Probability is the chance of something happening out of all outcomes. Odds are the ratio of it happening to it not happening.
Probability is the chance of something happening out of all outcomes. Odds are the ratio of it happening to it not happening. They are close when an outcome is rare and diverge sharply when it is common, which is where misreading begins.
An odds ratio compares the odds in one group with the odds in another. A value of one means no difference; above one means higher odds in the first group. It is a relative measure and carries no information about absolute frequency.
Where an outcome occurs frequently, an odds ratio is further from one than the corresponding risk ratio. Reporting an odds ratio as though it were a risk ratio therefore exaggerates, and this substitution is extremely common in secondary coverage.
Odds ratios come out of the standard regression used for yes-or-no outcomes, and they can be estimated from case-control data where risk ratios cannot. The prevalence of the measure reflects statistical convenience rather than interpretability.
A doubling of odds means very different things starting from one in a million and one in ten. Without the baseline, a ratio cannot be translated into anything a reader can act on, and the baseline is frequently omitted.
An adjusted odds ratio is conditional on the variables included. Adding or removing a variable changes it, sometimes substantially, so the figure belongs with the model specification rather than alone.
Ratios are analysed on a logarithmic scale, so the interval does not sit evenly around the estimate. Reading the midpoint of the two endpoints as the estimate is a specific and common error.
The baseline rate, the absolute difference, and whether the number quoted is odds or risk. All three are usually in the paper and seldom in the summary.
An odds ratio can be converted to a risk ratio if the outcome rate in the comparison group is known, and that figure is usually available in the same table. Doing the conversion takes a moment and frequently halves an impressive-looking number, which is why the unconverted figure survives into summaries.
Case-control studies that matched participants on age or sex must analyse them as matched pairs. Ignoring the matching biases the estimate toward no effect, and analysing unmatched data as matched does the opposite. The methods should state which was done, and the two are not interchangeable.
The claims on this page about the most commonly misread number in observational research can be checked against sources outside this site: