Qualitative Descriptors of Strength of Association and Effect Size

ABSTRACT Cohen's (1988) work in power analysis connects values of r and d(difference in means in standard deviation units) with the qualitative descriptors small, medium, and large. This paper discusses the pros and cons of using qualitative (nonmathematical) descriptors of strength of association and effect size in data interpretation. It proposes an extension of Cohen's classification scheme through the addition of a “very large” descriptive category. The paper presents advantages of the odds ratio for the analysis of categorical data, argues for increased use of the odds ratio, and develops qualitative descriptors of effect size for the odds ratio: about 1.5 to 1 = small effect (or weak association), about 2.5 to 1 = medium (or moderate), about 4 to 1 = large (or strong), about 10 to 1 = very large (or very strong). When percentages are between about 15 and 85, qualitative descriptors of effect size can be utilized for the difference in percentages: about 7 percentage points = small, about 18 points = medium, about 30 points = large, about 45 points = very large. Where treated as flexible guidelines rather than rigid rules and where sensitive to context and substantive area, qualitative description facilitates data interpretation and communication, particularly for the non-statistical audience: beginning students, administrators, practitioners.