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Cohen's f (ANOVA Effect Size) Calculator

Quantifies the effect size in ANOVA, representing the degree of population variance accounted for by the independent variable.

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Cohen's f

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Overview

Cohen's f is a crucial effect size measure used in the context of Analysis of Variance (ANOVA) to quantify the magnitude of the differences between group means. It represents the standard deviation of the standardized means, providing a dimensionless measure of effect size that is independent of sample size. This metric is particularly valuable for power analysis, allowing researchers to estimate the required sample size to detect a given effect with a certain probability.

Symbols

Variables

= Eta-squared, f = Cohen's f

Eta-squared
Variable
Cohen's f
Variable

Apply it well

When To Use

When to use: Use Cohen's f when conducting or planning an ANOVA to quantify the practical significance of your findings beyond statistical significance. It is essential for power analysis to determine the appropriate sample size needed to detect a hypothesized effect size.

Why it matters: Cohen's f is vital for moving beyond simple p-values to understand the real-world importance of research findings. It enables researchers to compare effect sizes across different studies, plan adequately powered experiments, and avoid Type II errors, thereby contributing to more robust and reproducible psychological science.

Avoid these traps

Common Mistakes

  • Confusing Cohen's f with Cohen's d; they are for different statistical tests.
  • Misinterpreting a statistically significant p-value as a practically significant effect without considering effect size.
  • Incorrectly calculating eta-squared, which is a prerequisite for f.

One free problem

Practice Problem

A researcher conducts an ANOVA and finds an eta-squared (η²) value of 0.15. Calculate Cohen's f to determine the effect size.

Eta-squared0.15

Solve for:

Hint: Remember the formula: f = sqrt(η² / (1 - η²)).

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.
  2. Wikipedia: Effect size
  3. Field, Andy. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE Publications.
  4. Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). SAGE Publications.
  5. Wikipedia: Effect size (statistics)
  6. Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences