# How to report a t-test: templates for Welch, Student and paired tests

> Copy-ready sentences for reporting Welch's, Student's and paired t-tests in a paper, with what each number means and the details reviewers check first.

Canonical: https://www.licklider.ai/guides/how-to-report-a-t-test/
Section: Guides › Comparing two groups
Author: Licklider · Published 2026-11-10 · Last reviewed 2026-11-10 (UTC)

> **Quick answer.** Report, in this order: what you compared and in how many independent units; each group's mean and SD; the **difference with its 95% confidence interval**, saying which group was subtracted; then the test — **which t-test** (Welch, Student or paired; two-sided unless justified), **t with its degrees of freedom**, and the **exact p-value**. For example: *mean 63.6 pg/mL (SD 13.0, n = 6) in treated mice and 50.9 pg/mL (SD 2.7, n = 12) in controls; difference (treated − control) 12.7 pg/mL, 95% CI −0.9 to 26.4; two-sided Welch's t(5.22) = 2.37, p = 0.062.*

## The checklist reviewers apply

| Report | Why | Typical gap |
| --- | --- | --- |
| The exact test: Welch's (no equal-variance assumption), Student's (assumes equal variances) or paired; one- or two-sided | Different tests give different p-values for the same data | "Data were analysed by t-test" |
| n per group and what n counts (animals, cultures, patients — the unit of analysis) | Lets the reader judge independence and power | Wells or cells (technical replicates) counted as n |
| Mean and **SD** (standard deviation, the typical spread of individual values) for each group | SD describes the data; SEM (standard error of the mean) only describes the precision of the mean | SEM shown as if it were variability |
| Difference between means with **95% CI** | Gives the size of the effect and its uncertainty | Only a p-value |
| t, degrees of freedom, exact p | Lets anyone check the numbers agree | "p < 0.05" or "p = 0.000" |
| Software and version | Defaults differ between programs | Missing |

These follow the SAMPL guidelines for basic statistical reporting in biomedical journals, which ask authors to name the test, state whether it was one- or two-sided and paired or independent, give the actual p-value and report estimates with confidence intervals ([Lang & Altman 2015](https://doi.org/10.1016/j.ijnurstu.2014.09.006)); the APA's reporting standards, which ask for effect-size estimates and confidence intervals for each inferential test ([Appelbaum et al. 2018](https://doi.org/10.1037/amp0000191)); and the t-test checklist of a review that found 53% of physiology papers using t-tests did not say whether any were paired ([Weissgerber et al. 2018](https://doi.org/10.7554/eLife.36163), Box 2). For p-values, APA style is to give exact values to two or three decimals and "p < .001" below that ([APA Numbers and Statistics Guide](https://apastyle.apa.org/instructional-aids/numbers-statistics-guide.pdf)); many biology journals keep the leading zero (p = 0.031).

## Where to find each number

| Number | R `t.test` output | SciPy result | GraphPad Prism |
| --- | --- | --- | --- |
| t | `t =` | `.statistic` | t |
| Degrees of freedom (df: how much information the variance estimate rests on) | `df =` | `.df` | df |
| p | `p-value =` | `.pvalue` | P value |
| 95% CI of the difference (the range of differences compatible with the data) | `95 percent confidence interval` | `.confidence_interval()` | 95% confidence interval |
| Which group was subtracted | First group listed minus second | First argument minus second | Shown in the results table |

"Two-sided" means the test looks for a difference in either direction; it is the default in all three.

## Templates

Replace the bracketed parts. Keep the order: estimate first, test second.

**Welch's t-test (two independent groups, the recommended default)**

> [Outcome] was [higher/lower] in [group A] (mean [x], SD [s], n = [n]) than in [group B] (mean [x], SD [s], n = [n]); difference ([A] − [B]) [d] [units], 95% CI [lower] to [upper]; two-sided Welch's t([df, to two decimals]) = [t], p = [exact p].

Example: *Mean serum marker was 63.6 pg/mL (SD 13.0, n = 6) in treated mice and 50.9 pg/mL (SD 2.7, n = 12) in controls; difference (treated − control) 12.7 pg/mL, 95% CI −0.9 to 26.4; two-sided Welch's t(5.22) = 2.37, p = 0.062.* (Worked through in [Welch vs Student](/guides/welch-vs-student-t-test/).)

Welch's degrees of freedom are usually not a whole number; report them as calculated, rounded to two decimals.

**Student's t-test (equal variances assumed, with a stated reason)**

> … difference [d], 95% CI [lower] to [upper]; Student's t([n₁ + n₂ − 2]) = [t], p = [p].

**Paired t-test (the same subjects measured twice)**

> [Outcome] changed from [mean before] (SD [s]) to [mean after] (SD [s]) in [n] [subjects]; mean change [d] (SD of changes [s]), 95% CI [lower] to [upper]; paired t([n − 1]) = [t], p = [p].

Example: *Fasting glucose fell from 9.19 mmol/L (SD 1.86) to 8.29 mmol/L (SD 1.67) in 8 mice; mean change −0.90 mmol/L (SD of changes 0.58), 95% CI −1.39 to −0.41; paired t(7) = −4.37, p = 0.003.*

**A non-significant result**

> … difference [d], 95% CI [lower] to [upper]; Welch's t([df]) = [t], p = [p]. The interval is compatible with [no difference / an increase of up to (upper)].

Say what the interval allows; do not write "there was no difference". A p-value above 0.05 is not evidence of no effect ([ASA statement on p-values](https://doi.org/10.1080/00031305.2016.1154108), principles 3 and 5).

**Figure legend**

> Each point is one [mouse]; bars show mean ± SD (n = [n] per group). Groups were compared with a two-sided Welch's t-test (p = [p]).

