# Computing effect sizes

**Cohen's d**which is used for t-tests may be computed with a calculator here and here or using free PC downloadable software. This can also be calculated in EXCEL (see here) or using, in the denominator, the pooled standard deviation given formula 1a in here. A suggestion for computing an overall Cohen's d comparing groups (over time) within each subject.SPSS computes

**partial eta-squared**, Partial eta^{2}, on request using ANOVAs. If using General Linear Model>univariate or General Linear Model>Repeated Measures click options and select*Estimates of Effect Size*. An extra column in the outputted anova tables is produced showing partial eta-squareds of terms in the anova table. Partial eta-squared represents the proportion of variance not attributable to any of the other observed factors which is explained by the factor of interest.For anovas, an alternative value

**Eta-squared**eta^{2}, can also be calculated. This value is defined as the sum of squares for a particular effect divided by the total of all the sums of squares of effects in the analysis of variance table. It is suggested, however, that partial eta-squared be used for repeated measures analysis of variance and eta-squared for between subjects anovas (which feature just one error term in the anova). Field(2005) advocates only using effect sizes when comparing a difference between two groups in repeated measures anova.

McShane and Bockenholt (2016) illustrate formulae and how to use G*Power to obtain sample sizes for comparisons of means (Cohen's d), correlations and proportions taking the variance of the difference into account.

An EXCEL spreadsheet calculator computes the one sample chi-square effect size measure, $$\omega$$.

- The Pearson correlation is, itself, an effect size.
Field (2005)(pp. 222-223) suggests evaluating a correlation based upon output from a logistic regression. This is based upon the Wald statistic which can give misleading results.

Field also suggests a nonparametric effect size for comparing two groups (see here).

A web-based calculator for computing a large range of effect sizes is here.

You might find A guide to magnitudes of effect sizes and Calculating, Interpreting and Reporting Estimates of "Effect Size" useful. The following spreadsheet by Jamie DeCoster (2012) converts a single effect size, such as Cohen's d, to several others including Odds Ratios using references mentioned in the spreadsheet. There is also an effect size calculator and converter for individual statistical tests here. One could also convert a partial eta-squared to a Cohen's d by regarding the partial eta-squared as a squared correlation. It follows square rooting the partial eta-squared and entering it in Jamie's spreadsheet as a r will then allow you to read off the Cohen's d. Jamie has written other EXCEL spreadsheet calculators here. Howell (2013) p.627-8 gives formulae for conversions of effect sizes such as odds ratios and correlations to Cohen's d.

References

Baguley T (2012) Serious Stats. A guide to advanced statistics for the behavioral sciences. Palgrave MacMillan:New York. R code and formulae for a range of commonly used effect sizes are in Chapter 7 on pages 235-276.

DeCoster J (2012) Spreadsheet for converting effect size measures. Available from: http://www.stat-help.com/spreadsheets/Converting%20effect%20sizes%202012-06-19.xls (accessed 04.09.2014)

Field A (2005) Discovering statistics using SPSS Sage:London.

Howell DC (2013) Statistical methods for psychologists. 8th Edition. International Edition. Wadsworth:Belmont,CA.

McShane BB and Bockenholt U (2016) Planning sample sizes when effect sizes are uncertain: the power-calibrated effect size approach. *Psychological Methods* **21(1)** 47-60. Available free as a pdf download via the psychnet website to CBUers.

Vacha-Haase T & Thompson B (2004) How to estimate and interpret various effect sizes. *Journal of Counseling Psychology* **51(4)** 473-481. Details computing effect sizes in SPSS for methods including ANOVA and regression as well as showing conversion formulae expressing one effect size in terms of another.