Exercise 2: A Worked Scenario Combining Small Sample Size and Publication Pressure — Possible Solution
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This exercise has no single correct scenario - the point is showing how
the two real factors compound. A worked example:

A graduate student runs a small study (say, 20 participants) testing
whether a brief motivational message improves task performance. With
only 20 participants, the study is genuinely underpowered - a real
effect that actually exists might easily fail to reach statistical
significance purely by chance, and conversely, ordinary random
variation in a small sample can sometimes produce a result that LOOKS
statistically significant even when no real effect is present at all.

Suppose, purely by chance, this small sample happens to show a large,
statistically significant improvement. The student, under real pressure
to publish a novel, positive finding rather than a null result, writes
up and submits this striking result. A journal, which is also more
likely to accept novel, significant findings over null ones, publishes
it.

No one else immediately attempts a larger, well-powered replication,
because replications are less rewarded professionally than new findings
(the same real cultural pattern the Open Science Collaboration
identified). The finding enters the literature and gets cited as
evidence the intervention works - even though it was, most likely, a
chance result from too small a sample that a properly powered study
would never have reproduced.

ANSWER: A small, underpowered study produces a result that appears
significant by chance; publication pressure favors publishing and
citing that novel, positive finding over a null result; and because
replications are professionally undervalued, no one promptly tests
whether the effect is genuinely real - allowing a likely-false finding
to persist in the literature, exactly the compounding pattern
Ioannidis's 2005 paper describes.

WHY THIS WORKS AS AN ANSWER
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This traces a concrete, plausible causal chain connecting both named
factors together, rather than treating them as two separate, unrelated
problems, matching how the chapter itself frames them as compounding.