# Effect-Size and Power Calculators

## Free Tools for Computing Effect Size and Related Statistics

**Wilson’s effect-size calculator.** This takes you to Dr. David B. Wilson’s online calculator that computes a variety of effect-size indices: Cohen’s d statistic, the correlation coefficients r and V, the odds ratio, and the risk ratio. In most cases it also provides the 95% confidence interval for the index. It is remarkably flexible, allowing users to input a wide variety of statistics to compute the desired index. For example, you can compute d by providing 30 different types of data: means and standard deviations, obtained t statistics and sample size, even mean-square errors, correlations, means, and sample size from ANCOVA. The calculator is tied to the book Practical Meta-Analysis by Mark W. Lipsey and David B. Wilson (2001) and published by Sage.

http://www.campbellcollaboration.org/escalc/html/EffectSizeCalculator-Home.php

**Psychometrica effect-size calculator.** This takes you to an effect size calculator at the German Psychometrica site (don’t worry—the page is in English). Depending on the nature of your study, it allows you to compute Cohen’s d, Glass’ Δ, Hedges g, Cohen’s f, the Binomial Effect Size Display (BESD), Number Needed to Treat (NNT), odds ratio, risk ratio, and eta squared. For several scenarios it will compute confidence intervals for d. It allows users to input several different types of statistics (e.g., means, standard deviations, t values, F values, cell frequencies) to compute the desired effect size. One very useful table allows users to input a specific value of d, r, eta squared, f, or the odds ratio, and convert it into any other effect index (d, r, eta squared, f, or the odds ratio).

https://www.psychometrica.de/effect_size.html

**Psychometrica sensitivity and specificity calculator.** The Psychometrica site also offers a calculator that allows users to assess the quality of predictions made on dichotomous criterion variable from a dichotomous predictor variable. Users enter frequencies into a 2 x 2 table, and the calculator reports sensitivity, specificity, hit ratio, random hit ratio, and more.

https://www.psychometrica.de/test_criteria_en.html

## Free Tools for Performing Statistical Power Analyses

**G*Power power calculator.** At the following link you can download G*Power: application for performing statistical power analysis. This is a procedure that estimates the probability that you will obtain statistically significant results given a specific sample size, the selected alpha level, and other assumptions. The software can estimate power for a wide variety of statistics, including the t test, F test, chi-square, z tests, and more. At the site you can also download a free PDF of the G*Power user manual.

http://www.gpower.hhu.de/en.html

**AI Therapy power calculator.** This takes you to AI-Therapy Statistics, a site that, among other things, offers a free online calculator that can compute statistic power for t tests (independent samples as well as paired samples) and one-way ANOVA (between factors as well as within-subjects). The user inputs the expected effect size, number of participant and similar information, and the calculator estimates the statistical power that the test will display.

https://www.ai-therapy.com/psychology-statistics/power-calculator

**AI Therapy sample-size calculator.** The AI-Therapy Statistics site also provides a calculator that estimate the number of participants that will be needed for the results of a specific study to be statistically significant. The calculator is somewhat limited, doing this only for the independent-samples t test, paired-samples t test, and correlation coefficient. The user chooses the alpha level and inputs the expected effect size and similar information. The calculator then returns the number of participants that will be necessary to reject the null hypothesis.

https://www.ai-therapy.com/psychology-statistics/sample-size-calculator