For a ratio metric, the null value is one

Question

A study reports a 95% confidence interval for an odds ratio of $[1.05,\ 1.60]$ , comparing the odds of an outcome between two groups.

Decide whether this effect is significant at the 5% level, being careful about which value represents "no effect."

Accepted Answer

Find the null value. For a difference of means the "no effect" value is 0. But for a ratio metric, such as an odds ratio, a hazard ratio, or a relative risk, "no effect" means the two groups are equal, which is a ratio of 1, not 0. A ratio of 1 says the odds are identical in both groups. Apply the duality rule. The effect is significant at the 5% level if and only if the 95% interval excludes the null value. Here the null value is 1, and the interval [1.05,\ 1.60] lies entirely above 1. Since it excludes 1, the effect is significant at the 5% level. Common mistake. People trained on mean diff…

For a ratio metric, the null value is one

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