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}}} (1)

2 way interaction

Abelson and Prentice (1997) suggest a way of converting a F statistic from a two-way interaction into Cohen's d:

$$\mbox{Cohen's d} = \sqrt{\mbox{2}} \frac{\sqrt{\mbox{F}}}{\sqrt{\mbox{n}}} (2)

where n is the assumed equal number of observations for each combination of the two factors. If these are unequal then we use the [http://en.wikipedia.org/wiki/Harmonic_mean harmonic mean] of the sample sizes.

Equation (1) is a special case of (2) since t equals $$\sqrt{F}$$ and df is made equal to 2n.

Pearson Correlation

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

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

References

Abelson, RP and Prentice, DA (1997) Contrast tests of interaction hypotheses. Psychological Methods 2(4) 315-328.

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.