies share the following common characteristics:

• They generally take place in a social setting
• Involve social observation and interaction
• Rely on inference and interpretation

Its drawbacks include but are not limited to the following:

• Results are based on interpretation and inference which may lead to a significant ‘error’ possibility in across the board application
• Given the significant social component of such studies, a lot of variability may be present in the results due to the presence of researcher bias, skill and participant composition

Quantitative research generally share the following characteristics:

• Typically rule based, involve a substantial amount of calculation as opposed to interpretation
• Frequently based on values assigned to a number of qualitative aspects
• Produce a quantifiable, measurable result that can be applied to a number of different settings.
• A number of variables such as preference, value and importance cannot be easily quantified
• Valuable input from the researcher is minimized, shifting bias error to the participant
• Quantifiable results are not always ‘generalized’ and are very specific to a certain set of variables and conditions.

Above all, research methodology helps set the reasonable boundaries of a research project at the start, and anticipate the various problems that may be encountered during the activity.In addition to the said components, research methodology can be greatly influenced by the judgment, skills and beliefs of the researcher as well. There may be wide variations in the adopted methodology as time, funds and other resources permit.

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Home » Research Methodology – Types, Examples and writing Guide

Research Methodology – Types, Examples and writing Guide

Table of Contents

Research Methodology

Definition:

Research Methodology refers to the systematic and scientific approach used to conduct research, investigate problems, and gather data and information for a specific purpose. It involves the techniques and procedures used to identify, collect , analyze , and interpret data to answer research questions or solve research problems . Moreover, They are philosophical and theoretical frameworks that guide the research process.

Structure of Research Methodology

Research methodology formats can vary depending on the specific requirements of the research project, but the following is a basic example of a structure for a research methodology section:

I. Introduction

• Provide an overview of the research problem and the need for a research methodology section
• Outline the main research questions and objectives

II. Research Design

• Explain the research design chosen and why it is appropriate for the research question(s) and objectives
• Discuss any alternative research designs considered and why they were not chosen
• Describe the research setting and participants (if applicable)

III. Data Collection Methods

• Describe the methods used to collect data (e.g., surveys, interviews, observations)
• Explain how the data collection methods were chosen and why they are appropriate for the research question(s) and objectives
• Detail any procedures or instruments used for data collection

IV. Data Analysis Methods

• Describe the methods used to analyze the data (e.g., statistical analysis, content analysis )
• Explain how the data analysis methods were chosen and why they are appropriate for the research question(s) and objectives
• Detail any procedures or software used for data analysis

V. Ethical Considerations

• Discuss any ethical issues that may arise from the research and how they were addressed
• Explain how informed consent was obtained (if applicable)
• Detail any measures taken to ensure confidentiality and anonymity

VI. Limitations

• Identify any potential limitations of the research methodology and how they may impact the results and conclusions

VII. Conclusion

• Summarize the key aspects of the research methodology section
• Explain how the research methodology addresses the research question(s) and objectives

Research Methodology Types

Types of Research Methodology are as follows:

Quantitative Research Methodology

This is a research methodology that involves the collection and analysis of numerical data using statistical methods. This type of research is often used to study cause-and-effect relationships and to make predictions.

Qualitative Research Methodology

This is a research methodology that involves the collection and analysis of non-numerical data such as words, images, and observations. This type of research is often used to explore complex phenomena, to gain an in-depth understanding of a particular topic, and to generate hypotheses.

Mixed-Methods Research Methodology

This is a research methodology that combines elements of both quantitative and qualitative research. This approach can be particularly useful for studies that aim to explore complex phenomena and to provide a more comprehensive understanding of a particular topic.

Case Study Research Methodology

This is a research methodology that involves in-depth examination of a single case or a small number of cases. Case studies are often used in psychology, sociology, and anthropology to gain a detailed understanding of a particular individual or group.

Action Research Methodology

This is a research methodology that involves a collaborative process between researchers and practitioners to identify and solve real-world problems. Action research is often used in education, healthcare, and social work.

Experimental Research Methodology

This is a research methodology that involves the manipulation of one or more independent variables to observe their effects on a dependent variable. Experimental research is often used to study cause-and-effect relationships and to make predictions.

Survey Research Methodology

This is a research methodology that involves the collection of data from a sample of individuals using questionnaires or interviews. Survey research is often used to study attitudes, opinions, and behaviors.

Grounded Theory Research Methodology

This is a research methodology that involves the development of theories based on the data collected during the research process. Grounded theory is often used in sociology and anthropology to generate theories about social phenomena.

Research Methodology Example

An Example of Research Methodology could be the following:

Research Methodology for Investigating the Effectiveness of Cognitive Behavioral Therapy in Reducing Symptoms of Depression in Adults

Introduction:

The aim of this research is to investigate the effectiveness of cognitive-behavioral therapy (CBT) in reducing symptoms of depression in adults. To achieve this objective, a randomized controlled trial (RCT) will be conducted using a mixed-methods approach.

Research Design:

The study will follow a pre-test and post-test design with two groups: an experimental group receiving CBT and a control group receiving no intervention. The study will also include a qualitative component, in which semi-structured interviews will be conducted with a subset of participants to explore their experiences of receiving CBT.

Participants:

Participants will be recruited from community mental health clinics in the local area. The sample will consist of 100 adults aged 18-65 years old who meet the diagnostic criteria for major depressive disorder. Participants will be randomly assigned to either the experimental group or the control group.

Intervention :

The experimental group will receive 12 weekly sessions of CBT, each lasting 60 minutes. The intervention will be delivered by licensed mental health professionals who have been trained in CBT. The control group will receive no intervention during the study period.

Data Collection:

Quantitative data will be collected through the use of standardized measures such as the Beck Depression Inventory-II (BDI-II) and the Generalized Anxiety Disorder-7 (GAD-7). Data will be collected at baseline, immediately after the intervention, and at a 3-month follow-up. Qualitative data will be collected through semi-structured interviews with a subset of participants from the experimental group. The interviews will be conducted at the end of the intervention period, and will explore participants’ experiences of receiving CBT.

Data Analysis:

Quantitative data will be analyzed using descriptive statistics, t-tests, and mixed-model analyses of variance (ANOVA) to assess the effectiveness of the intervention. Qualitative data will be analyzed using thematic analysis to identify common themes and patterns in participants’ experiences of receiving CBT.

Ethical Considerations:

This study will comply with ethical guidelines for research involving human subjects. Participants will provide informed consent before participating in the study, and their privacy and confidentiality will be protected throughout the study. Any adverse events or reactions will be reported and managed appropriately.

Data Management:

All data collected will be kept confidential and stored securely using password-protected databases. Identifying information will be removed from qualitative data transcripts to ensure participants’ anonymity.

Limitations:

One potential limitation of this study is that it only focuses on one type of psychotherapy, CBT, and may not generalize to other types of therapy or interventions. Another limitation is that the study will only include participants from community mental health clinics, which may not be representative of the general population.

