FAQ/td - CBU statistics Wiki

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How do I convert a t-statistic into an effect size?

One sample t

Since $$\frac{\sqrt{\mbox{n}} \mbox{mean}}{\mbox{sd}}$$ = t

Cohen's d = $$\frac{t}{\sqrt{n}}$$

Two sample t

Rosenthal (1994) states for sample sizes $$\mbox{n}_text{1}$$, $$\mbox{n}_text{2}$$,

Cohen's d = $$\frac{t(\mbox{n}_text{1}+\mbox{n}_text{2})}{\sqrt{\mbox{df}}\sqrt{\mbox{n}_text{1}}\sqrt{\mbox{n}_text{2}} }$$

When $$\mbox{n}_text{1}$$ = $$\mbox{n}_text{2}$$

Cohen's d = $$\frac{\mbox{2t}}{\sqrt{\mbox{df}}}

Pearson Correlation

Rosenthal (1994) also gives a conversion formula to turn a t-statistic into a correlation

Correlation = $$\sqrt{\frac{\mbox{t}text{2}}{\mbox{t}text{2} + \mbox{df}}$$

Reference

Rosenthal, R. (1994) Parametric measures of effect size. In H. Cooper and L.V. Hedges (Eds.). The handbook of research synthesis. New York: Russell Sage Foundation.