Effect size: the number your p-value forgot
“Statistically significant” is where too many results stop — and it’s the least interesting thing you can say about a finding. The question that matters more, and gets asked less, is simply: how big is it?
Significant is not the same as large
The single most useful habit in reading statistics is to separate two questions that the word “significant” blurs together: is there an effect? and how big is it? A p-value speaks to the first. An effect size speaks to the second — and for most real decisions, the second is what actually matters.
Why you can’t skip it
With a large enough sample, almost any difference becomes statistically significant, no matter how trivial. A weight-loss program that reliably takes off 200 grams will show p < 0.001 in a big enough trial — statistically certain, practically pointless. Without an effect size, “significant” can mean “real but negligible” just as easily as “real and important,” and your reader has no way to tell which.
Statistical significance tells you an effect probably exists. Effect size tells you whether it’s worth caring about.
The common measures
- Cohen’s d — the gap between two means, in standard-deviation units. Roughly: 0.2 is small, 0.5 medium, 0.8 large.
- Correlation (r) — the strength of a relationship, from 0 to 1. It doubles as its own effect size.
- Eta-squared (η²) — in ANOVA, the share of variance explained by the grouping.
- Odds ratio / risk ratio — how much more likely an outcome is in one group than another.
The labels “small / medium / large” are conventions, not verdicts — a “small” effect on a matter of life and death can be enormously important, and a “large” one on a trivial outcome may not be.
Report it with a confidence interval
An effect size is a single best estimate; a confidence interval around it shows how precisely you’ve measured it. “d = 0.5, 95% CI [0.1, 0.9]” is honest in a way a bare p-value never is: it states the size, and it admits the uncertainty. This pairing — estimate plus interval — is what modern reporting guidelines and APA style ask for.
The number that travels
Effect sizes are also what let findings accumulate. Because they’re standardised, they can be compared across studies and combined in meta-analyses — something raw p-values can never do. When you report an effect size, you’re not just describing your result; you’re contributing a number other researchers can actually use. thericerca reports one for every test it runs, right beside the p-value — because a result without a magnitude is only half a finding.
The habit worth keeping. Never report significance alone. State what was found, how big it was, and how uncertain you are — p-value, effect size, and confidence interval together. That trio is the difference between a number and an insight.