Conclusion:

This research aims to investigate the effectiveness of CBT in reducing symptoms of depression in adults. By using a randomized controlled trial and a mixed-methods approach, the study will provide valuable insights into the mechanisms underlying the relationship between CBT and depression. The results of this study will have important implications for the development of effective treatments for depression in clinical settings.

How to Write Research Methodology

Writing a research methodology involves explaining the methods and techniques you used to conduct research, collect data, and analyze results. It’s an essential section of any research paper or thesis, as it helps readers understand the validity and reliability of your findings. Here are the steps to write a research methodology:

• Start by explaining your research question: Begin the methodology section by restating your research question and explaining why it’s important. This helps readers understand the purpose of your research and the rationale behind your methods.
• Describe your research design: Explain the overall approach you used to conduct research. This could be a qualitative or quantitative research design, experimental or non-experimental, case study or survey, etc. Discuss the advantages and limitations of the chosen design.
• Discuss your sample: Describe the participants or subjects you included in your study. Include details such as their demographics, sampling method, sample size, and any exclusion criteria used.
• Describe your data collection methods : Explain how you collected data from your participants. This could include surveys, interviews, observations, questionnaires, or experiments. Include details on how you obtained informed consent, how you administered the tools, and how you minimized the risk of bias.
• Explain your data analysis techniques: Describe the methods you used to analyze the data you collected. This could include statistical analysis, content analysis, thematic analysis, or discourse analysis. Explain how you dealt with missing data, outliers, and any other issues that arose during the analysis.
• Discuss the validity and reliability of your research : Explain how you ensured the validity and reliability of your study. This could include measures such as triangulation, member checking, peer review, or inter-coder reliability.
• Acknowledge any limitations of your research: Discuss any limitations of your study, including any potential threats to validity or generalizability. This helps readers understand the scope of your findings and how they might apply to other contexts.
• Provide a summary: End the methodology section by summarizing the methods and techniques you used to conduct your research. This provides a clear overview of your research methodology and helps readers understand the process you followed to arrive at your findings.

When to Write Research Methodology

Research methodology is typically written after the research proposal has been approved and before the actual research is conducted. It should be written prior to data collection and analysis, as it provides a clear roadmap for the research project.

The research methodology is an important section of any research paper or thesis, as it describes the methods and procedures that will be used to conduct the research. It should include details about the research design, data collection methods, data analysis techniques, and any ethical considerations.

The methodology should be written in a clear and concise manner, and it should be based on established research practices and standards. It is important to provide enough detail so that the reader can understand how the research was conducted and evaluate the validity of the results.

Applications of Research Methodology

Here are some of the applications of research methodology:

• To identify the research problem: Research methodology is used to identify the research problem, which is the first step in conducting any research.
• To design the research: Research methodology helps in designing the research by selecting the appropriate research method, research design, and sampling technique.
• To collect data: Research methodology provides a systematic approach to collect data from primary and secondary sources.
• To analyze data: Research methodology helps in analyzing the collected data using various statistical and non-statistical techniques.
• To test hypotheses: Research methodology provides a framework for testing hypotheses and drawing conclusions based on the analysis of data.
• To generalize findings: Research methodology helps in generalizing the findings of the research to the target population.
• To develop theories : Research methodology is used to develop new theories and modify existing theories based on the findings of the research.
• To evaluate programs and policies : Research methodology is used to evaluate the effectiveness of programs and policies by collecting data and analyzing it.
• To improve decision-making: Research methodology helps in making informed decisions by providing reliable and valid data.

Purpose of Research Methodology

Research methodology serves several important purposes, including:

• To guide the research process: Research methodology provides a systematic framework for conducting research. It helps researchers to plan their research, define their research questions, and select appropriate methods and techniques for collecting and analyzing data.
• To ensure research quality: Research methodology helps researchers to ensure that their research is rigorous, reliable, and valid. It provides guidelines for minimizing bias and error in data collection and analysis, and for ensuring that research findings are accurate and trustworthy.
• To replicate research: Research methodology provides a clear and detailed account of the research process, making it possible for other researchers to replicate the study and verify its findings.
• To advance knowledge: Research methodology enables researchers to generate new knowledge and to contribute to the body of knowledge in their field. It provides a means for testing hypotheses, exploring new ideas, and discovering new insights.
• To inform decision-making: Research methodology provides evidence-based information that can inform policy and decision-making in a variety of fields, including medicine, public health, education, and business.

Advantages of Research Methodology

Research methodology has several advantages that make it a valuable tool for conducting research in various fields. Here are some of the key advantages of research methodology:

• Systematic and structured approach : Research methodology provides a systematic and structured approach to conducting research, which ensures that the research is conducted in a rigorous and comprehensive manner.
• Objectivity : Research methodology aims to ensure objectivity in the research process, which means that the research findings are based on evidence and not influenced by personal bias or subjective opinions.
• Replicability : Research methodology ensures that research can be replicated by other researchers, which is essential for validating research findings and ensuring their accuracy.
• Reliability : Research methodology aims to ensure that the research findings are reliable, which means that they are consistent and can be depended upon.
• Validity : Research methodology ensures that the research findings are valid, which means that they accurately reflect the research question or hypothesis being tested.
• Efficiency : Research methodology provides a structured and efficient way of conducting research, which helps to save time and resources.
• Flexibility : Research methodology allows researchers to choose the most appropriate research methods and techniques based on the research question, data availability, and other relevant factors.
• Scope for innovation: Research methodology provides scope for innovation and creativity in designing research studies and developing new research techniques.

Research Methodology Vs Research Methods

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Researcher, Academic Writer, Web developer

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Short courses

Introduction to Research Methods and Statistics

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This five-day short course will give you a comprehensive introduction to the fundamental aspects of research methods and statistics . It's suitable for those new to quantitative research.

You'll look at topics ranging from study design, data type and graphs through to choice and interpretation of statistical tests - with a particular focus on standard errors, confidence intervals and p-values.

This course takes place over five days (9:30am to 5pm).  

This course is delivered by UCL's Centre for Applied Statistics Courses (CASC), part of the UCL Great Ormond Street Institute of Child Health (ICH).

Course content

During this basic introductory course in research methodology and statistical analyses you'll cover a variety of topics.

This is a theory-led course, but you'll be given plenty of opportunities to apply the concepts via practical and interactive activities integrated throughout.

The topics covered include:

• Introduction to quantitative research
• Research question development
• Study design, sampling and confounding
• Types of data
• Graphical displays of data and results
• Summarising numeric and categorical data
• Numeric and categorical differences between groups
• Hypothesis testing
• Confidence intervals and p-values
• Parametric statistical tests
• Non-parametric tests
• Bootstrapping
• Regression analysis

Many examples used in the course are related to health research, but the concepts you'll learn about can be applied to most other fields.

Eligibility

The course is suitable for those new to quantitative research.

