Check what a flag really tells you
See this course’s project requirements
Audit the supplied fictional claim about a reminder app using sampling, summary, conditional-rate, uncertainty, and causal-reasoning tools.
Keep your working files in your own notebook or software. Save a private description, checklist, and work link in My Proof.
What to include
- Identify the claim, population, sample, unit of observation, and sampling limits.
- Calculate and compare mean, median, absolute change, and relative change where appropriate.
- Use a natural-frequency table to compute a conditional percentage with the correct denominator.
- Interpret a supplied confidence interval without treating it as individual variation or certainty.
- Write a claim verdict that separates supported description from unsupported causation and names needed evidence.
Review and revise
Use these criteria to check your work and choose what to improve.
- Calculation: quantities and denominators are correct and reproducible.
- Scope: sample and population claims are distinguished.
- Uncertainty: intervals and study limits are explained accurately.
- Judgment: the conclusion is proportional to the evidence and identifies a useful next question.
Want more background?
The idea in everyday life
A detection system can find most actual problems while still producing many false alarms when problems are uncommon. Understanding that apparent contradiction requires counting the relevant subgroups. This lesson uses fictional incomplete-file screening rather than a medical test. You will calculate both detection among incomplete files and the share of flags that are truly incomplete.
Among flagged cases is a different denominator from among actual cases.
One step at a time.
Use the sample or information you have permission to use. Keep your work as you go. You can pause between steps.
- 1
Build a two-by-two table with actual incomplete/complete as rows and flagged/not flagged as columns. Enter all four supplied counts and check row and column totals.
- 2
Compute the base rate as actual incomplete files divided by all files. State what was known about the population before using the checker’s flag.
- 3
Compute detection among incomplete files using 18 divided by 20. Then compute the share of flagged files that are incomplete using 18 divided by 116.
- 4
Explain why the denominators differ and why the two percentages answer different questions. Use the natural counts in your explanation rather than relying only on probability notation.
- 5
Write a decision note treating a flag as a reason to review the file, not proof of incompleteness. Save the table, calculations, and denominator explanation for the final statistical audit.
See how it works.
Fictional scenario: Among 1,000 files, 20 are actually incomplete and 980 are complete. A checker flags 18 incomplete files and 98 complete files. It misses two incomplete files and correctly leaves 882 complete files unflagged. The checker detects 18/20 = 90% of incomplete files. However, only 18 of 116 total flags are truly incomplete, about 15.5%. Taylor sees why “90% detection” does not mean a flagged file has a 90% chance of being incomplete in this population. The low two-percent base rate and false flags both matter.
Did you cover these?
- The four cells total 1,000 files.
- There are 116 flagged files in total.
- 18/116 is approximately 15.5%, distinct from 90% detection.
What to finish
A natural-frequency table with base rate, detection rate, and proportion of true problems among flags.
Watch for this
Reversing a conditional percentage by using detection among actual problems as accuracy among flags.
How can I tell I understand it?
You select the denominator that matches the question and explain why a high detection rate can coexist with many false flags.
Quick knowledge check
Answer all 3 questions. Get at least 2 right and the lesson completes automatically.
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Pass the check. We’ll save the progress.
Answer all 3 questions above and get at least 2 right. You can review the explanations and try again.
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Sources and further reading
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Source & access notes · checked 2026-09-10
Opened contingency-table and conditional-probability discussion. The incomplete-file example is an original natural-frequency table.
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