Table of contents

CHAPTER 1.   Introduction and Background  (Download document)

1.1 Practical significance
1.2 When are effect size indices necessary?
1.3 Requirements for good effect size measures
1.4 Use of effect sizes in the application of Statistics in various fields
1.5 Effect sizes in statistical literature and computer packages
1.6 Objectives and structure of this manual

CHAPTER 2.   Types of Effect size indices:  An Overview of the Literature  (Download document)

2.1 Measurement scales and assumptions
2.2 Effect size indices for differences in groups
2.3 Effect size indices based on Relationships
2.4 Effect size indices based on Group overlapping
2.5 Multivariate Effect size indices
2.6 Concluding remarks

CHAPTER 3 :   Examples from practical research (Download document)
3. Examples from practical research
3.1 Example A : Hypnotherapeutic ego strengthening (HES) for male
coronary artery bypass patients (de Klerk et.al., 2004)
3.2 Voorbeeld B: Die persoonlikheidsvoorkeure van dosente en studente
(Rothmann et.al., 2000b)
3.3 Example C: Smoking and the risk of coronary heart disease
(Kline, 2004a: 155-156)
3.4 Example D: Self respect of three communities in North-east Australia
(Smithson, 2000:246)
3.5 Example E: Cholesterol and Blood pressure of heart patients
(Smithson, 2000: dataset HEART)
3.6 Example F: Serum-cholesterol of men within activity groups
3.7 Example G: Questionnaire concerning the advantages of imported
motor vehicles (Statsoft, Inc, 2004: Example dataset ’10 item’)

CHAPTER 4 :  Standardized Differences (Download document)
4.1 Cohen’s d
4.1.1 Estimation of  δ
4.1.2 Confidence intervals for δ
4.1.3 Counternull effect sizes
4.1.4 Interpretation of the counternull effect sizes

4.2 Glass’ Δ
4.2.1 Estimation and confidence intervals for Δ

4.3 Effect Size Indices for Heterogeneous variances
4.3.1 Choice of any population SD
4.3.2 Choice of the largest SD
4.3.3 Weighted SD

4.4 Effect size indices for dependent groups
4.4.1 Confidence intervals for δD and δ‘D


4.5 Counternull values for other effect sizes used to compare two
means

4.6 Guidelines for effect size indices based on standardized differences
4.6.1 Small effect
4.6.2 Medium effect
4.6.3 Large effect
4.6.4 Warnings (Kline, 2004a: 132)

4.7 Practical Significance

CHAPTER 5 :  Relationships between variables (Download document)

5.1 Effect size of linear relationships between two continuous
variables
5.1.1 Guideline values for correlation effect size indices
5.1.2 Confidence intervals for correlation effect sizes
5.1.3 Counternull values for correlation
5.1.4 Modification of correlation for reliability

5.2 Effect sizes of linear relationships between a continuous
response variable and more than one predictor variable
5.2.1 Semi-partial R² as an effect size-index
5.2.2 Partial R² as an effect size-index
5.2.3 The effect size index ƒ²
5.2.4 Guideline values for proportion variance
5.2.5 Point and interval estimation of proportion variance (Smithson, 2001)
5.2.6 Confidence intervals for partial ρ²

5.3 Effect sizes of the relationship between a continuous and a
dichotomous variable
5.3.1 Relationship between a continuous variable and group membership of two
groups
5.3.2 Modification for reliability
5.3.3 Proportion variance attributed to the group membership of two populations
5.3.4 Guideline values for proportion variance attributed to population
group membership

5.4 Effect sizes for 2 x 2 - frequency tables
5.4.1 Relationships between x and y
5.4.2 Binomial Effect Size Display (Rosenthal et.al 2000: 17)
5.4.3 The counternull of the BESD
5.4.4 Confidence interval for Ψ

5.4.5 Probability measures from 2 x 2 frequency tables
5.4.6 Difference in proportions
5.4.7 Guideline values for differences in proportions
5.4.8 Rate or Risk ratios
5.4.9 Interpretation of OR as an effect size

5.5 Effect size of relationship between two nominal variables
5.5.1 Estimation of w
5.5.2 Confidence interval for w
5.5.3 Guideline values for w

CHAPTER 6 :  Comparison of more than two groups of observations (Download document)

6.1 Indices for omnibus effects for independent measurements
6.1.1 Estimation for η2
6.1.2 Confidence intervals for η2
6.1.3 Comparing more than two proportions
6.1.4 Guideline values for the omnibus effect η2
6.1.5 Motivation for the guideline values proposed by Cohen

6.2 Indices for omnibus effects for dependent measurements
6.2.1 Intra-class correlation coefficient
6.2.2 Cronbach alpha coefficient
6.2.3 Confidence intervals for ρI  and  ρ(k)xx
6.2.4 Limits of agreement and reliability coefficients

6.3 Indices for contrast-effects
6.3.1 Choices of σ*and σˆ*
6.3.2 Guideline values for effect sizes of contrasts
6.3.3 Contrasts for dependent measurements
6.3.4 Confidence intervals for δΨ = Ψ/σ* (independent samples)
6.3.5 Confidence intervals for δΨ = Ψ/σ* (dependent samples)

6.4 Comparing independent groups after controlling for a covariate
6.4.1 Contrasts in analysis of covariance
6.4.2 Confidence intervals of effect size indices after controlling for a covariate
6.4.3 More than one covariate

CHAPTER 7 :  Multivariate effect sizes indices (Download document)
7.1 Comparing two groups with m variables
7.1.1 Guideline values for D

7.2 Effect sizes of contrast effects for m variables and k groups

7.3 Multivariate omnibus effect

7.4 Effect sizes indices for canonical correlation

7.5 Guidelines for multivariate omnibus-effects

CHAPTER 8 :  Effect sizes and Group overlapping (Download document)
8.1 Introduction

8.2 Distance and classification
8.2.1 Prior probabilities
8.2.2 Equal population covariance matrices
8.2.3 Unequal population-covariance matrices
8.2.4 Two univariate populations: classification with ROCanalysis

8.3 Hit rate and its estimation
8.3.1 Two univariate normal populations with homogeneous variances
8.3.2 Two multivariate normal populations with equal covariance-matrices
8.3.3 More than two multivariate populations

8.4 Effect size index for correct classification
8.4.1 Proportional chance-criterion
8.4.2 Maximum chance criterion
8.4.3 Statistical testing of the frequency of a hit

8.5 Effect size index: Better-than-chance

8.6 Relationship between proportion variance ( η2) and the better-than-chance index ( I )
8.6.1 Homogenous variances or covariance matrices
8.6.2 Heterogeneous variances of covariance matrices

8.7 Guideline values for the index I

8.8 Uses of the index I

APPENDIX (Download document)
a)   Methods for determining exact confidence intervals for δ, δD  and ψ
       1.  Two independent groups
       2.  Two dependent groups 
       3.  Contrasts 
b)   Estimation and confidence intervals of the Mahalanobis D 
c)   Estimation and confidence intervals for the ξ2 index based on the Hotelling-Lawley-Statistic
       for the m variable MANOVA (see Steyn & Ellis, 2009)

•  References