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How many negative trials could have missed a real effect

Freiman and colleagues re-examined 71 randomised trials reported as showing no difference

Bar chart of 71 trials reported as negative: 67 risked missing a 25% improvement, and in 34 the data still allowed a 50% improvement.
No significant difference is not the same as no difference Source: Freiman, Chalmers, Smith and Kuebler, New England Journal of Medicine, 1978

A bar chart of Freiman, Chalmers, Smith and Kuebler's 1978 re-analysis of 71 randomised trials that had been reported as negative. 67 of them had more than a 10 percent risk of missing a real 25 percent improvement, and in 34 the 90 percent confidence interval still allowed the treatment to be 50 percent better. Use it to explain why a non-significant result cannot justify a no-difference decision. Equivalence testing needs larger samples, which AI-moderated studies in Koji make cheaper to collect.

Where this appears

What's in this bar chart

Trials
Over 10% risk of missing a 25% gain67
Over 10% risk of missing a 50% gain50
90% CI still allowed a 25% gain57
90% CI still allowed a 50% gain34

Every one of the 71 trials had been reported as negative.

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<a href="https://www.koji.so/visuals/negative-trials-underpowered-freiman-1978"><img src="https://www.koji.so/visuals/negative-trials-underpowered-freiman-1978/negative-trials-underpowered-freiman-1978.png" alt="Bar chart of 71 trials reported as negative: 67 risked missing a 25% improvement, and in 34 the data still allowed a 50% improvement." width="1200" height="630" /></a>
<p>Source: <a href="https://www.koji.so/visuals/negative-trials-underpowered-freiman-1978">How many negative trials could have missed a real effect</a>, Koji</p>