Learning outcomes

By the end of this course you should have a good, practical understanding of:

• research design considerations (question formulation, sample selection and randomisation, study design, and research protocols)
• data types, and appropriate summaries and graphs of samples and differences
• standard errors, confidence intervals and p-values
• parametric and nonparametric assumptions and tests
• how to select an appropriate statistical test

Cost and concessions

The fees are:

• External delegates (non UCL) - £750
• UCL staff, students, alumni - £375*
• ICH/GOSH staff and doctoral students - free

* valid UCL email address and/or UCL alumni number required upon registration.

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You can request a certificate of attendance for all of our courses once you've completed it. Please send your request to [email protected]

Include the following in your email:

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• how you'd like your name presented on the certificate (if the name/format differs from the details you gave during registration)

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Read the cancellation policy for this course on the ICH website. Please send all cancellation requests to  [email protected]

Find out about CASC's other statistics courses

CASC's stats courses are for anyone requiring an understanding of research methodology and statistical analyses. The courses will allow non-statisticians to interpret published research and/or undertake their own research studies.

Find out more about CASC's full range of statistics courses , and the continuing statistics training scheme (book six one-day courses and get a seventh free.)

Course team

Dr Eirini Koutoumanou

Eirini has a BSc in Statistics from Athens University of Economics and Business and an MSc in Statistics from Lancaster University (funded by the Engineering and Physical Sciences Research Council). She joined UCL GOS Institute of Child Health in 2008 to develop a range of short courses for anyone interested in learning new statistical skills. Soon after, CASC was born. In 2014, she was promoted to Senior Teaching Fellow. In 2019, she successfully passed her PhD viva on the topic of Copula models and their application within paediatric data. Since early 2020 she has been co-directing CASC with its founder, Emeritus Professor Angie Wade, and has been the sole Director of CASC since January 2022. Eirini was promoted to Associate Professor (Teaching) with effect from October 2022.

Dr Chibueze Ogbonnaya

Since joining the teaching team at CASC in February 2019, Chibueze has contributed to the teaching and development of short courses. He currently leads and co-leads short courses on MATLAB, missing data, regression analysis and survival analysis. Chibueze has a BSc in Statistics from the University of Nigeria, where he briefly worked as a teaching assistant after graduation. He then moved to the University of Nottingham for his MSc and PhD in Statistics. His research interests include functional data analysis, applied machine learning and distribution theory.

Dr Catalina Rivera Suarez

Catalina has been an Associate Lecturer (Teaching) at CASC since January 2021. She has a PhD in Psychology and an MSc in Applied Statistics from Indiana University. She’s passionate about teaching courses in research methods, statistics, and statistical software. Catalina’s research focuses on studying how caregivers support the development of children's attentional control and language. She implements multilevel modeling techniques to investigate the moment-to-moment dynamics of shared joint visual engagement, as well as the quality of the language input, influencing infant learning and sustained attention at multiple timescales.  

Dr Manolis Bagkeris

Manolis has a BSc in Statistics and Actuarial-Financial Mathematics from the University of the Aegean and an MSc in Medical Statistics from the Athens University of Economics and Business (AUEB). He’s worked as a research assistant at University of Crete, UCL and Imperial College London. He’s been working at CASC since November 2021, providing short courses in research methods and statistics for people who want to develop or enhance their knowledge in interpreting and undertaking their own research. His interests include paediatric epidemiology, clinical and population health, HIV, mental health and development. He was awarded a PhD from UCL in 2021 on the topic of frailty, falls, bone mineral density and fractures among HIV-positive and HIV-negative controls in England and Ireland.

"All sessions were exceptionally organised and presented in a clear and engaging style. The lecturers were incredibly knowledgeable and flexible and patient to the different levels of understanding in the room. The key concepts of making inferences set out at the beginning and carried throughout were especially helpful.

"Explaining the visual representation of data was very useful, as was having examples in the workbooks to learn from and 'correct'."

"The most memorable session for me was the one about significance testing. I am sure it will be very useful in my practice."

Course information last modified: 25 Mar 2024, 09:38

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• Time commitment: 9:30am to 5pm
• Course length: 5 days
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5 Statistical Analysis Methods for Research and Analysis

It all boils down to using the power of statistical analysis methods, which is how academics collaborate and collect data to identify trends and patterns.

Over the last ten years, everyday business has undergone a significant transformation. It’s not very uncommon for things to still appear to be the same, whether it’s the technology used in workspaces or the software used to communicate.

There is now an overwhelming amount of information available that was once rare. But it could be overwhelming if you don’t have the slightest concept of going through your company’s data to find meaningful and accurate meaning.

5 different statistical analysis methods will be covered in this blog, along with a detailed discussion of each method.

What is a statistical analysis method?

The practice of gathering and analyzing data to identify patterns and trends is known as statistical analysis . It is a method for eliminating bias from data evaluation by using numerical analysis. Data analytics and data analysis are closely related processes that involve extracting insights from data to make informed decisions.

And these statistical analysis methods are beneficial for gathering research interpretations, creating statistical models, and organizing surveys and studies.

Data analysis employs two basic statistical methods:

• Descriptive statistics, which use indexes like mean and median to summarize data,
• Inferential statistics , extrapolate results from data by utilizing statistical tests like the student t-test.

LEARN ABOUT: Descriptive Analysis

The following three factors determine whether a statistical approach is most appropriate:

• The study’s goal and primary purpose,
• The kind and dispersion of the data utilized, and
• The type of observations (Paired/Unpaired).

“Parametric” refers to all types of statistical procedures used to compare means. In contrast, “nonparametric” refers to statistical methods that compare measures other than means, such as medians, mean ranks, and proportions.

For each unique circumstance, statistical analytic methods in biostatistics can be used to analyze and interpret the data. Knowing the assumptions and conditions of the statistical methods is necessary for choosing the best statistical method for data analysis.

Whether you’re a data scientist or not, there’s no doubt that big data is taking the globe by storm. As a result, you must be aware of where to begin. There are 5 options for this statistical analysis method:

Big data is taking over the globe, no matter how you slice it. Mean, more often known as the average, is the initial technique used to conduct the statistical analysis. To find the mean, add a list of numbers, divide that total by the list’s components, and then add another list of numbers.

When this technique is applied, it is possible to quickly view the data while also determining the overall trend of the data collection . The straightforward and quick calculation is also advantageous to the method’s users.

The center of the data under consideration is determined using the statistical mean. The outcome is known as the presented data’s mean. Real-world interactions involving research, education, and athletics frequently use derogatory language. Consider how frequently a baseball player’s batting average—their mean—is brought up in conversation if you consider yourself a data scientist. As a result, you must be aware of where to begin.

Standard deviation

A statistical technique called standard deviation measures how widely distributed the data is from the mean.

When working with data, a high standard deviation indicates that the data is widely dispersed from the mean. A low deviation indicates that most data is in line with the mean and can also be referred to as the set’s expected value.

Standard deviation is frequently used when analyzing the dispersion of data points—whether or not they are clustered.

Imagine you are a marketer who just finished a client survey. Suppose you want to determine whether a bigger group of customers will likely provide the same responses. In that case, you should assess the responses’ dependability after receiving the survey findings. If the standard deviation is low, a greater range of customers may be projected with the answers.

