Description
Book SynopsisThis 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.
Table of ContentsPreface
Acknowledgements
1 Introduction to Sample Size Determination
Introduction
Issue of Power due to inappropriate sample size
Some case studies
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
Estimating Population Proportion
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
Bi-Serial Correlation: Testing Significance
Sample Size Determination: Illustration 6.17
Goodness of Fit: Testing With Chi-Square
Sample Size Determination in Goodness of Fit: Illustration 6.18
Linear Multiple Regression Model
Sample Size Determination in Linear Multiple Regression: Illustration 6.19
Logistic Regression
Sample Size Determination for Continuous Predictors: Illustration 6.20
Sample Size Determination for a Dichotomous Predictor: Illustration 6.21
Summary
7 Determining Sample Size in General Linear Models
Introduction
Analysis of Variance
One–Way Analysis of Variance
Sample Size Determination: Illustration 6.8
Two–Way Analysis of Variance
Sample Size Determination for Main and Interaction Effect: Illustration 6.9
Repeated Measures ANOVA Between Factors
Sample Size Determination: Illustration 6.10
Repeated Measures ANOVA Within Factors
Sample Size Determination: Illustration 6.11
Repeated ANOVA Within-Between Interaction
Manova Experiment: for Testing the Significance of Global Effect
Sample Size Determination: Illustration 6.12
Manova Experiment: Testing Significance of Interaction Effect
Sample Size Determination: Illustration 6.13
Summary
Appendix
Bibliography
