Effect size calculator

An effect size only becomes meaningful once you read it against a benchmark, and each metric has its own. For Cohen's d the conventional cut points are 0.2 for a small effect, 0.5 for medium, and 0.8 for large, while a Pearson's r reads 0.1, 0.3, and 0.5 across the same three bands. For an ANOVA, an eta-squared of 0.01, 0.06, and 0.14 marks small, medium, and large shares of variance explained. These thresholds are starting points, not laws.

The effect size meaning that matters most is the practical one: a small standardised value can still be important in a field where effects are typically tiny, and a large value can be unremarkable where big effects are the norm. Interpret your number against what is usual in your own literature, then state plainly what the difference or relationship means for your research question rather than leaving the reader to decode the benchmark.

The metric you report follows directly from the test you ran. For a difference between two group means, such as a t-test, report Cohen's d or the bias-corrected Hedges' g. For the relationship between two continuous variables, report the correlation coefficient. For an analysis of variance, report eta-squared or partial eta-squared, and for a 2x2 outcome table or a logistic model, report an odds ratio or risk ratio.

Matching the metric to the design is what keeps your results chapter coherent: a reader should be able to look at the test and predict which effect size accompanies it. When the design is mixed, report the effect size that the test statistic naturally produces rather than converting between scales unless a conversion is genuinely needed.

When you run an analysis of variance with more than one factor, two versions of the same idea appear. Eta-squared is the factor's sum of squares over the total sum of squares, so the values for all effects in the model add up toward one. Partial eta-squared divides the factor's sum of squares by itself plus the error term, which removes the other factors from the denominator and usually returns a larger number.

Statistical software, SPSS in particular, reports partial eta-squared by default, so make clear which one you are quoting. Mixing the two, or comparing a partial value from one study against a non-partial value from another, is a common source of confusion in a results chapter write-up. State the version by name every time.

In APA style the effect size travels in the same sentence as the test statistic and the exact p-value, never as a footnote. Report the metric by name and its value to two decimal places, for example a t-test result followed by d = 0.62, and give an interval around the estimate where the convention allows. Drop the leading zero on correlation coefficients and other values that cannot exceed one.

For the full formatting of statistics, signs, and decimals, follow the APA conventions for results. Done well, the effect size is the sentence your committee remembers, because it is the one that says how much your finding actually matters.

The effect size you expect is the input that drives every power analysis, and it carries more weight than any other design decision. Because statistical power is the probability of detecting an effect of a stated magnitude, the required sample grows steeply as the expected effect shrinks: detecting d = 0.8 between two groups takes about 26 participants per group at 80% power, d = 0.5 takes about 64, and d = 0.2 needs nearly 400. That curve is why the value you assume should come from prior studies or a pilot rather than a hopeful guess, and why it pays to plan the sample your study needs before a single response is collected.

Two habits keep the relationship honest. First, resist post-hoc “observed power”, computed after the fact from the effect you happened to find: it is a direct restatement of the p-value and adds no new information, which is why reviewers increasingly reject it. The power argument only means something when it is made before the data exist, a logic our explainer on what statistical power actually buys you sets out in full. Second, report a confidence interval around d or g, because the interval is what communicates precision. A d of 0.6 spanning 0.1 to 1.1 says the study saw something but cannot pin down its size, while the same estimate spanning 0.45 to 0.75 supports a far stronger claim. The width of that interval, not the point estimate, tells the reader how much the study actually learned.