Regression in statistics studies the connection between an independent variable and a dependent variable (the information you’re trying to assess) (the data used to predict the dependent variable).

It can also be explained in terms of how one variable influences another, or how changes in one inconsistent result in changes in another, or vice versa, simple cause and effect. It suggests that the result depends on one or more factors.

Regression analysis graphs and charts employ lines to indicate trends over a predetermined period as well as the strength or weakness of the correlations between the variables.

Hypothesis testing

The two sets of random variables inside the data set must be tested using hypothesis testing, sometimes referred to as “T Testing,” in statistical analysis.

This approach focuses on determining whether a given claim or conclusion holds for the data collection. It enables a comparison of the data with numerous assumptions and hypotheses. It can also help in predicting how choices will impact the company.

A hypothesis test in statistics determines a quantity under a particular assumption. The test’s outcome indicates whether the assumption is correct or whether it has been broken. The null hypothesis, sometimes known as hypothesis 0, is this presumption. The first hypothesis, often known as hypothesis 1, is any other theory that would conflict with hypothesis 0.

When you perform hypothesis testing, the test’s results are statistically significant if they demonstrate that the event could not have occurred by chance or at random.

Sample size determination

When evaluating data for statistical analysis, gathering reliable data can occasionally be challenging since the dataset is too huge. When this is the case, the majority choose the method known as sample size determination , which involves examining a sample or smaller data size.

You must choose the appropriate sample size for accuracy to complete this task effectively. You won’t get reliable results after your analysis if the sample size is too small.

You will use several data sampling techniques to achieve this result. To accomplish this, you may send a survey to your customers and then use the straightforward random sampling method to select the customer data for random analysis.

Conversely, excessive sample size can result in time and money lost. You can look at factors like cost, time, or the ease of data collection to decide the sample size.

Are you confused? Don’t worry! you can use our sample size calculator .

LEARN ABOUT: Theoretical Research

The ability to think analytically is vital for corporate success. Since data is one of the most important resources available today, using it effectively can result in better outcomes and decision-making.

Regardless of the statistical analysis methods you select, be sure to pay close attention to each potential drawback and its particular formula. No method is right or wrong, and there is no gold standard. It will depend on the information you’ve gathered and the conclusions you hope to draw.

By using QuestionPro, you can make crucial judgments more efficiently while better comprehending your clients and other study subjects. Use the features of the enterprise-grade research suite right away!

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The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organisations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organise and summarise the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalise your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarise your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, frequently asked questions about statistics.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

• Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
• Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
• Null hypothesis: Parental income and GPA have no relationship with each other in college students.
• Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

• In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
• In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
• In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

• In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
• In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
• In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
• Experimental
• Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalise your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

• Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
• Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

• Probability sampling: every member of the population has a chance of being selected for the study through random selection.
• Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalisable findings, you should use a probability sampling method. Random selection reduces sampling bias and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to be biased, they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

• your sample is representative of the population you’re generalising your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalise your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialised, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalised in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

• Will you have resources to advertise your study widely, including outside of your university setting?
• Will you have the means to recruit a diverse sample that represents a broad population?
• Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

• Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
• Expected effect size : a standardised indication of how large the expected result of your study will be, usually based on other similar studies.
• Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarise them.

Inspect your data

There are various ways to inspect your data, including the following:

• Organising data from each variable in frequency distribution tables .
• Displaying data from a key variable in a bar chart to view the distribution of responses.
• Visualising the relationship between two variables using a scatter plot .

By visualising your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

• Mode : the most popular response or value in the data set.
• Median : the value in the exact middle of the data set when ordered from low to high.
• Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

• Range : the highest value minus the lowest value of the data set.
• Interquartile range : the range of the middle half of the data set.
• Standard deviation : the average distance between each value in your data set and the mean.
• Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

• Estimation: calculating population parameters based on sample statistics.
• Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

• A point estimate : a value that represents your best guess of the exact parameter.
• An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

• A test statistic tells you how much your data differs from the null hypothesis of the test.
• A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

• Comparison tests assess group differences in outcomes.
• Regression tests assess cause-and-effect relationships between variables.
• Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

• A simple linear regression includes one predictor variable and one outcome variable.
• A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

• A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
• A z test is for exactly 1 or 2 groups when the sample is large.
• An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

• If you have only one sample that you want to compare to a population mean, use a one-sample test .
• If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
• If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
• If you expect a difference between groups in a specific direction, use a one-tailed test .
• If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

• a t value (test statistic) of 3.00
• a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

• a t value of 3.08
• a p value of 0.001

The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimise the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasises null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
• If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Statistical analysis is the main method for analyzing quantitative research data . It uses probabilities and models to test predictions about a population from sample data.

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Statistical methods in research

Affiliation.

• 1 The Sackler Institute of Pulmonary Pharmacology, School of Biomedical Science, King's College London, 5th Floor Franklin Wilkins Building, SEI9NH Waterloo Campus, London, UK. [email protected]
• PMID: 21607874
• DOI: 10.1007/978-1-61779-126-0_26

Statistical methods appropriate in research are described with examples. Topics covered include the choice of appropriate averages and measures of dispersion to summarize data sets, and the choice of tests of significance, including t-tests and a one- and a two-way ANOVA plus post-tests for normally distributed (Gaussian) data and their non-parametric equivalents. Techniques for transforming non-normally distributed data to more Gaussian distributions are discussed. Concepts of statistical power, errors and the use of these in determining the optimal size of experiments are considered. Statistical aspects of linear and non-linear regression are discussed, including tests for goodness-of-fit to the chosen model and methods for comparing fitted lines and curves.

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Modernizing the Data Infrastructure for Clinical Research to Meet Evolving Demands for Evidence

• 1 Verily Life Sciences, South San Francisco, California
• 2 Center for Biostatistics & Qualitative Methodology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania
• 3 Bakar Computational Health Sciences Institute, University of California, San Francisco
• 4 Center for Data-Driven Insights and Innovation, University of California Health, Oakland
• 5 Faculty of Health Sciences, McMaster University, Hamilton, Ontario, Canada
• 6 Departments of Surgery and Radiology and Institute for Health Policy Studies, University of California, San Francisco
• 7 Anesthesiology and Critical Care, University of Pennsylvania Perelman School of Medicine, Philadelphia
• 8 Biogen, Boston, Massachusetts
• 9 Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland
• 10 Yale University School of Medicine, New Haven, Connecticut
• 11 National Institute for Health and Care Research (NIHR) Health and Social Care Delivery Research Programme, London, United Kingdom
• 12 Intensive Care National Audit & Research Centre (ICNARC), London, United Kingdom
• 13 Highlander Health, Dallas, Texas

Importance   The ways in which we access, acquire, and use data in clinical trials have evolved very little over time, resulting in a fragmented and inefficient system that limits the amount and quality of evidence that can be generated.

