Effect size

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article may require cleanup to meet Wikipedia's quality standards. The specific problem is: Math notation uses different symbols to represent the same quantities in similar formulas. Please help improve this article if you can. (May 2011) (Learn how and when to remove this message) This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (February 2014) (Learn how and when to remove this message) (Learn how and when to remove this message)

In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size value.^[1] Examples of effect sizes include the correlation between two variables,^[2] the regression coefficient in a regression, the mean difference, or the risk of a particular event (such as a heart attack) happening. Effect sizes complement statistical hypothesis testing, and play an important role in power analyses, sample size planning, and in meta-analyses. The cluster of data-analysis methods concerning effect sizes is referred to as estimation statistics.

Effect size is an essential component when evaluating the strength of a statistical claim, and it is the first item (magnitude) in the MAGIC criteria. The standard deviation of the effect size is of critical importance, since it indicates how much uncertainty is included in the measurement. A standard deviation that is too large will make the measurement nearly meaningless. In meta-analysis, where the purpose is to combine multiple effect sizes, the uncertainty in the effect size is used to weigh effect sizes, so that large studies are considered more important than small studies. The uncertainty in the effect size is calculated differently for each type of effect size, but generally only requires knowing the study's sample size (N), or the number of observations (n) in each group.

Reporting effect sizes or estimates thereof (effect estimate [EE], estimate of effect) is considered good practice when presenting empirical research findings in many fields.^[3][4] The reporting of effect sizes facilitates the interpretation of the importance of a research result, in contrast to its statistical significance.^[5] Effect sizes are particularly prominent in social science and in medical research (where size of treatment effect is important).

Effect sizes may be measured in relative or absolute terms. In relative effect sizes, two groups are directly compared with each other, as in odds ratios and relative risks. For absolute effect sizes, a larger absolute value always indicates a stronger effect. Many types of measurements can be expressed as either absolute or relative, and these can be used together because they convey different information. A prominent task force in the psychology research community made the following recommendation:

Always present effect sizes for primary outcomes...If the units of measurement are meaningful on a practical level (e.g., number of cigarettes smoked per day), then we usually prefer an unstandardized measure (regression coefficient or mean difference) to a standardized measure (r or d).^[3]