Odds Ratio

Step 1: Calculate the Probabilities

For each group, calculate two probabilities: probability of outcome occurrence and outcome nonoccurrence. Outcome occurrence represents the number of times a desired outcome, for example, low anxiety in public speaking, happens within a sample. Outcome nonoccurrence represents the number of times an outcome does not happen within a sample. These numbers are complementary; occurrence outcomes plus nonoccurrence outcomes must equal total outcomes. In addition, occurrence and nonoccurrence outcomes must be mutually exclusive, meaning that each recorded outcome fits in one, and only one, category, preventing double counting and/or data omission.

Probability and odds represent two different, but related, statistics. Generally speaking, probability (P) indicates the number (n) of occurrence (1) or nonoccurrence (2), as a percentage of total occurrences, denoted as a number between, or equal to, 0 and 1. Greater numbers reflect greater chances of a given outcome. Mathematically, the following formulas reflect probability calculations and a check figure.

$$\begin{array}{l}\mathrm{Probability}\mathrm{(}P\mathrm{)}\mathrm{of}\mathrm{occurrence}(1)\mathrm{:}{P}_1=\frac{n_1}{n}.\\ \mathrm{Probability}\mathrm{(}P\mathrm{)}\mathrm{of}\mathrm{nonoccurrence}(2)\mathrm{:}{P}_2=\frac{n_2}{n}.\\ \mathrm{Check:}{n}_1+n_2=n.\end{array}$$

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