Show the individual points rather than a bar alone: bar graphs of small samples can hide very different distributions ([Weissgerber et al. 2015](https://doi.org/10.1371/journal.pbio.1002128)).

**Methods paragraph**

> Two groups were compared with a two-sided Welch's t-test, which does not assume equal variances[, specified before the data were analysed]. Paired measurements were compared with a paired t-test on the within-subject differences. The unit of analysis was the [animal]; technical replicates were averaged within each [animal]. Results are reported as mean differences with 95% confidence intervals. Analyses used [R 4.3.3 / SciPy 1.18.1]; p < 0.05 was considered statistically significant.

## Numbers that reviewers check for consistency

- **df must match the design.** Student's: n₁ + n₂ − 2. Paired: number of pairs − 1. Welch's: a decimal between the smaller group's n − 1 and n₁ + n₂ − 2 — for 5 vs 7 mice, between 4 and 10.
- **t, df and p must agree.** Reviewers and automated checkers recompute p from t and df; a mismatch suggests a copying error.
- **The CI and p must agree.** A two-sided 95% CI excludes zero exactly when p < 0.05 for the same test.
- **Means, SDs and n must reproduce the t.** For Welch's test, t = (mean₁ − mean₂) ÷ √(SD₁²/n₁ + SD₂²/n₂). Recompute from the unrounded data where you can: rounded summaries shift the last digit (the paired example's t = −4.37 comes from the raw values; the rounded SD of 0.58 would give −4.39).
- **Several t-tests in one paper need a plan.** If you test many outcomes or many pairs of groups, either correct for multiple comparisons (Holm's method, a step-down version of Bonferroni, is a safe default) or name one primary comparison and label the rest exploratory. For three or more groups, compare them together first (ANOVA) rather than with t-tests between every pair.

## Effect sizes: which d?

Standardised effect sizes help comparisons across studies and power calculations, but different designs need different versions ([Lakens 2013](https://doi.org/10.3389/fpsyg.2013.00863)):

- **Two independent groups:** Cohen's d_s = difference ÷ pooled SD (Hedges' g corrects its small-sample bias).
- **Paired:** d_z = mean change ÷ SD of the changes — the one used for paired power calculations — or d_av, which divides by the average of the two SDs and is comparable with between-subject studies.

Name the version you report. The raw difference with its CI remains the primary result in most biology papers.

## Rewrite these phrases

Each row turns a phrase reviewers query into one they accept.

| Instead of | Write |
| --- | --- |
| "p = 0.000" | "p < 0.001" |
| "p < 0.05" alone | The exact p-value, e.g. "p = 0.031" |
| "There was a trend towards significance (p = 0.07)" | "difference 4.1, 95% CI −0.4 to 8.6; p = 0.07" |
| "No difference between groups (p = 0.4)" | "difference 1.2, 95% CI −2.0 to 4.4; p = 0.4" |
| "Data were analysed by t-test" | "two-sided Welch's t-test" |
| "mean ± SEM" for describing data | "mean ± SD" (use SEM or CI only to show precision, and say which) |

## References

- Appelbaum M, Cooper H, Kline RB, et al. (2018). Journal article reporting standards for quantitative research in psychology: the APA Publications and Communications Board task force report. *American Psychologist* 73(1):3–25. [doi:10.1037/amp0000191](https://doi.org/10.1037/amp0000191)
- Lakens D (2013). Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. *Frontiers in Psychology* 4:863. [doi:10.3389/fpsyg.2013.00863](https://doi.org/10.3389/fpsyg.2013.00863)
- American Psychological Association (2022). APA Style Numbers and Statistics Guide (7th ed.). [PDF](https://apastyle.apa.org/instructional-aids/numbers-statistics-guide.pdf)
- Lang TA, Altman DG (2015). Basic statistical reporting for articles published in biomedical journals: the "Statistical Analyses and Methods in the Published Literature" or the SAMPL Guidelines. *International Journal of Nursing Studies* 52(1):5–9. [doi:10.1016/j.ijnurstu.2014.09.006](https://doi.org/10.1016/j.ijnurstu.2014.09.006)
- Wasserstein RL, Lazar NA (2016). The ASA statement on p-values: context, process, and purpose. *The American Statistician* 70(2):129–133. [doi:10.1080/00031305.2016.1154108](https://doi.org/10.1080/00031305.2016.1154108)
- Weissgerber TL, Milic NM, Winham SJ, Garovic VD (2015). Beyond bar and line graphs: time for a new data presentation paradigm. *PLOS Biology* 13(4):e1002128. [doi:10.1371/journal.pbio.1002128](https://doi.org/10.1371/journal.pbio.1002128)
- Weissgerber TL, Garcia-Valencia O, Garovic VD, Milic NM, Winham SJ (2018). Why we need to report more than 'Data were analyzed by t-tests or ANOVA'. *eLife* 7:e36163. [doi:10.7554/eLife.36163](https://doi.org/10.7554/eLife.36163)

## Related

- [How to write the statistical methods section](https://www.licklider.ai/guides/how-to-write-statistical-methods-section/)
- [Welch's t-test vs Student's t-test](https://www.licklider.ai/guides/welch-vs-student-t-test/)
- [Paired vs unpaired t-test](https://www.licklider.ai/guides/paired-vs-unpaired-t-test/)
- [Sample size calculator (with a copy-ready methods paragraph)](https://www.licklider.ai/tools/sample-size-calculator/)

## How this page was made

- Written and published by Licklider. Reporting recommendations cite official guidelines and peer-reviewed methods papers listed under References; cited items were checked against the source text.
- Every number in the templates comes from worked examples whose stored code (Python with SciPy 1.18.1; R 4.3.3) is linked from the related guides.
- Separate review passes checked the statistics, the citations and readability before publication.