Score examples
Work through the logic of a score with synthetic numbers. These examples do not administer an instrument or evaluate a person.
A positive screen depends on prevalence
Original synthetic model
Imagine 1,000 people, a reference assessment and a hypothetical screener with 80% sensitivity and 90% specificity. These are invented teaching values, not the accuracy of a named instrument. Change prevalence while keeping accuracy fixed.
| Screen result | Reference: condition present | Reference: condition absent |
|---|---|---|
| Positive | 80 true positives | 90 false positives |
| Negative | 20 false negatives | 810 true negatives |
At 10% prevalence, 80 of 170 positive screens are true positives: about 47.1%.
Why does the meaning of a positive screen change?
At 1% prevalence, the same model gives 8 true positives and 99 false positives. At 50%, it gives 400 true positives and 50 false positives. A false-positive rate of 10% applies to very different numbers of people without the condition. Predictive value therefore differs even while sensitivity and specificity stay fixed.
This is a model with known inputs. Real accuracy estimates have uncertainty and depend on the reference assessment, threshold and sample. Read the PHQ-9 and GAD-7 profiles for examples of study-specific evidence.
Reverse the direction before combining responses
Original synthetic scale, not a published instrument
A fictional three-item scale uses responses from 1 to 5. Two items point toward the construct, while one points in the opposite direction. With responses 4, 2 and 5, reverse-keying the middle response gives 6 − 2 = 4. The correctly oriented mean is (4 + 4 + 5) ÷ 3 = 4.33; the uncorrected mean would be 3.67.
What does this calculation establish?
It aligns item direction. It does not establish that the items measure one construct, that a mean is the right summary or that 4.33 has a validated interpretation. Apply only the actual instrument’s key, including its missing-response rules.
A raw score needs a reference
Original synthetic example
A fictional task gives a raw total of 24. In reference group A, 18 of 100 people scored below 24. In group B, 62 of 100 did. The same raw total has a different position in each distribution. These counts illustrate the idea of rank; they are not normative tables or a formal percentile-conversion rule.
What information is still missing?
We need the reference sample, age range, administration, score distribution and handling of ties. A percentile is not percent correct or a probability that someone has a condition. A change of reference group is not evidence that the person changed.
Read about edition-specific reference data in WAIS-5 and Raven’s 2.
A task effect is different from a stable ranking
Original synthetic example
In session 1, four fictional participants have conflict costs of 60, 70, 80 and 90 milliseconds. In session 2, the costs are 90, 80, 70 and 60. The mean is 75 milliseconds both times, but the ranking reverses. A stable mean alone does not establish reliable individual differences.
How would you investigate reliability?
Estimate repeatability of the exact score under the intended conditions, with enough participants and trials. Inspect uncertainty, error rates, practice and score variance. These four invented observations demonstrate the distinction; they are not a reliability estimate or a description of a real study.
Compare Stroop, flanker and the reading guide.