Counting and radical expressions

Book Isle proofreading ratios: distinguish recall, precision and false-positive rate

Use an invented thousand-position ledger to keep denominators distinct rather than equating error coverage with correct flags.

English translation of the Chinese original, translated on . Original publication dates, attribution, code and version notes are retained.

“Found ninety percent of the errors” is not “ninety percent of flags are correct.” Read a self-made proofreading description in Book Isle and manually calculate three ratios with explicit denominators. Use the app for reading, returning to a location and available notes. Ground-truth errors and flags are invented exercise conditions, not automatic proofreading or evaluation features.

1. Fix the fictional objects and counting unit

Prepare an original readable exercise stating that there are one thousand numbered character positions, each judged once as error or not. Use an existing trusted authoring tool, or keep an external ledger beside a readable exercise passage; do not assume Book Isle generates a thousand rows. Record filename, edition, chapter and a phrase anchor. A position is not a sentence, note or distinct vocabulary item. Exclude multi-position and multiple-error complications from this sample and do not turn someone else’s work into an unauthorized evaluation. Fix the unit before adding counts.

2. List error positions and flagged positions separately

Positions one through ten are declared errors; the other 990 are correct. Flag positions one through nine and 100 through 198. These are invented author-supplied ground truth and flags, not app judgements. Count inclusive intervals: 100–198 contains 99 positions. Compare membership before calculating percentages. Remove duplicate records of the same position, but do not merge identical characters occupying different positions.

All positions: 1..1000
Actual errors: 1..10
Flagged positions: 1..9 and 100..198

3. Rebuild four cells before the totals

The intersection contains nine true errors correctly flagged. Error position ten is one miss. The 99 flagged correct positions are false positives, leaving 891 correct unflagged positions. Label the four cells with both conditions. Check errors as 9+1=10, correct positions as 99+891=990, and all four as 1000. Flags total 108; unflagged positions total 892. For a mismatch, return to position membership instead of adjusting rounded percentages to conceal a missing item.

4. State each question before dividing

Using the denominator definitions in Google’s classification metrics guide, recall asks how many actual errors were found: 9/10=90%. Precision asks how many flagged positions are real errors: 9/108=1/12, approximately 8.33%. False-positive rate asks how many correct positions were wrongly flagged: 99/990=10%. Keep the original fraction and object beside each result. Do not silently replace the second denominator, 108, with ten. These are definitions applied to invented data, not measured Book Isle proofreading performance. Do not call all three an unspecified correctness rate.

5. Use full sentences to prevent denominator reversal

Write three complete statements: nine of ten actual errors found; nine of 108 flags are real errors; 99 of 990 correct positions wrongly flagged. Add percentages afterward. Cover the numbers and identify each denominator from the sentence. High recall and low precision coexist in this example; no false positives need to be deleted to make the results agree. If an author only says ninety percent hits without defining the object, mark the meaning unresolved and consult context. Keep quotations separate from your supplied interpretation.

6. Do not force zero-denominator cases into scores

Save a control retaining ten errors but flagging nothing. Recall is 0/10=0, while precision is 0/0 and is not directly defined by this formula. Do not fill zero or 100% without an explicit extra convention. A separate no-error sample gives recall a zero denominator too. Keep both controls separate from the original thousand-position result. If software or a textbook supplies a convention, identify it as that convention rather than a value derived from division itself. Otherwise retain an undefined or not-applicable status.

7. Troubleshoot endpoints and rounding

A flag total of 107 calls for checking inclusive endpoints. A false-positive rate of 99% calls for checking whether 100 was wrongly used as the denominator. Turning 9/108 into 90% requires returning to the fraction, not reverse-engineering the desired conclusion. Retain 1/12 until final rounding to approximately 8.33%. For unsearchable position references, return through chapter and phrase with an external ledger rather than deleting and reimporting a book to fix arithmetic. Open exported notes and check cell conditions, denominator objects and approximation wording, not merely the presence of a title.

8. Finish by returning to the original definitions

Exit and return to the same exercise edition. Rebuild the four cells without the answer and explain why the first two numerators of nine yield different ratios and why the third numerator is 99. Save identity, counting unit, cells, denominators, full interpretations and zero-denominator boundaries. Another reader should recount the thousand positions and obtain 90%, approximately 8.33% and 10%. Completion is traceable arithmetic, not a verdict on a real system or invented app marketing data. Rebuild the table if a later passage counts words, sentences or books rather than character positions.

Exclusive and independent events, Bases for relative change.

Checked on November 11, 2026 against the official Book Isle App Store listing and Apple public lookup: Book Isle 1.1.4, requiring iOS / iPadOS 15.6 or later. Use existing reading, available notes or external records and verify controls in your installed version. Original samples and manual calculations are not new automatic analysis features. No physical-device, private-file or universal export-environment testing is claimed.