Observations   Clinical trial design has advanced steadily over several decades. Yet the infrastructure for clinical trial data collection remains expensive and labor intensive and limits the amount of evidence that can be collected to inform whether and how interventions work for different patient populations. Meanwhile, there is increasing demand for evidence from randomized clinical trials to inform regulatory decisions, payment decisions, and clinical care. Although substantial public and industry investment in advancing electronic health record interoperability, data standardization, and the technology systems used for data capture have resulted in significant progress on various aspects of data generation, there is now a need to combine the results of these efforts and apply them more directly to the clinical trial data infrastructure.

Conclusions and Relevance   We describe a vision for a modernized infrastructure that is centered around 2 related concepts. First, allowing the collection and rigorous evaluation of multiple data sources and types and, second, enabling the possibility to reuse health data for multiple purposes. We address the need for multidisciplinary collaboration and suggest ways to measure progress toward this goal.

Read More About

Franklin JB , Marra C , Abebe KZ, et al. Modernizing the Data Infrastructure for Clinical Research to Meet Evolving Demands for Evidence. JAMA. Published online August 05, 2024. doi:10.1001/jama.2024.0268

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• Open access
• Published: 08 August 2024

The gap between statistical and clinical significance: time to pay attention to clinical relevance in patient-reported outcome measures of insomnia

• Zongshi Qin 1   na1 ,
• Yidan Zhu 1   na1 ,
• Dong-Dong Shi 2 ,
• Rumeng Chen 3 ,
• Sen Li 3 &
• Jiani Wu 4  

BMC Medical Research Methodology volume  24 , Article number:  177 ( 2024 ) Cite this article

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Appropriately defining and using the minimal important change (MIC) and the minimal clinically important difference (MCID) are crucial for determining whether the results are clinically significant. The aim of this study is to survey the status of randomized controlled trials (RCTs) for insomnia interventions to assess the inclusion and interpretation of MIC/MCID values.

We conducted a cross-sectional study to survey the status of RCTs for insomnia interventions to assess the inclusion and appropriate interpretation of MIC/MCID values. A literature search was conducted by searching the main sleep medicine journals indexed in PubMed, the Excerpta Medica Database (EMBASE), and the Cochrane Central Register of Controlled Trials (CENTRAL) to identify a broad range of search terms. We included RCTs with no restriction on the intervention. The included studies used the Insomnia Severity Index (ISI) or the Pittsburgh Sleep Quality Index (PSQI) questionnaire as the outcome measures.

81 eligible studies were identified, and more than one-third of the included studies used MIC/MCID ( n  = 31, 38.3%). Among them, 21 studies with ISI as the outcome used MIC defined as a relative decrease ranging from 3 to 8 points. The most frequently used MIC value was a 6-point decrease ( n  = 7), followed by 8-point ( n  = 6) and 7-point decrease ( n  = 4), a 4 to 5-points decrease ( n  = 3), and a 30% reduction from baseline; 6 studies used MCID values, ranging from 2.8 to 4 points. The most frequently used MCID value was a 4-point decrease in the ISI ( n  = 4). 4 studies with PSQI as the outcome used a 3-point change as the MIC ( n  = 2) and a 2.5 to 2.7-point difference as MCID ( n  = 2). 4 non-inferiority design studies considered interval estimation when drawing clinically significant conclusions in their MCID usage.

Conclusions

The lack of consistent MIC/MCID interpretation and usage in outcome measures for insomnia highlights the urgent need for further efforts to address this issue and improve reporting practices.

Peer Review reports

Introduction

Insomnia, characterized by difficulties initiating or maintaining sleep, accompanied by symptoms such as irritability or fatigue during wakefulness, is a prevalent and costly health complaint [ 1 , 2 ]. The prevalence of insomnia disorders ranges from 5.8 to 19% in European countries [ 3 ], while the prevalence of insomnia symptoms in the general adult population ranges from 35 to 50% [ 4 ]. Given the subjective nature of insomnia symptoms, patient-reported outcome measures (PROMs) play an important role in for evaluating insomnia symptom severity and treatment-related changes. PROMs provide information directly from the patient, without interpretation by a clinician or any other party, and remain important for assessing insomnia despite the common use of objective assessments, such as actigraphy, in recent clinical studies.

The two most frequently utilized PROMs for insomnia are the Insomnia Severity Index (ISI) and the Pittsburgh Sleep Quality Index (PSQI), which are used to assess insomnia severity and evaluate treatment effects [ 5 , 6 ]. To properly interpret changes in PROMs, it is essential to differentiate between statistically significant and clinically meaningful differences [ 7 ]. Various terms are used to describe clinically meaningful effects, often inconsistently, making interpretation difficult. The concept of the Minimal Important Change (MIC) represents the smallest change in health status perceivable by patients compared to a baseline. On the other hand, the Minimal Clinically Important Difference (MCID) refers to the smallest difference between two groups that is deemed beneficial enough by patients to be clinically important [ 8 , 9 ].

Despite many studies demonstrating statistically significant effects of interventions for both pharmacological and non-pharmacological treatments of insomnia [ 10 , 11 , 12 ], the focus of current research often lies solely on statistical significance, neglecting clinical significance. Evaluating the efficacy of insomnia treatments requires considering both statistical and clinical significance. Furthermore, appropriately defining and reporting the MIC/MCID is crucial to concluding whether the results are clinically significant. Currently, the concepts of MIC and MCID are frequently confused in clinical study reporting. The question is then, what is the status of MIC/MCID reporting in clinical studies related to insomnia? The aim of this study is to survey the status of RCTs for insomnia interventions to assess the inclusion and appropriate interpretation of MIC/MCID values.

The reporting of the current study was based on the PRISMA 2020 statement whenever possible [ 13 ].

Literature search

The literature search was conducted in 30-Sep-2023. Considering the terminology of MIC/MCID various a lot, MIC/MCID were not defined as an item in the search strategies. First, literature search was conducted by searching the main sleep medicine journals indexed in PubMed, Excerpta Medica Database (EMBASE), and the Cochrane Central Register of Controlled Trials (CENTRAL) to identify a broad range of search terms. Next, Endnote X20 was used to screen the records. Two investigators independently reviewed titles and abstracts of search results to identify potentially eligible references. The full texts were screened by researchers independently based on inclusion and exclusion criteria. Discrepancies were resolved through discussion with corresponding authors. By a prior search in Scimago Journal & Country Rank ( https://www.scimagojr.com/ ), we identified 22 journals in sleep medicine and general medicine, includes “Sleep”, “Sleep medicine”, “Journal of Sleep Research”, “Journal of clinical sleep medicine”. Four of them were excluded as they were listed as predatory journals. A full list of the remaining 18 journals detailed and search strategy was presented in the Supplementary file 1 and has been recorded in the previous study [ 14 ].

