For the reader to fully understand the importance of your findings, it is almost always necessary to include some index of effect size or strength of relationship in your Results section (APA 2001).
p is dependent on sample size
N mean SD t p Choen's d
Experiment 1 1.52 > 0.05 0.56
Group A 15 25 9
Group B 15 20 9
Experiment 2 2.15 < 0.05 0.56
Group A 30 25 9
Group B 30 20 9
p-value can not show: uncertaintity, direction and intensity of effect
Effect size
t-test: d
ANOVA: f, f2, η, η2
η2 = f2/(1 + f2)
ANCOVA: f
(multiple) regression: f
MANOVA: f2
χ2-test: w
Confidence interval of effect size
Interval estimates: should be given for any effect sizes involving principal outcomes
R packages
rpsychi
compute.es
MBESS
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Table 1. Guidelines for calculating, reporting, and interpreting effect sizes (ESs) (Durlak 2009)
- Choose the most suitable type of effect based on the purpose, design, and outcome(s) of a research study
- Provide the basic essential data for the major variablesa
- for group designs, present means, standard deviations, and sample size for all groups on all outcomes at all time points of measurement
- for correlational studies, provide a complete correlation matrix at all time points of measurement
- for dichotomous outcomes, present the cell frequencies or proportions and the sample sizes for all groups
- Be explicit about the type of ES that is used
- Present the effects for all outcomes regardless of whether or not statistically significant findings have been obtained
- Specify exactly how effects were calculated by giving a specific reference or providing the algebraic equation used
- Interpret effects in the context of other research
- the best comparisons occur when the designs, types of outcomes, and methods of calculating effects are the same across studies
- evaluate the magnitude of effect based on the research context and its practical or clinical value
- if effects from previous studies are not presented, strive to calculate some using the procedures described here and in the additional references
- use Cohen's (1988) benchmarks, only if comparisons to other relevant research are impossible
a These data have consistently been recommended as essential information in any report, but they also can serve a useful purpose in subsequent research if readers need to make any adjustments to your calculations based on new analytic strategies or want to conduct more sophisticated analyses. For example, the data from a complete correlation matrix is needed for conducting meta-analytic mediational analyses.
Table 1. Strategies for obtaining effect sizes for selected SPSS analyses (Vacha-Haase & Thompson 2004)
- Contingency table (r or odds ratio): Run the CROSSTABS procedure and select the desired effect from the STATISTICS submenu
- Independent t test (d, η2, or ω2): Compute a Cohen's d by hand. Or, run the analysis as a one-way ANOVA using the GLM program; click on the OPTION requesting an effect size to obtain η2. Use the Hay's correction formula (ω2) if an adjusted estimate is desired
- ANOVA (η2 or ω2): Run the analysis as an ANOVA using the GLM program; click on the OPTION requesting an effect size to obtain η2. Use the Hay's correction formula by hand if an adjusted estimate is desired
- Regression (R2 or R2*) Run the REGRESSION procedure. Both the uncorrected R2 and the corrected variance accounted for (R2*) estimates are displayed, by default
- MANOVA (multivariate η2 or ω2): Run the analysis as a MANOVA using the GLM program; click on the OPTION requesting an effect size to obtain η2. A corrected estimate, multivariate ω2, (Tatsuoka 1973), can be computed by hand
- Descriptive discriminant analysis (multivariate η2 or ω2): Run the analysis as a MANOVA using the GLM program; click on the OPTION requesting an effect size to obtain η2. A corrected estimate, multivariate ω2 (Tatsuoka 1973), can be computed by hand.
- Canonical correlation analysis (Rc2 or Rc2*): Run the analysis in the MANOVA procedure using the syntax suggested by Thompson (2000). The Rc2 is reported. Apply the Ezekiel correction by hand if a corrected value (Rc2*) is desired
Note. ANOVA = analysis of variance; GLM = general linear model; MANOVA = multivariate analysis of variance
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