Statistical reports

Why this matters

An analysis that nobody can follow, check or reproduce is not finished. Whether the audience is a journal, a regulator, a client or your own team in six months, the methods and results sections are where your statistical work becomes evidence. Good statistical writing is plain, specific and complete. It tells the reader what was done in enough detail to repeat it, and what was found with enough context (effect sizes, uncertainty) to judge it.

The methods section: enough to reproduce

A reader should be able to redo your analysis from the methods. Cover, in order:

1. Design. Units, factors and levels, blocking, randomisation (how it was done), replication, blinding. Planned sample size and how it was chosen (the power calculation).
2. Measurements. The response(s), instrument, units, any transformations, how detection limits or missing values were handled.
3. Statistical model. Name it and write its terms: "a linear mixed model with buffer and day of week as fixed effects and plate as a random intercept". State the link and distribution for GLMs.
4. Inference. Tests and intervals used, the significance level, the multiple-comparison adjustment, one- or two-sided.
5. Assumption checks and what you did when they failed.
6. Software and versions, with the key packages: "Python 3.12, statsmodels 0.14". Point to code and data if they can be shared.
7. Deviations from the plan (excluded runs and why, a changed model).

Example paragraph:

Four buffers were compared in a randomised complete block design with day
(n = 4) as the block; within each day, the run order of the buffers was
randomised by computer (seed recorded). Enzyme activity (U/mL) was analysed
with a linear model containing buffer and day as fixed effects. Pairwise
differences between buffers were assessed with Tukey's HSD at a family-wise
alpha of 0.05. Residual plots showed no departures from constant variance or
normality. Analyses used Python 3.12 with statsmodels 0.14; code is available
in the project repository.

The results section: estimates first

Lead with what you found and how big it is, then the uncertainty, then the test. Not "the result was significant (p < 0.05)", but:

Mean activity with buffer B was 6.2 U/mL higher than with buffer A
(95% CI 3.1 to 9.3; Tukey-adjusted p = 0.002). Buffers A, C and D did
not differ by more than 2.1 U/mL (all adjusted p > 0.4).

Rules of thumb:

• Report effect sizes with confidence intervals, in the units of the response.
• Give exact p-values (p = 0.03, p = 0.21), with p < 0.001 as the floor. Never just "n.s.".
• Report sample sizes for every comparison, and say if any data were excluded.
• Use tables for many numbers (an ANOVA table, a coefficient table) and figures for patterns (interaction plots, residual plots, response surfaces). Do not repeat the same numbers in both.
• Round sensibly: two or three significant figures for effects, matching the measurement precision.
• Keep interpretation separate. The results say what the data show; the discussion says what it means.

Writing for non-statisticians

Many reports go to managers or clients. Add a short summary at the top in plain English: the question, the answer, how sure you are, and what you recommend. Then the technical detail. For example: "Buffer B gives about 6 U/mL more activity than our current buffer, roughly a 10% improvement. The experiment was designed to detect differences of 5 U/mL, so this result is reliable. We recommend switching to B and confirming over the next month's production."

Reporting guidelines

Many fields have checklists that reviewers expect:

• CONSORT for randomised clinical trials, STROBE for observational studies, ARRIVE for animal research.
• SAMPL (Statistical Analyses and Methods in the Published Literature) for general statistical reporting.
• The EQUATOR Network (equator-network.org) indexes these and many more.

Check your target journal's or agency's current requirements; they change. Checked on 2026-10-23.

Common mistakes

• "Statistically significant" without an effect size, or "no effect" when the interval is wide.
• Unnamed tests ("a t-test was used") with no indication of paired or unpaired, equal or unequal variances.
• Missing software versions and seeds, which make reproduction impossible.
• Selective reporting: only the analyses that "worked". Report all planned analyses and label exploratory ones as exploratory.
• Too many decimal places (p = 0.0432187) and inconsistent rounding.
• Causal language for observational results without the assumptions from the causal inference lesson.

Quick recap

• Methods: design, measurements, model, inference, assumption checks, software, deviations.
• Results: estimate, interval, then p-value; exact p-values and sample sizes.
• Add a plain-language summary for non-specialists; follow your field's reporting guideline.

Try it

In the Do tab you will write a methods and results section for the catalyst ANOVA from module 2 and check it against a short checklist.