How Much More Likely? The Implications of Odds Ratios for Probabilities

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Abstract
Binary outcome data are common in research and evaluation. They are often analyzed using logistic regression, and results of these analyses are often reported in the form of odds ratios (ORs). However, ORs are not directly interpretable in the metric commonly used in policy-relevant discussions, which concerns probabilities. ORs are unfamiliar to nonresearchers, and their relationship to probability implications is not well understood by researchers. For example, the common practice of taking ORs as direct estimates of changes in probabilities (i.e., as risk ratios) systematically inflates effect sizes in probability terms. Fortunately, the probability implications of ORs can be derived simply and can be presented concretely as contrasting pairs of probabilities. These probability pairs are easily understandable by both the research and the lay audiences for evaluation results. After reviewing the relationship between probabilities, odds, and their ratios, this article shows how to explore ORs’ implications for probabilities, illustrating with recent examples from the literature.