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Abstract:
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Effect size has gained much attention in the past couple of decades as an important component of power analysis. Many journals in the areas of social science, psychology and education now require or recommend the report of the effect size of the associated hypothesis testing problem in addition to the popular p-value. However, there are still much confusion and misunderstanding among practitioners on effect size and its connection to other statistical concepts such as $p$-value, sample size, and power. In this work, we give a unified definition of effect size,which starts from the most general meaning of the effect of an factor,and becomes clearer through continuous specification of the context.Another particular problem is the interpretation of the magnitude of the measured effect size. While most researchers refer to Cohen's (1988)interpretation of large, medium and small effect sizes,it is widely agreed that such categorizations should depend on the area of research among other factors. In this work we propose a universal method for defining the magnitude of effect size for various kinds of hypothesis testing problems, yet keeping it flexible enough to suit researchers' need.
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