Exercise 3: What Made the Mars Effect's Rescue "Ad Hoc" — Possible Solution
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The "eminence test" and "IMQ bias indicator" were introduced only
AFTER the original Mars effect claim failed to replicate cleanly under
independent testing. Crucially, these new constructs were tuned to fit
the specific data already in hand - they determined, after the fact,
which athletes should count as sufficiently "eminent" for the effect to
apply to, in a way that happened to preserve the original claim.

That order of operations is exactly what makes something an ad hoc
rescue rather than a legitimate refinement: the new criteria were
built to protect a specific conclusion the researchers were already
committed to, using the very data that was supposed to be a neutral
test of that conclusion. Critics correctly note this presupposes the
effect it's meant to be demonstrating - it doesn't provide independent
evidence of anything.

A legitimate methodological refinement would work the opposite way: a
researcher would need to specify the eminence criteria and any bias
adjustments IN ADVANCE, before looking at the new data, and then that
refined method would need to be tested again on a genuinely fresh,
independent dataset that had no role in shaping the criteria in the
first place. If the refined method still showed the effect on new
data collected under pre-registered rules, that would be real,
legitimate evidence - rather than a rescue invented specifically to
explain away one particular failure.

ANSWER: What made it ad hoc was that the new statistical criteria were
invented after the original claim failed replication, and were tuned
specifically to the existing data to preserve that original
conclusion. It would have been legitimate only if the criteria had
been specified in advance and then tested against a genuinely fresh,
independent dataset, rather than built backward from a result the
researchers already wanted to defend.

WHY THIS WORKS AS AN ANSWER
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This identifies the precise timing/independence problem (criteria
invented after seeing the failed result, tuned to that same data) that
distinguishes an ad hoc rescue from a real refinement, and states the
concrete condition (advance specification, independent fresh data)
that would make the difference.