FoMind
You’ve just interviewed at a company you really like, and afterward you put your chances of an offer at about one in five. A few days later HR calls and asks, “How soon could you start?” Your pulse quickens. How much should this move your estimate? What matters isn’t whether it sounds like good news, but how well it distinguishes between “they’ll hire me” and “they won’t.”
What a likelihood ratio is
Likelihood ratio = the chance of seeing this evidence if the thing is true ÷ the chance of seeing it if the thing is false.
Suppose 60% of candidates who end up with an offer get asked about their start date, but so do 20% of those who don’t (HR sometimes asks in passing). The likelihood ratio is 60% ÷ 20% = 3.
- Greater than 1: the evidence favors “true” — the bigger, the stronger.
- Equal to 1: equally common either way, so it tells you nothing.
- Less than 1: the evidence favors “false.”
Updating with odds
Write the probability as odds — “true : false” — and updating becomes a single multiplication:
New odds = old odds × likelihood ratio
- Start at 20%, which is 1 : 4.
- Multiply by 3 to get 3 : 4, which converts back to 3 ÷ 7 ≈ 43%.
- Later HR also asks about your salary expectations. Say that evidence has a likelihood ratio of 2 and doesn’t overlap with the first: 3 : 4 becomes 6 : 4, or 60%.
Back to the screening test in 3.1: 90% sensitivity and a 9% false-positive rate give a likelihood ratio of 90% ÷ 9% = 10. A 1% prior is 1 : 99; times 10 gives 10 : 99, or about 9.2% — the same answer the 1,000-person grid gave.
This is where the interactive demo “Likelihood-ratio update chain” lives: in the FoMind app you can drag the controls and see results update live.
In the update chain below, add pieces of evidence one at a time and watch how the probability moves at each step.
Two common mistakes
- Treating “sounds relevant” as strong evidence. The interviewer was friendly? They’re friendly to everyone. The likelihood ratio is close to 1, so it should barely move you.
- Double counting. Three news articles quoting the same source are one piece of evidence, not three. Only independent pieces of evidence can be multiplied in a row.
The strength of evidence is its likelihood ratio — ask, “If I’m wrong, how likely would I be to see this anyway?”