P-Value and Confidence Interval Explained for Research Results
Understand what p-values and confidence intervals can and cannot tell you, and how to report statistical results without overstating them.
A p-value is calculated under a statistical model
A p-value describes how compatible the observed data are with a specified null hypothesis under the assumptions of the test. It is not the probability that the null hypothesis is true. A small p-value may indicate evidence against the null model, but it does not tell you whether the effect is large, important or free from bias.
The significance threshold is a convention
Researchers often compare p-values with 0.05, but the boundary is not a natural dividing line between truth and falsehood. Results just above and just below a threshold can represent very similar evidence. Report the exact p-value where appropriate and interpret it together with effect size, confidence interval, design and prior evidence.
Confidence intervals show a range of plausible values
A confidence interval provides information about the precision of an estimate under repeated-sampling assumptions. Narrow intervals indicate greater precision than wide intervals. The interval can also show whether effects that are clinically or practically important remain plausible even when a conventional significance test is inconclusive.
Effect size gives the result scale
Means, differences, odds ratios, risk ratios, correlations and regression coefficients express the magnitude and direction of findings. Report these alongside confidence intervals. A statistically significant effect that is too small to matter should not be presented as a major finding solely because the p-value is below a threshold.
Sample size influences both statistics
Large samples can detect very small differences, while small samples may produce wide intervals and unstable estimates. This is why “not statistically significant” does not automatically mean “no effect.” Examine whether the interval includes effects that would be practically meaningful and whether the study had adequate precision.
Use cautious language in conclusions
Statistical results should be interpreted in the context of bias, measurement, missing data and study design. Avoid phrases such as “proved,” “no relationship exists” or “the hypothesis is true.” A stronger conclusion states what was estimated, how precise it was and what limitations affect confidence in the result.