Welch's t-test compares the means of two independent groups without assuming the groups have equal variances. SPSS shows it on the row labelled "Equal variances not assumed"; R's t.test() runs it by default. The write-up is almost the same as for a Student's t-test, with one giveaway that reviewers look for: degrees of freedom that are not a whole number. This guide gives you the exact APA 7 format, a worked example and the mistakes to avoid.
What you need before you write a single word
An APA 7 write-up of Welch's t-test needs these values from your output:
- The mean (M) and standard deviation (SD) of each group, and each group's n.
- The t statistic from the Welch (unequal variances) row.
- The Welch-Satterthwaite degrees of freedom, usually a decimal such as 33.11.
- The exact p value.
- An effect size, usually Cohen's d, and the 95% confidence interval of the mean difference.
- Optionally, the Levene's test result that led you to Welch's version.
The APA 7 format template
Because the group variances differed, Welch's t-test was used. [Group 1] (M = X.XX, SD = X.XX) scored significantly lower on [outcome] than [group 2] (M = X.XX, SD = X.XX), t(XX.XX) = X.XX, p = .XXX, d = X.XX, 95% CI [X.XX, X.XX].
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Formatting rules reviewers actually check:
- Report the fractional degrees of freedom to two decimals: t(33.11), not t(66). The whole-number df belongs to Student's t-test.
- Say that equal variances were not assumed (or name Welch's test), so the reader knows which row of the output you used.
- Italicize M, SD, t, p and d. Keep the leading zero on d and the CI; drop it on p.
- Report the exact p value; below .001 write p < .001.
A worked example
Suppose you compared final exam scores between students who took a course online and students who attended in person. The online scores were far more spread out.
- Online (n = 28): M = 74.02, SD = 13.75
- In person (n = 40): M = 81.12, SD = 5.51
- Levene's test: F(1, 66) = 20.53, p < .001
- Welch's test: t(33.11) = −2.59, p = .014, d = −0.68, 95% CI of the difference [−12.67, −1.52]
Written up in APA 7, that becomes:
Levene's test indicated unequal variances, F(1, 66) = 20.53, p < .001, so Welch's t-test was used. Students who took the course online (M = 74.02, SD = 13.75) scored significantly lower on the final exam than students who attended in person (M = 81.12, SD = 5.51), t(33.11) = −2.59, p = .014, d = −0.68, 95% CI [−12.67, −1.52].
The negative t, d and interval simply follow the order of subtraction (online minus in person). You can report the absolute values instead, as long as the sentence says which group scored higher.
The APA 7 table (optional)
| Group | n | M | SD |
|---|---|---|---|
| Online | 28 | 74.02 | 13.75 |
| In person | 40 | 81.12 | 5.51 |
Note. Welch's t(33.11) = −2.59, p = .014, d = −0.68.
Mistakes reviewers catch
- Whole-number df with Welch's t. If your df is 66 you have copied the Student's t row. Welch's df is almost always fractional.
- Not saying which test you ran. "An independent-samples t-test" leaves the reader guessing whether variances were pooled.
- Choosing the row by the result. Decide on Welch's test from the design or from Levene's test, not from whichever row gives the smaller p. Many statisticians recommend Welch's test by default.
- No effect size. Report Cohen's d (or Hedges' g for small samples) alongside t.
- Writing p = .000. Report p < .001.
Let KyroStat do the write-up for you
KyroStat checks the variances, runs Welch's test when they differ, and writes the APA 7 sentence with the right degrees of freedom, effect size and confidence interval from your own data. Upload your spreadsheet, and the report is done in seconds.
Frequently asked questions
Should I always use Welch's t-test? Many methodologists say yes: it performs as well as Student's t when variances are equal and much better when they are not. If you use it by default, say so in your Methods.
Do I need to report Levene's test? It is good practice if Levene's test is what led you to Welch's version. If you use Welch's test by default, a sentence in the Methods is enough. See how to report Levene's test.
How is this different from a regular independent t-test? Only the standard error and the degrees of freedom change. The sentence otherwise follows the independent t-test format.
What if I have three or more groups with unequal variances? Use Welch's ANOVA with Games-Howell post hoc tests.