I regularly forget standard rules of interpretation for effect sizes when running analyses. I figured I’d put these here so I can quickly refer to them when needed. For more details on most effect sizes, Wikipedia is always useful.

## Cohen’s d

Cohen’s d is typically used when doing t-tests. The basic calculation is the difference between two means divided by a standard deviation (usually the pooled standard deviation). Here’s the interpretation.

Effect Size | d |

Very small | 0.01 |

Small | 0.20 |

Medium | 0.50 |

Large | 0.80 |

Very Large | 1.20 |

Huge | 2.00 |

The standard citations are to Jacob Cohen’s work:

Cohen, Jacob. 1988. *Statistical Power Analysis for the Behavioral Sciences*. Mahwah, N.J.: Lawrence Erlbaum.

Cohen, Jacob. 1992. “A Power Primer.” *Psychological Bulletin* 112(1):155–59.

However, the new citation is to Sawilowsky:

Sawilowsky, Shlomo S. 2009. “New Effect Size Rules of Thumb.” *Journal of Modern Applied Statistical Methods* 8(2):597–99.

## Pearson’s r

Pearson’s r is a standard measure of correlation. It can also be calculated for other statistical tests.

Effect Size | r |

Small | 0.10 |

Medium | 0.30 |

Large | 0.50 |

These interpretations also come from Cohen’s work:

Cohen, Jacob. 1988. *Statistical Power Analysis for the Behavioral Sciences*. Mahwah, N.J.: Lawrence Erlbaum.

## R-Square (Coefficient of Determination)

Technically, R^{2} is not an effect size. It’s a measure of the amount of variation in the dependent variable that is accounted for by the independent variables. However, because it captures the magnitude or size of a relationship rather than the existence of a relationship, it can be interpreted as similar to an effect size. Cohen provided some rough measures for interpreting the magnitude of R^{2}, though it is important to note that this will vary by what is under investigation.

Effect Size | R^{2} |

Small | 0.02 |

Medium | 0.13 |

Large | 0.26 |

These interpretations come from Cohen’s work:

Cohen, Jacob. 1988. *Statistical Power Analysis for the Behavioral Sciences*. Mahwah, N.J.: Lawrence Erlbaum.

## Cohen’s F-Square

Cohen’s F^{2} is an effect size measure that can be used with OLS regression. It is calculated using R^{2}, or the coefficient of determination.

Effect Size | F^{2} |

Small | 0.02 |

Medium | 0.15 |

Large | 0.35 |

These interpretations come from Cohen’s work:

Cohen, Jacob. 1988. *Statistical Power Analysis for the Behavioral Sciences*. Mahwah, N.J.: Lawrence Erlbaum.