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Effect Size Input

Guide: Understanding Effect Size

Effect size measures the practical (or clinical) significance of a result — how large the difference between groups actually is, independent of sample size. A p-value only tells you whether a difference exists; effect size tells you how meaningful that difference is.

A study with a very large sample can find a statistically significant result (p < 0.05) for a tiny, practically useless difference. Effect size prevents this misinterpretation.

Cohen's d is the most widely used effect size measure for comparing two group means. It expresses the difference in means as a number of standard deviations:

d = (M₁ − M₂) / SDpooled

A Cohen's d of 0.5 means the groups differ by half a standard deviation. A d of 1.0 means they differ by one full standard deviation — a large and clearly noticeable effect.

Hedge's g is a corrected version of Cohen's d that accounts for the slight overestimation of effect size in small samples. It applies a correction factor that becomes negligible once n per group exceeds ~20.

As a rule of thumb: use Hedge's g when your sample sizes are small (<20 per group), and Cohen's d when they are larger. Both values are reported by this calculator.

  • Two-sample: Two different, independent groups — e.g. control vs treatment, men vs women
  • One-sample: One sample compared to a known population mean — e.g. testing whether your class's average differs from the national average
  • Paired: The same subjects measured twice — e.g. before/after intervention, matched pairs

The overlap visualisation shows two normal distributions with the same standard deviation, separated by the Cohen's d effect size you calculated. A larger d produces less overlap between the distributions — a clearer separation between groups.

At d = 0, the distributions are identical (100% overlap). At d = 2, only ~16% of values from one distribution overlap with the other. This is a powerful way to communicate effect sizes to non-statisticians.

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