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Math / Statistics / Grade 7 / mt7e2

More Catches, More False Alarms

Use two fractions to explain a tradeoff between review rules.

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Watch the lesson | Compare the first checked batch

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Learn the skill

First identify all checked errors and all checked flags. The fraction of errors caught uses all errors as its denominator. The fraction of flags that identify errors uses all flags as its denominator. Include missed errors in the first denominator and false alarms in the second. Compare the same checked batch. A larger catch fraction need not mean a larger correct fraction among flags. Unknown checks stay unresolved. Do not claim that one invented batch predicts future performance.

Worked example

In a separate checked batch, a rule flags 3 errors, misses 3 errors, and flags 2 correct records. It catches 3/6 of the errors. Its 5 flags contain 3 errors, so 3/5 of the flags identify errors. A fraction must name the group it describes.

Worked example shows 3 caught and 3 missed errors, and 3 error flags with 2 false alarms. Three sixths of errors are caught; three fifths of flags identify errors.
Same numerator, different groups: read the denominator before comparing.

Checked batch

An invented batch has 30 independently checked records: 6 errors and 24 correct records. Rule C flags 4 errors and 4 correct records. Rule D flags all 6 errors and 12 correct records. A different set of 4 flagged records lacks independent checks and is NOT included in this checked batch.

Question 1 What fraction of the 6 checked errors does C catch?
Question 2 What fraction of C's checked flags identify errors?
Question 3 Compared with C, what happens under D on this batch?
Question 4 What can we conclude about the different set of 4 unchecked flags?
Question 5 D catches all 6 errors here. Does that prove it will never miss an error?