Effect Size

Effect size is any of a family of standardized measures quantifying the magnitude of a phenomenon, a difference between group means, the strength of a relationship, or the size of an association, independent of sample size, in contrast to a p-value, which conflates effect magnitude with sample size and is not itself a measure of practical importance. Different families of effect size measures suit different data structures: standardized mean differences (Cohen's d, Hedges' g, Glass's delta) for comparing two group means, variance-explained measures (eta squared, partial eta squared, omega squared) for ANOVA designs, and association measures (phi coefficient, Cramer's V) for categorical data. Reporting effect size alongside a p-value is now standard practice in most fields, since it allows readers to judge practical significance and enables meta-analyses to combine results across studies measured on different scales.

• Effect size and statistical significance are logically independent, a very small, practically unimportant effect can be statistically significant with a large enough sample, while a genuinely large effect can fail to reach significance with a small sample, this is the central reason effect size reporting has become standard alongside p-values.
• Effect size measures are the fundamental input to meta-analysis, which combines results across multiple studies that may have used different sample sizes, measurement scales, or even different specific tests, a standardized effect size (like Cohen's d) puts these disparate results on a common, combinable scale in a way raw p-values or unstandardized differences cannot.
• Conventional benchmarks for 'small,' 'medium,' and 'large' effect sizes, originally proposed by Jacob Cohen for measures like Cohen's d and eta squared, are widely used but are explicitly rules of thumb rather than universal truths, what counts as a practically important effect size genuinely depends on the specific field and research question.