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Formulas: f-square Effect Size Confidence Interval

f-square Effect Size Confidence Interval Formulas

Below you will find descriptions and details for the 3 formulas that are used to compute confidence intervals for regression-based f-square effect sizes.

Confidence interval for an R2 value:
Confidence interval for an R<sup>2</sup> value formula
where R2 is the squared multiple correlation, α is the desired confidence interval percentage, SER2 is the standard error for R2, t is a t-value, k is the number of predictors in the model, and n is the total sample size.
Squared multiple correlation for Cohen's f2 effect size:
Squared multiple correlation for Cohen's f<sup>2</sup> effect size formula
where f2 is Cohen's effect size measure for an F-test.
Standard error for an R2 value (Olkin and Finn's approximation):
Standard error for an R<sup>2</sup> value (Olkin and Finn's approximation) formula
where R2 is the squared multiple correlation, k is the number of predictors in the model, and n is the total sample size.
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