Study screening and selection criteria

We included randomized controlled trials with no restriction on the intervention. Included randomized controlled trials used ISI or/and PSQI questionnaire as the outcomes and published in the aforementioned journals of sleep medicine without restriction to study type (i.e., superiority, non-inferiority, or equivalence trails). Interim analyses, pooled analyses, and post-hoc analyses (i.e., subgroup analysis, secondary analysis) of RCTs were excluded. Non-human studies and studies not published as full papers (such as conference abstracts, study protocols) were excluded. Pre-print articles or grey literature without peer-review process were also excluded. Regarding the aspects of insomnia, the MIC values from Morin and Yang were the most frequently referenced sources, primarily estimated through an anchor-based approach [ 6 , 9 ]. Table  1 provides a summary of the sources of MIC/MCID values for ISI and PSQI. Studies that defined the post-treatment endpoint to achieve certain value (remission) were excluded.

Data collection and statistics

An information extraction table using Microsoft Excel 365 was made. Before formal data collection, two researchers were trained. Three included studies were assessed using the extraction table as a pretest for consistency validation. Data was collected and coded by two researchers. Discrepancies were resolved through discussion and confirmed by corresponding authors. The category data was presented as number and percent. The details items were as follows: (1) Basic characteristics: title, authors, publication years and the journal, the country and region where the study was carried out, target population, sample size, type of intervention, and types of PROM. (2) MIC/MCID related characteristics: The complete article was reviewed for mention and definition of MIC/MCID. Credit was given if MIC/MCID was defined for the primary outcomes and was mentioned in any section of the article. As the definition of MIC/MCID various a lot, we mainly focus on the clinically instead of minimal, that is, the moderate clinical meaning was also included (e.g., more than 30% reduction compared with baseline). The studies were placed into 1 of 3 categories according to (a) only defined and used MIC, (b) only defined and used MCID, and (c) defined and used both MIC/MCID. The classification for MIC/MCID was based on a two-stage procedure. First, we classified the value based on the terminology. Specifically, if the authors used terminology such as response, change, decrease, or improvement, we expected it as MIC. Conversely, if the authors used terminology difference, we expected it as MCID. Second, we determine whether the MIC or MCID that was actually used by examining if the value was within-group (classified as MIC) or between-group (classified as MCID). For articles that did not mention MCID, the published literature was searched to determine if the MCID for the reported outcome existed prior to publication of the article.

Search results

After screening titles and abstracts, a total of 164 studies were assessed for edibility. Among them, 81 RCTs met the inclusion criteria and were included in the final dataset. Figure  1 illustrates the study flowchart. The majority of included studies focused on non-pharmacological interventions, followed by complementary medicine and therapies. Cognitive Behavioral Therapy for Insomnia (CBT-I) studies compromised the largest proportion. Only 5 studies assessed the effectiveness of hypnotics. Out of the eligible studies, 31 used MIC/MCID values. Among the included RCTs, MIC/MCID were used under 11 different definitions including “treatment response”, “minimal significant difference”, “clinically meaningful improvement”, “clinically significant improvement”, “clinically significant treatment effect”, “clinically significant change”, “clinically relevant difference”, “minimally important difference”, “minimally clinically important differences”, “slight clinical improvement”, and “clinically important difference”. All included studies evaluated at least one intervention group and one comparison group. Among them, 3 studies utilized a cross-over design, 2 studies employed a cluster design, and 4 studies followed a non-inferiority design.

The MIC/MCID used condition

A total of 31 studies used MIC/MCID, 23 studies used MIC and 8 studies used MCID. Table  2 provides a summary of the characteristics, as well as the defined and used MIC/MCID values of the included studies. Most MIC were used as a relative decrease from 3 to 8 points. 6-points of ISI was the most frequently used value for the MIC ( n  = 7), followed by 8- and 7-points of ISI ( n  = 6 and 4, respectively), and a range from 4- to 4.7-points ( n  = 3). Two source to justify the choice of value or definition of MIC (ranges from 6 to 8) accompanied most of the definitions [ 6 , 9 ]. A decrease of 30% reduction of ISI was also defined as a MIC in 1 study (Table  2 ). The eFigure 1 of supplemental file 1 present the chronological illustration of MIC/MCID source and citations by included studies. All MCIDs were used as a relative decrease from 2.8 to 4 points. 4-points of ISI was the most frequently used value for the MCID ( n  = 4). 4 studies with PSQI as the outcome used a 3-point change as the MIC ( n  = 2) and a 2.5 to 2.7-point difference as MCID ( n  = 2). Although all studies discount the MCID, the source to justify the choice of value or definition of MCID accompanied most [ 9 ]. For MCID usage, 4 non-inferiority designed studies considered the interval estimation when drawing the conclusion of clinically significant. Figure  2 illustrates the distribution pattern of MIC/MCID values in the included RCTs.

The mismatches from studies and sources

Based on the criteria, treatment responses reported by 6 studies were classified as MIC. Additionally, 5 out of 8 studies used MCID were judged as MIC. Among the 23 studies used MIC terminology, 4 were judged as MCID (Fig.  1 ). Among 19 studies referring MIC as a source, the values in 17 studies aligned with the source. Among 5 studies referring MCID as a source, the values in 3 studies matched the sources (Fig.  1 ). Table  3 represents the frequency of comparison of expected vs. used (judgement) MIC/MCID values.

Included studies reported responder analysis

We further aggregated the outcomes of responder analyses, which were documented in 11 studies utilizing 5 distinct definitions of responder. The selection of the cut-off value to define a responder appeared arbitrary. Among the various definitions employed, the most prevalent approach was based on an ISI reduction of less than 8 points ( n  = 5), followed by a reduction of over 50% in ISI ( n  = 3). These references are provided in Supplemental file 2 .

Study flowchart

Distribution pattern of MIC/MCID values in the included RCTs

To date, there has been considerable variation in the definitions of MIC and MCID, leading to confusion in terminologies found within clinical study reports. However, it is important to note that this study does not aim to emphasize spelling of the distinction between “MIC” and “MCID” or similar words. Rather, its focus is to encourage clinical researchers to provide clarity on what constitutes clinically significant changes, whether in terms of change from baseline to end-of-treatment (MIC) or differences between intervention and control groups (MCID). The primary function of an RCT is to compare groups and identify differences between them. Consequently, in the reporting of RCT results, the focus should be on the difference between groups although the change within a group is important for individual. This emphasis on MCID is crucial, as relying on MIC could potentially diminish the distinctive role of RCTs. This is because a single-group study has the capacity to ascertain MIC, but not MCID.

In this study, we identified an analysis of 81 studies focusing on the MIC/MCID for two PROMs used to assess interventions for insomnia. Our findings revealed that out of these 81 studies, 31 reported MIC/MCID values. Most of the included studies focused on describing the MIC rather than the MCID. According to the criteria, out of 18 studies that reported and defined (minimal) clinically significant change, 12 were categorized as MIC and 5 were categorized as MCID. Out of 7 studies that reported and defined (minimal) clinically important difference, 3 were classified as MCID and 4 were categorized as MIC. This lack of standardized MIC/MCID values and inconsistent methodologies present a significant challenge. Different MIC/MCID values can lead to varying interpretations of clinical significance. Considering the crucial role that MIC/MCID plays in assessing the meaningfulness of changes or differences in PROMs, it is surprising that less than half of the RCTs published in prominent sleep medicine journals provide MIC/MCID values. Although many of these studies report statistically significant results, the absence of defined and reported MIC/MCID values is concerning. The lack of MIC/MCID reporting hampers the interpretation of clinical context of the study findings [ 50 ]. The current reporting practices surrounding MIC/MCID in RCTs investigating interventions for insomnia offer limited assistance in facilitating meaningful interpretation or providing additional insights. Given these challenges, urgent efforts are required to standardize the methodology for reporting MIC/MCID values in research on insomnia.

