Thirteen effect size conversions: t to Cohen’s d, F to partial eta squared, odds ratio to risk ratio, r to Fisher’s z. Each with its formula and assumption.
Thirteen conversions between the test statistics and effect sizes a manuscript is most often asked for: t to Cohen’s d, F to partial eta squared, odds ratio to risk ratio, r to Fisher’s z and nine more. Each one is a calculator with its formula in plain view, so you can redo the number by hand.
What sets them apart from the converters you find online is that, besides the number, they tell you the assumption you accept when you convert. Some conversions are exact identities and assume nothing; others take for granted that the groups are equal or that a continuum lies beneath your binary variable. That is exactly what a reviewer will ask you about.
You have the t, the F or the chi-square in your output and the journal asks for an effect size. These four follow exactly from what you already have.
For a meta-analysis, to compare with a study that used another metric, or because the reviewer wants the other one. This is where assumptions come in, and each page names yours.
G*Power does not work in the metrics you publish but in Cohen’s. The two conversions you always need before you justify your sample size.
Getting the standard error out of a published interval, and translating a d into something a non-statistician understands.
The ones that simply rearrange a formula are exact and assume nothing: t to r, F to partial eta squared, chi-square to Cramér’s V, eta squared to f and R squared to f squared. If the inputs are right, so is the result.
The ones that change scale carry an assumption: odds ratio to d assumes a continuous latent variable with a logistic distribution; d to r, that you know how the groups are split; confidence interval to standard error, that the interval is symmetric and was built on the normal distribution. When you convert for a meta-analysis, that assumption belongs in your Method section.
Yes, with Chinn’s (2000) formula, d = ln(OR) × √3/π, and it is the usual route when some studies report binary outcomes and others continuous ones. What you accept is that the dichotomy cuts a continuous underlying variable. State it in your Method and, if you can, check in a sensitivity analysis that the result does not hinge on that choice.
Almost always because the paper used the short formula d = 2t/√df, which is only right with equal group sizes, or computed d with a single group’s standard deviation. With both group sizes, the t-to-d conversion is exact.
Cohen’s f for an ANOVA and f squared for a regression, never eta squared or R squared directly. Both conversions are exact; what you need to justify is where the expected effect comes from, not the arithmetic.
Converting is easy once you know which effect size you are missing. The hard part is reading the whole manuscript to see which ones are missing, which do not match their own test statistic, and what a reviewer will object to. Previum · AI peer review does that on the complete manuscript.
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