Your test came back positive. What are the odds it is real?
A screening test that is 90% accurate sounds nearly certain. But when the condition affects 1 in 1,000 people, a positive result is right just 0.89% of the time. This calculator rebuilds that famous result with plain head counts, then sweeps the base rate so you can see exactly when a positive is worth trusting.
Health Intermediate Data Table free
After you install, this is the model to open.
Positive Test, Real Risk
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
The answer
Run the data table and Sortia sweeps the base rate from 0.1% to 50%, reporting the real probability of a true positive and the false alarms per real case at every level.
- Chance a positive is real
- 0.89 %
- False alarms per real case
- 111 to 1
- Base rate for a coin-flip positive
- 10 %
- Flagged per 10,000 screened
- 1,008 people
At a 1-in-1,000 base rate, a positive from a 90% accurate screen is real just 0.89% of the time. Screening 10,000 people flags 1,008 of them, yet only 9 truly have the condition, which is 111 false alarms for every real case. The sweep shows the flip point: the base rate must reach 10% before a positive is even a coin flip, and the test only delivers its advertised 90% when half the population already has the condition.
The model
Three rates and one population size rebuild Bayes' rule as a head count per 10,000 people screened.
| Base rate (prevalence) | 0.10% (1 in 1,000) |
| True-positive rate (sensitivity) | 90% |
| False-positive rate | 10% |
| People screened | 10,000 |
| Base rates tested | 0.1% to 50% (7 scenarios) |
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
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Every model like this one, and the method behind them: What-if analysis in Google Sheets.