Type M & Type S Errors

Errors of Magnitude and Sign in noisy studies

Not significant
Significant, correct sign
Type S error (wrong sign)
Type M error (|est| > 2× true)
Power
Type S Rate
among significant
Type M Rate
among significant
Exaggeration Ratio
median |est| / true

Type S Error Sign

When a statistically significant result has the wrong sign — concluding an effect is positive when it's actually negative (or vice versa). Most dangerous when true effects are small and noise is large.

Type M Error Magnitude

When a statistically significant result greatly exaggerates the true effect size. Publication bias amplifies this: only large, noisy estimates clear the significance threshold, inflating apparent effect sizes.