Why are most of your flags false alarms?
Your screen catches 90 out of every 100 real cases. That number is P(flagged given present). What you actually want to know, when a flag lands on your desk, is P(present given flagged). With a condition that affects 1 person in 100, that second number is 10.2%. This template computes both from the same four counts, so the gap is impossible to miss.
Analytics Intermediate Statistics free
After you install, this is the model to open.
Bayes Flip: P(A|B) vs P(B|A)
- 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
Both conditional probabilities come out of the same 2x2 table, and they are nowhere near each other.
- Detection rate, P(flagged | present)
- 90.0 %
- Posterior, P(present | flagged)
- 10.2 %
- Flip gap
- 79.8 points
- False alarms per true catch
- 8.8 to 1
The screen is right about the people it should catch. 90% of real cases get flagged. But only 10.2% of the flags are real cases, because 792 of the 9,900 people without the condition get flagged too. That is 8.8 false alarms for every true catch, and it is a property of how rare the condition is, not a flaw in the screen. Raise the base rate to 8.2% and the very same screen becomes a coin toss.
The model
The default sheet screens 10,000 people for something that affects 1 in 100. The screen catches 90 of the 100 real cases, and it also fires on 8% of everyone who does not have the condition.
| Population screened | 10,000 |
| Base rate of the condition | 1% (100 people) |
| Detection rate (sensitivity) | 90% (90 of the 100 caught) |
| False-positive rate | 8% (792 of the 9,900) |
| Total flags raised | 882 |
| Real cases among those flags | 90 |
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: Statistics in Google Sheets.