Several methods are available to estimate the MIC, including distribution-based method, anchor-based method, and consensus-based method. However, the appropriate values of MCID for insomnia related PROMs are still lacking. The most frequently reported MIC and MCID values for the ISI were 6 points and 4 points, respectively. It is crucial to note that MIC and MCID are fundamentally different concepts, although they are often used interchangeably, leading to confusion among clinicians and researchers. MIC represents the change in the score on an outcome measure compared to the score at an earlier time point within a person or the mean change within a group over time. However, the challenge arises when within-group mean change is erroneously referred to as the treatment effect or response to treatment. Change from baseline to follow-up incorporates changes resulting from the natural course of the condition, regression to the mean, nonspecific effects, and treatment effects. It is important to consider these factors, regardless of the specific condition and treatment being studied. Within-group change over time should not be equated with the treatment effect, although change scores provide valuable information. They estimate what is likely to happen when a patient receives the study treatment, but they are distinct from the treatment effect and do not represent the treatment response. On the other hand, the calculation of difference requires data from two groups of people. The between-group difference is determined by subtracting the mean score on an outcome measure in the comparison group from the mean score in the treatment group. This difference, typically assessed at follow-up or as the difference in change between the two groups, can reasonably be referred to as the treatment effect or treatment response because it does not include natural history, regression to the mean, or nonspecific effects. It is important to emphasize that the treatment effect is a comparative effect, reflecting what can be expected if a patient receives treatment compared to what can be expected if the same patient receives the comparison. Confusion may arise when authors draw conclusions solely based on within-group changes in RCTs, particularly when there is no difference between the treatment and comparison groups. Stating that both treatments are effective is rarely a valid conclusion from an RCT, unless specific circumstances warrant it. Within-group change in an RCT does not represent the treatment effect any more than the results from a single-group study, as it still incorporates natural history, regression to the mean, and nonspecific effects. Interpreting RCT findings in this manner undermines the purpose of randomization and the inclusion of a comparison group.

In addition to the mean change, reductions of more than 30% have been suggested to indicate the MIC one study [ 40 ], and consensus on this threshold has also been informed by researchers considering the effects of measurement error from distribution studies [ 51 , 52 ]. Although some studies proposed values do not strictly define a MIC, they provide a responder analysis in terms of PROMs. A reduction of more than 50% has been reported in some studies to reflect a more substantial improvements compared to MIC. In a recent consensus statement to improve the interpretation of clinical trials, 50% was suggested to reflect an acceptable responsive ratio [ 53 ]. Some studies have also reported the effect size (Cohen’s d) as a parameter to suggest clinically significance. However, it is important to note that the responder analysis and effect size cannot replace MIC/MCID [ 54 , 55 ]. Responder analyses, which often require continuous outcomes to be categorized, may result in the loss of information and reduced statistical power, especially when high rates missingness dilute the dataset, multiply imputing the continuous variable was less biased and had well-controlled coverage probabilities of the 95% confidence interval (CI) compared to imputing the dichotomous response [ 56 ]. Therefore, they are recommended as secondary analyses to enhance the interpretability of the main analysis. It is worth noting that responder analyses may introduce relative reporting methods (e.g. as percentage of participants who improved) which, in the case of small absolute differences, can make interventions appear more effective [ 57 ].

One major advantage in adding MIC/MCID into the interpretation is the ability to determine when the available evidence is insufficient to draw a conclusion. The recent CONSORT PRO Extension (Consolidated Standards of Reporting Trials patient reported outcomes) encourages authors to include discussion of an MIC/MCID in reports of clinical trials if the PROM used in the study is validated [ 58 , 59 ]. This concept is also particularly valuable in systematic reviews that synthesize data from different studies, as it allows for an assessment of the adequacy of the evidence [ 60 ]. However, given the multiplicity of MCID estimates often available for a given patient reported outcome measure and non-standardized methodology, researchers and decision makers in search of MCIDs need to critically evaluate the quality of the estimates [ 61 , 62 ], it is crucial to accurately interpret the MCID to arrive at an appropriate conclusion. CIs that fall within the range defined by the MCID indicate evidence of no difference, while CIs outside this range are considered establishing clinically significant differences. Most included studies (86.2%) reporting MIC/MCID did not take 95% CI into consideration when drawing a clinically significant conclusion. Only four non-inferiority designed RCTs reporting MCID studies take the CIs into consideration when drawing conclusions. Study results are considered statistically significant when the lower limit of the 95% CI exceeds the null effect. Similarly, study results could be considered clinically significant if the MCID lies outside the 95% CI of the PROM scores. A previous review summarized 4 conditions of clinical importance, depending on the relationship of the MCID of the intervention to the point estimate and the 95% CI surrounding it: (1) when the MCID is smaller than the lower limit of the 95% CI (definite clinical importance); (2) when the MCID is greater than the lower limit of the 95% CI, but smaller than the point estimate of the efficacy of the intervention (probable clinical importance); (3) when the MCID is less than the upper limit of the 95% CI, but greater than the point estimate of the efficacy of the intervention (possible clinical importance); and (4) when the MCID is greater than the upper limit of the 95% CI (definitely not clinical importance) [ 63 ]. Moreover, previous research has highlighted considerable variability in MIC/MCID as a function of estimation method, population and context, suggesting the importance of considering such factors when appraising the appropriateness of published MIC/MCID for use in clinical research and practice. However, we found that the included studies mostly only refer to the study by Yang et al. in 2009 [ 9 ]. Based on results of this study, a 6-point reduction is recommended to represent a clinically meaningful improvement in individuals with primary insomnia. It also noted that research on generalizability of the recommended MIC in this study to other patient populations and other type of treatment interventions is needed.

Several limitations should be acknowledged in this study. First, the data were exclusively obtained from mainstream sleep medicine journals, without considering other general medicine or psychiatric journals. Besides, the analysis focused solely on two frequently used PROMs for insomnia, while other relevant PROMs such as Sleep Assessment Questionnaire (SAQ), St. Mary’s Hospital Questionnaire, Leeds Sleep Evaluation Questionnaire, Post-Sleep Evaluation Questionnaire were not included [ 64 ]. Consequently, the generalizability of the findings may be constrained. Moreover, this study did not provide a recommendation in terms of choosing an appropriate MIC or MCID for further study. Last, the study did not explore the reporting of MIC/MCID values in meta-analysis and clinical practice guidelines, which is crucial for interpretation of results that encompass synthesized data with clinically significance [ 65 , 66 ].

