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Chapter 1.   Introduction and Background

          

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




Chapter 2.   Types of Effect size indices:  An Overview of the Literature

          

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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

          

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3.1
Example A: Hypnotherapeutic ego strengthening (HES) for male coronary artery bypass patients (de Klerk et.al., 2004)
 
3.2     Example B:

The personality preferences of lecturers and students   (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: data set 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, 2007: Example dataset ’10 item’ )




CHAPTER 4 :  Standardized Differences

          

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4.1 Cohen's d
4.1.1 Estimation of δ
4.1.2 Confidence intervals for δ
 
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 Guidelines for effect size indices based on standardized differences
4.5.1 Small effect 
4.5.2 Medium effect 
4.5.3 Large effect
4.5.4  Warnings (Kline, 2004a:  132)
 
4.6

Practical Significance




CHAPTER 5 :  Relationships between variables

          

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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

Adjustment 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  Adjustment 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 Confidence interval for φ
5.4.3 Probability measures from 2 x 2 frequency tables
5.4.4 Difference  in proportions
5.4.5 Guideline values for differences in proportions
5.4.6 Rate or Risk ratios
5.4.7 Odds ratio (OR)
5.4.8 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

          

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6.1 Indices for omnibus effects for independent measurements
6.1.1 Estimation of η2
6.1.2 Confidence intervals for  η2
6.1.3 Guideline values for the omnibus effect  η2
6.1.4 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
 
6.3

Indices for contrast-effects

6.3.1 Choice of σ* and d_kappie
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

          

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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 andk  groups
 
7.3 Multivariate omnibus effect
 
7.4

Effect sizes indices for canonical correlation

 
7.5

Effect sizes indices for canonical correlation




CHAPTER 8 :  Effect sizes and Group overlapping

          

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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
8.3

Hit rate and its estimation

8.3.1

Two univariate normal-populations with variances homogenous

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 2) and the better-than-chance index ( I )
8.6.1 Heterogeneous variances of 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

          

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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)



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REFERENCES

          

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