The right base 2.0
About this app
Rebuild 2.0 (preview): the same risk as relative and absolute risk, natural frequency, odds and betting odds.
Six readings of one difference
When two groups differ in risk, p₀ and p₁, there are many correct measures. Relative risk RR = p₁/p₀ and the odds ratio OR = odds₁/odds₀ are ratios without a base. The absolute difference p₁ − p₀ and the number needed to treat, NNT = 1/|p₁ − p₀|, tell you how many people are affected. Odds are p/(1 − p), and betting odds are written “1 to x” with x = (1 − p)/p. For rare events OR ≈ RR. For common events the odds ratio exaggerates: 40 % versus 60 % gives RR 1.5 but OR 2.25.
What the app shows
You pick an example or set p₀ and p₁ yourself, and choose the base: 100, 1,000 or 10,000 people per group. The readings appear side by side, and ratios without a base are marked in red. The examples are sourced: bacon and bowel cancer from IARC Monograph 114, the 1995 UK pill warning (thrombosis risk from about 1 to 2 in 7,000 women per year), the Harding Center fact box on mammography screening (5 versus 4 in 1,000) and a constructed common event.
Switching the denominator
The “Right base” view holds two cases with the same numerator and a changing denominator. In the O. J. Simpson case, of 100,000 battered women about 45 are murdered per year, 40 of them by their partner. Divided by all 100,000 that gives 0.04 %; divided by the 45 murdered women it gives 89 %. For suicide, the share of all deaths falls with age, while the rate per 100,000 living people rises. Also watch at which base both groups round to the same number.
Frequently asked questions
- What is the number needed to treat (NNT)?
- The NNT tells you how many people need a treatment or test for one additional event to be prevented. It is the reciprocal of the absolute risk difference, NNT = 1/|p₁ − p₀|. If risk falls from 5 to 4 in 1,000, the NNT is 1,000. For harmful effects the measure is called NNH, number needed to harm.
- What is the difference between an odds ratio and relative risk?
- Relative risk divides two probabilities, while the odds ratio divides two odds p/(1 − p). For rare events the two are close. For common events the odds ratio is clearly larger than the relative risk and makes an effect look stronger.
- How are probability and betting odds related?
- Betting odds of “1 to x” mean that there are x misses for every hit. From a probability p you get x = (1 − p)/p, so p = 20 % gives “1 to 4”. The odds ratio, by contrast, is a ratio of two odds and not a betting quote.
- What is different in this version?
- Besides relative and absolute risk, the app shows NNT or NNH, odds, the odds ratio and betting odds. You choose a base from 100 to 10,000 people and see when a small difference disappears through rounding. Every example comes with a source.
Subject: Data & decisions
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