In conclusion, future researchers of insomnia related RCT should be more vigilant in using PROMs that have a defined MIC/MCID in the stage of the study design. If the PROM does not have a defined MCID, researchers should be cautious about interpreting results as clinically significant based solely on a P -value or MIC. Researchers should consider MIC/MCID and 95% CI in decision making. The width of the CIs and its location with respect to the MIC/MCID are important considerations in making clinical conclusion. Implementation guidelines on MIC/MCID reporting and estimation for future studies are urgently needed.

Data availability

The data that support the findings of this study are available in Supplementary files.

Abbreviations

Minimal clinically important difference

Minimal important change

Patient-reported outcomes measures

Randomized controlled trial

Insomnia Severity Index

Pittsburgh Sleep Quality Index

Cognitive Behavioral Therapy for Insomnia

Confidence interval

Preferred Reporting Items for Systematic reviews and Meta-Analyses

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Acknowledgements

The authors thank Prof. Chang Xu for his professional suggestion and helps regarding study concepts and data extraction process.

This study is funded by the International Postdoctoral Exchange Fellowship Program (Talent-Introduction Program, Grant No. YJ20220238) and China Postdoctoral Science Foundation (Grant No. 2023TQ0018).

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Zongshi Qin and Yidan Zhu contributed equally to this study.

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Clinical Research Institute, Institute of Advanced Clinical Medicine, Peking University, Beijing, China

Zongshi Qin & Yidan Zhu

Shanghai Mental Health Center, Shanghai Jiao Tong University School of Medicine, Shanghai, China

Dong-Dong Shi

School of Life Sciences, Beijing University of Chinese Medicine, Beijing, China

Rumeng Chen & Sen Li

Guang’anmen Hospital, China Academy of Chinese Medical Sciences, Beijing, China

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Conception and design: ZQ, SL, and JW; Manuscript drafting: ZQ and YZ; Data collection: ZQ, YZ, and RC; Data analysis and result interpretation: ZQ, YZ, DS, SL, and JW; Methodology guidance: ZQ and JW; Manuscript editing: ZQ, YZ, SL, and JW. All authors have read and approved the manuscript.

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Correspondence to Zongshi Qin , Sen Li or Jiani Wu .

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Qin, Z., Zhu, Y., Shi, DD. et al. The gap between statistical and clinical significance: time to pay attention to clinical relevance in patient-reported outcome measures of insomnia. BMC Med Res Methodol 24 , 177 (2024). https://doi.org/10.1186/s12874-024-02297-0

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• Choosing the Right Statistical Test | Types & Examples

Choosing the Right Statistical Test | Types & Examples

Published on January 28, 2020 by Rebecca Bevans . Revised on June 22, 2023.

Statistical tests are used in hypothesis testing . They can be used to:

• determine whether a predictor variable has a statistically significant relationship with an outcome variable.
• estimate the difference between two or more groups.

Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.

If you already know what types of variables you’re dealing with, you can use the flowchart to choose the right statistical test for your data.

Statistical tests flowchart

Table of contents

What does a statistical test do, when to perform a statistical test, choosing a parametric test: regression, comparison, or correlation, choosing a nonparametric test, flowchart: choosing a statistical test, other interesting articles, frequently asked questions about statistical tests.

Statistical tests work by calculating a test statistic – a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship.

It then calculates a p value (probability value). The p -value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true.

If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables.

If the value of the test statistic is less extreme than the one calculated from the null hypothesis, then you can infer no statistically significant relationship between the predictor and outcome variables.

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You can perform statistical tests on data that have been collected in a statistically valid manner – either through an experiment , or through observations made using probability sampling methods .

For a statistical test to be valid , your sample size needs to be large enough to approximate the true distribution of the population being studied.

To determine which statistical test to use, you need to know:

• whether your data meets certain assumptions.
• the types of variables that you’re dealing with.

Statistical assumptions

Statistical tests make some common assumptions about the data they are testing:

• Independence of observations (a.k.a. no autocorrelation): The observations/variables you include in your test are not related (for example, multiple measurements of a single test subject are not independent, while measurements of multiple different test subjects are independent).
• Homogeneity of variance : the variance within each group being compared is similar among all groups. If one group has much more variation than others, it will limit the test’s effectiveness.
• Normality of data : the data follows a normal distribution (a.k.a. a bell curve). This assumption applies only to quantitative data .

If your data do not meet the assumptions of normality or homogeneity of variance, you may be able to perform a nonparametric statistical test , which allows you to make comparisons without any assumptions about the data distribution.

If your data do not meet the assumption of independence of observations, you may be able to use a test that accounts for structure in your data (repeated-measures tests or tests that include blocking variables).

Types of variables

The types of variables you have usually determine what type of statistical test you can use.

Quantitative variables represent amounts of things (e.g. the number of trees in a forest). Types of quantitative variables include:

• Continuous (aka ratio variables): represent measures and can usually be divided into units smaller than one (e.g. 0.75 grams).
• Discrete (aka integer variables): represent counts and usually can’t be divided into units smaller than one (e.g. 1 tree).

Categorical variables represent groupings of things (e.g. the different tree species in a forest). Types of categorical variables include:

• Ordinal : represent data with an order (e.g. rankings).
• Nominal : represent group names (e.g. brands or species names).
• Binary : represent data with a yes/no or 1/0 outcome (e.g. win or lose).

Choose the test that fits the types of predictor and outcome variables you have collected (if you are doing an experiment , these are the independent and dependent variables ). Consult the tables below to see which test best matches your variables.

Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests.

The most common types of parametric test include regression tests, comparison tests, and correlation tests.

Regression tests

Regression tests look for cause-and-effect relationships . They can be used to estimate the effect of one or more continuous variables on another variable.

Comparison tests

Comparison tests look for differences among group means . They can be used to test the effect of a categorical variable on the mean value of some other characteristic.

T-tests are used when comparing the means of precisely two groups (e.g., the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g., the average heights of children, teenagers, and adults).

Correlation tests

Correlation tests check whether variables are related without hypothesizing a cause-and-effect relationship.

These can be used to test whether two variables you want to use in (for example) a multiple regression test are autocorrelated.

Non-parametric tests don’t make as many assumptions about the data, and are useful when one or more of the common statistical assumptions are violated. However, the inferences they make aren’t as strong as with parametric tests.

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This flowchart helps you choose among parametric tests. For nonparametric alternatives, check the table above.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient
• Null hypothesis

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Statistical tests commonly assume that:

• the data are normally distributed
• the groups that are being compared have similar variance
• the data are independent

If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.

A test statistic is a number calculated by a  statistical test . It describes how far your observed data is from the  null hypothesis  of no relationship between  variables or no difference among sample groups.

The test statistic tells you how different two or more groups are from the overall population mean , or how different a linear slope is from the slope predicted by a null hypothesis . Different test statistics are used in different statistical tests.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

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• DOI: 10.1007/s41980-023-00855-8
• Corpus ID: 268141265

The Holomorphic Statistical Structures of Constant Holomorphic Sectional Curvature on Complex Space Forms

• Mingming Yan , Xin Wu , Liang Zhang
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