TL;DR
The p-value tells you whether there's likely an effect; the effect size tells you how big it is, and the confidence interval tells you how precisely you've measured it. Journals increasingly require both alongside p. Always report the effect with its CI.
Reporting the effect size with its 95% confidence interval (not just the p-value) is the single highest-leverage habit in your whole results section.
Effect size: how big is the difference?
An effect size is a number that quantifies the magnitude of a result on a meaningful scale.
- Raw/absolute effect: the difference in means in real units, such as "treated cells were 23 µm larger on average." Often the most interpretable for biology, because it's in units your reader understands.
- Standardized effect (Cohen's d): the difference in means divided by the pooled standard deviation. Useful for comparing across studies or when units aren't intuitive. Rough conventions: ~0.2 small, ~0.5 medium, ~0.8 large, but these are generic, not biology-specific; interpret in context.
- Correlation/association: r (or r², the proportion of variance explained) for continuous relationships → correlation and regression.
- Categorical: odds ratio, risk ratio, or risk difference → categorical data.
Report the effect in the units a biologist cares about whenever you can. "A 1.8-fold increase (95% CI 1.3–2.5)" communicates far more than "p = 0.002."
Confidence intervals: how precise is the estimate?
A 95% confidence interval is a range of plausible values for the true effect, computed so that, across many repeated studies, about 95% of such intervals would contain the true value.
Practical reading:
- A narrow CI means a precise estimate (usually larger n, less variability).
- A wide CI means a lot of uncertainty, common with small samples. A "significant" result with a CI spanning from "trivial" to "huge" is weak evidence about the effect's size.
- If a CI for a difference includes 0 (or a CI for a ratio includes 1), the result is not significant at that level. The CI and the p-value are two views of the same information, but the CI also shows magnitude.
Hold the effect size fixed and shrink the sample size: the same estimate flips from significant to not as its interval widens past the "no effect" line.
Every bar has the same point estimate (1.2); only precision differs. As n grows the interval narrows. When it stops crossing the "no effect" line the result becomes significant: same effect, different certainty.
A biology example
Two studies both report p = 0.04 for a drug lowering tumor volume.
- Study A: mean reduction 30%, 95% CI 25%–35%. Precise, clearly meaningful.
- Study B: mean reduction 30%, 95% CI 2%–58%. Same point estimate, same p, but the true effect could be trivial or enormous: much weaker evidence.
The p-values are identical; the confidence intervals tell you these are very different results. This is why "report the CI" is the single highest-leverage habit in this whole library.
How to get them
- R:
t.test(...)prints the difference and its 95% CI directly;effsize::cohen.d(x, y)for Cohen's d;confint(model)for regression coefficients. - GraphPad Prism: check "Report CI of the difference" in the t-test/ANOVA options; Prism shows effect sizes in newer versions.
- Python:
pingouin.ttest(x, y)returns Cohen's d and CI;statsmodelsgivesconf_int()for model coefficients.
Common mistakes
- Reporting p without effect size or CI. The most common reviewer complaint after "wrong test."
- Confusing a CI with an SD or SEM error bar. They answer different questions → error bars.
- Reading "95% CI" as "95% probability the true value is in this exact interval." The strictly correct framing is about the procedure across repeated studies; in practice people use it as a plausible range, which is fine for interpretation but worth knowing.
- Treating a non-significant result as "no effect" when the CI is wide enough to include large effects: that's an underpowered study, not a negative result.