How do I report statistics in a paper?

TL;DR

A reader should be able to tell exactly what you did and what you found without guessing. For each analysis, state the test, what your n represents, the effect size with a confidence interval, and the exact p-value. Describe the analysis plan in the methods; report the numbers in the results; label every figure's error bars and n.

What every analysis should report

For each comparison, give:

The test used and why, including paired vs. unpaired, one- vs. two-sided, and any correction. "Welch's two-sample t-test (two-sided)."
What n is: the number of independent units, stated explicitly (animals? experiments? patients?) → replicates and pseudoreplication.
The effect size with a 95% CI: the difference, ratio, HR, OR, or r, in interpretable units → effect size and confidence intervals.
The exact p-value (e.g., "p = 0.013"), not just "p < 0.05," and report non-significant p-values too, rather than "NS."
The test statistic and degrees of freedom where conventional (t, F, χ², with df).

Report, for every comparison

The test, and whyPaired vs. unpaired, one- vs. two-sided, and any correction.
What n isThe number of independent units — animals, experiments, or patients.
Effect size with a 95% CIThe difference, ratio, HR, OR, or r in interpretable units.
The exact p-value“p = 0.013”, not “p < 0.05” — and report non-significant p’s too.
Test statistic and dft, F, or χ² with degrees of freedom, where conventional.

A reporting template

"Tumor volume was compared between treated (n = 8 mice) and control (n = 8 mice) groups using a two-sided Welch's t-test. Treated mice had smaller tumors (mean difference 142 mm³, 95% CI 60–224 mm³; t(13.2) = 3.6, p = 0.003)."

For ANOVA: report the omnibus result and the specific post-hoc comparisons with their corrected p-values. For regression: report coefficients with CIs. For survival: KM curves, log-rank p, and a hazard ratio with CI. For categorical: counts, a risk/odds ratio with CI, and the test (chi-square or Fisher's).

The methods section

State, ideally as if pre-specified:

The primary outcome and primary comparison.
The software and version (e.g., R 4.x, package names; or GraphPad Prism version).
How n was determined (a sample-size/power justification) → power and sample size.
Assumption checks and what you did if they failed (transform, non-parametric, robust test) → checking assumptions.
Any multiple-comparison correction and which method → multiple comparisons.
Outlier and exclusion rules, decided in advance.
Whether analyses were pre-specified or exploratory (label exploratory results as such).

Figures

Label every error bar (SD, SEM, or CI) and state n in the legend → error bars.
Show individual data points for small samples.
Make sure the figure's statistic matches the text's (same test, same n).

A biology example

A results sentence that passes review: "Across three independent experiments (n = 3), normalized expression increased 1.8-fold with treatment (95% CI 1.3–2.5; paired t-test on per-experiment means, p = 0.02)." It names the test, defines n at the experiment level, gives a magnitude with a CI, and reports the exact p: everything a reader or reviewer needs.

Common mistakes

"p < 0.05" with no effect size, CI, or exact value.
Not defining n, or defining it as wells/cells/images → replicates and pseudoreplication.
"NS" for non-significant results instead of the actual p and CI (which may show the study was just underpowered).
Mismatch between methods, results, and figures (different tests or n in different places).
Reporting only the comparisons that "worked." Describe all pre-specified analyses, and disclose exploratory ones.
No software/version or correction method, making the analysis impossible to reproduce.

Effect size and confidence intervals · Replicates and pseudoreplication · Error bars