The short answer
A changed outcome can reflect a changed condition, changed participants or both. An original small ledger makes those possibilities visible without pretending to reproduce a confidential historical dataset.
Record comparison
Different observations identify different contrasts
Keep the historical record distinct from the stipulated model.
| Question | Record or stipulated input | Consequence and limit |
|---|---|---|
| Pooled | Four observations in each condition | Different people enter the two groups. |
| Paired | A and B only | The same people appear under both conditions. |
| Causal interpretation | Neither contrast gets randomisation for free | Time-varying explanations remain possible. |
Chronology
A timeline of the turning points
Joint study
The selected audition paper appeared.
The selected identification problem
Goldin and Rouseโs paper uses person-round observations and examines candidates appearing under screened and unscreened conditions. Its individual fixed-effects comparison aims to account for time-invariant differences between people; estimates vary across rounds and samples.
The relevant question is which observations actually identify a within-person comparison. A large pooled total need not supply the same information as a smaller repeated-person sample, and a repeated-person contrast does not eliminate every time-varying influence.
Sources for this section: [1]
A fully invented ledger
Let 0 mean no advancement and 1 mean advancement. Candidate A has open 0 and screened 1. Candidate B has open 1 and screened 1. Candidates C and D have only open observations, each 1. Candidates E and F have only screened observations, each 0. There are eight person-round observations from six people.
First calculate each conditionโs pooled success rate. Then calculate the mean screened-minus-open change using only the two paired candidates. Which people supply the paired comparison, and which people change only the pooled composition?
Sources for this section: [1]
Two correct calculations with different answers
Open outcomes are 0, 1, 1, 1, giving 3/4=0.75. Screened outcomes are 1, 1, 0, 0, giving 2/4=0.50. The pooled screened-minus-open contrast is โ0.25.
For the paired candidates, A changes by +1 and B by 0; their mean change is +0.50. C, D, E and F do not identify this within-person contrast. Their inclusion changes the pooled groupsโ composition enough to reverse the sign. These are different estimands, not an arithmetic contradiction.
Sources for this section: [1]
What neither number proves
The fixture has no random assignment, uncertainty calculation or assurance that candidatesโ ability remains constant. The paired result could still reflect practice, changing repertoire or an unmeasured time-related influence.
The historical method motivates asking who is compared with whom. The invented answer illustrates composition rather than establishing a universal effect of screening, reproducing the paperโs estimates or judging any real orchestraโs conduct.
Sources for this section: [1]
Continue the chronology
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The working life behind the record
Quick answers
Common questions
- Are the eight outcomes historical audition records?
- No. They are invented for this study.
- Does a within-person comparison remove every possible confounder?
- No. It can account for fixed differences while leaving time-varying differences unresolved.
Primary and institutional sources
How this history was checked
Selected records support the historical discussion. Invented inputs and original answers are labelled; no complete uninspected work is claimed. This article was reviewed on 31 October 2026.