Why a small trial can make an effect look bigger than it is
A trial is "underpowered" when it enrolls too few people to reliably detect the effect it is looking for. That sounds like a simple shortage of data, but it has a subtler consequence: in a small sample, results bounce around more, and the trials that happen to land on a large positive effect are the ones most likely to get published and noticed. The average of what you read can therefore drift upward, away from the true effect.
The exercise-and-cognition literature shows exactly this kind of fragility. A reply in the debate over exercise and cognitive benefits lists underpowered designs alongside salami slicing (splitting one study into several publications), regression toward the mean, placebo-like effects, selective reporting, and publication bias as critical problems that undercut confident claims of benefit [2]. These are not minor bookkeeping issues; each one can push reported effects in the same optimistic direction.
The trials themselves admit they were too small
Several individual trials in this area openly describe themselves as underpowered, which shows how common the problem is. A randomized trial of lifestyle changes, including exercise, in older adults with cognitive impairments notes that it may have been underpowered to detect differences between exercise and comparison groups [4]. A trial of exergaming (exercise combined with video-game play) in people with dementia reports that, despite being underpowered, it found positive effects on secondary cognitive and social outcomes [5].
That last example is instructive. A small trial reporting positive effects is not proof of inflation, but it is precisely the pattern that makes inflation hard to rule out: a modest sample produces encouraging results, and the caveat about low power travels with it. A meta-analysis of exercise training in older adults with mild cognitive impairment likewise flags low statistical power among the trials it pooled [1], and a study of exercise dose and cognitive function in older adults describes itself as underpowered to detect the effects it examined [3].
How confident can we be that exercise helps cognition at all?
The uncertainty runs deeper than sample size. The same critical reply points out that most of the evidence on physical activity and cognitive function was rated as low or very low certainty in the scientific report underpinning World Health Organization guidelines, meaning the true effect may be substantially different from the estimated one [2]. For adults, six systematic reviews were rated low or very low certainty, with one moderate-certainty review finding no significant effect once active control groups were considered [2].
This matters for the original question because it changes what "overestimation" would even mean. If the underlying benefit is small or uncertain, then inflated estimates from small trials are not a peripheral worry but a central explanation for why the literature looks more encouraging than the certainty ratings suggest. Still, none of these papers ran the head-to-head comparison of underpowered versus adequately powered trials, so the size of any inflation remains unmeasured here [1][2].
What would actually answer the question
To know whether underpowered trials overestimate benefits, you would need to compare effect sizes from trials grouped by their statistical power, ideally while accounting for publication bias and selective reporting. The papers here establish the ingredients for that analysis, namely widespread underpowering and a cluster of inflating biases, but they stop short of performing it [1][2].
For a reader trying to weigh claims about exercise and cognition, the practical takeaway is to treat small positive trials with calibrated skepticism and to look for whether a result held up in a larger trial or in a review that checked for these biases. The concern about underpowered trials is well grounded; the specific magnitude of the overestimate is still an open question.
Sources used in this answer
The effect of exercise training on cognitive function in older adults with mild cognitive impairment: a meta-analysis of randomized controlled trials
This meta-analysis of exercise training in older adults with mild cognitive impairment highlights low statistical power in the included trials but does not test whether underpowered trials overestimate benefits.
Reply to: Do not underestimate the cognitive benefits of exercise
This reply argues that the exercise-and-cognition literature suffers from underpowered designs, salami slicing, regression toward the mean, placebo-like effects, selective reporting, and publication bias, and notes that most relevant evidence was rated low or very low certainty.
Is there a dose-response relationship between exercise and cognitive function in older adults?
This study of exercise dose and cognitive function in older adults reports that it was underpowered to detect the effects it examined.
Lifestyle and neurocognition in older adults with cognitive impairments: a randomized trial
This randomized trial of lifestyle modification in older adults with cognitive impairments acknowledges it may have been underpowered to detect differences between exercise and comparison groups.
Effects of exergaming on cognitive and social functioning of people with dementia: a randomized controlled trial
This randomized trial of exergaming in people with dementia reports that, despite being underpowered, it found positive effects on secondary cognitive and social outcomes.