This book addresses sample size and power in the context of research, offering valuable insights for graduate and doctoral students as well as researchers in any discipline where data is generated to investigate research questions. It explains how to enhance the authenticity of research by estimating the sample size and reporting the power of the tests used. Further, it discusses the issue of sample size determination in survey studies as well as in hypothesis testing experiments so that readers can grasp the concept of statistical errors, minimum detectable difference, effect size, one-tail and two-tail tests and the power of the test. The book also highlights the importance of fixing these boundary conditions in enhancing the authenticity of research findings and improving the chances of research papers being accepted by respected journals.

Further, it explores the significance of sample size by showing the power achieved in selected doctoral studies. Procedure has been discussed to fix power in the hypothesis testing experiment. One should usually have power at least 0.8 in the study because having power less than this will have the issue of practical significance of findings. If the power in any study is less than 0.5 then it would be better to test the hypothesis by tossing a coin instead of organizing the experiment. It also discusses determining sample size and power using the freeware G*Power software, based on twenty-one examples using different analyses, like t-test, parametric and non-parametric correlations, multivariate regression, logistic regression, independent and repeated measures ANOVA, mixed design, MANOVA and chi-square.

Prof. J P Verma is the founder Vice Chancellor of Sri Sri Aniruddhadeva Sports University of Assam. This is a state university of Assam Government established at Chabua in Dibrugarh. The university is a high-class university dedicated for the sports education and research activities in the north eastern region of India. Prior to this assignment Prof. Verma was Head, Department of Sport Psychology and Dean of Student Welfare at Lakshmibai National Institute of Physical Education, Gwalior. He has more than 38 years of teaching and research experience. He also worked as the Director of the Centre for Advanced Studies for three years. He holds three master's degrees; in Statistics, Psychology and Computer Application and a Ph.D. in Mathematics. Prof. Verma has published eleven books on research and statistics in the area of management, psychology, exercise science, health, sports and physical education, and 45 research papers/articles, and has developed sports statistics as an academic discipline. He was a visiting fellow at the University of Sydney in 2002 and has held academic visits in universities in Japan, Bulgaria, Qatar, Australia, Poland and Scotland, where he conducted numerous workshops on research methodology, research designs, multivariate analysis and data modeling in the area of management, social sciences, physical education, sports sciences, economics and health sciences.

Priyam Verma is currently pursuing his Ph.D. Economics at the University of Houston, Texas. He completed his M.Phil. in Development Economics and masters in Economics at Indira Gandhi Institute of Development Research (IGIDR), Mumbai. He has worked on monetary policy issues of developing countries, land valuations in rural India and economics of child labor in India. His current interests include econometrics, behavioral economics, experimental economics and macroeconomics.

Preface

Acknowledgements

Introduction

Issue of Power due to inappropriate sample size

Flow Diagram of Determining sample size and power

Summary

2 Understanding Statistical Inference

Introduction

Estimating Parameters

Estimating Population Mean

Confidence Coefficient

Confidence Interval

Factors Affecting Confidence Interval

Hypothesis Testing

Type I and Type II Errors

Power of the Test

Relationship between Type I and Type II Errors

One Tailed and Two Tailed Tests

Procedure in Hypothesis Testing Experiment

Effect Size

Summary

3 Understanding Concepts in Estimating Sample Size in

Survey Studies

Introduction

Determining Sample Size in Estimating Population Mean

Factors Affecting Sample Size

Sample Size Determination for Estimating Mean when Population SD Known: Illustration 3.1

Sample Size Determination for Estimating Mean when Population SD Unknown: Illustration 3.2

Sample Size Determination for Estimating Mean when Population SD Unknown: Illustration 3.3

Sample Size Determination for Estimating Mean when Population SD Unknown: Illustration 3.4

Determining Sample Size in Estimating Population Proportion

Sample Size Determination for Estimating Proportion: Illustration 3.5

Sample Size Determination for Estimating Proportion: Illustration 3.6

Sample Size Determination for Estimating Proportion: Illustration 3.7

Sample Size Determination for Estimating Proportion: Illustration 3.8

Determining Sample Size in Estimating Difference Between Two Population Means

Summary

4 Understanding Concepts in Estimating Sample Size in Hypothesis Testing Experiment

Introduction

Sample Size on the Basis of Power

One Sample Testing of Mean

Determining Sample Size

Estimation of Minimum Sample Size to Test H₀ : µ=37 : Illustration 4.1

Minimum Detectable Difference

Estimation of Minimum Detectable Difference for Testing H₀: µ=37: Illustration 4.2

Estimation of Power in One Sample t Test

Estimation of Power in Testing H₀: µ=37: Illustration 4.3

Testing Difference Between Two Means

Determining Sample Size in Two Sample t Test

Estimation of Sample Size for Two Sample t Test for Mean : Illustration 4.4

Estimation of Power in Two Sample t Test

Estimation of Power in Two Sample t Test for Mean : Illustration 4.5

Summary

5 Use of G*Power Software

Introduction

Procedure of Installing G*Power 3.1

Summary

6 Determining Sample Size in Experimental Studies

Introduction

One Sample Testing

Testing Difference of Sample Mean from Population Mean

Sample Size and Power Determination: Illustration 6.1

Testing Difference of Sample Proportion from Population Proportion

Sample Size Determination: Illustration 6.2

Two Sample Testing

Comparing Group Means in Two Independent Samples

Sample Size and Power Determination: Illustration 6.3

Comparing Paired Group Means

Sample Size Determination: Illustration 6.4

Comparing two Group Means Using Mann Whitney Test

Sample Size Determination: Illustration 6.5

Comparing Paired Group Means Using Wilcoxon Signed Rank Test

Sample Size Determination: Illustration 6.6

Comparing Two Proportions

Sample Size Determination: Illustration 6.7

Correlation Coefficient: Testing Significance

Case I: Testing Whether Sample Correlation Differs From 0

Sample Size Determination: Illustration 6.14

Case II: Testing Whether Sample Correlation Differs from a Known Value

Sample Size Determination: Illustration 6.15

Correlation Coefficients: Testing Significant Difference Between Two Independent Correlations

Sample Size Determination: Illustration 6.16 <…