How to Report a t Test in APA 7: Independent, Paired and One-Sample

The t test is the first comparison anyone learns and the one that comes back from reviewers with a pencil mark more often than any other. It is rarely the arithmetic. It is the half-line that never made it in: degrees of freedom nobody explains, a “p < .05” where APA 7 asks for the exact value, a Cohen's d with no interval and no indication of which flavor it is. This is the write-up for all three versions — independent samples, paired samples and one sample — number by number, and why Welch's correction has moved from exception to default across much of the field. The wider guide is how to report results in APA 7.

What every version has to contain

Five pieces, none of them decorative. The t statistic with its degrees of freedom in parentheses, the exact p value to two or three decimals, an effect size with a confidence interval, a description of each group or time point (M, SD, n), and a sentence saying which way the difference runs. Leave that last sentence out and your reader has a significant result without knowing who scored higher, which was the question they came with.

Degrees of freedom are the only thing that distinguishes the three versions on the page. For independent samples they are n₁ + n₂ − 2, so 52 and 50 participants give t(100). For paired samples they are the number of pairs minus one, not the number of participants minus one: recruit 44 and lose 4 at follow-up and you have 40 pairs, so t(39). For one sample they are n − 1. Under Welch's correction they stop being a whole number, which has a section of its own further down.

Italicize t, p, M, SD, d, n and N. The leading zero is where most manuscripts slip: it belongs to statistics that can exceed 1, and t, M, SD and d all can, so you write t(45) = 0.87 and d = 0.54 with the zero in place. A p value cannot exceed 1 and takes no leading zero: p = .007, never 0.007. Below .001 you write p < .001, which is essentially the only place APA 7 tolerates a less-than sign in a p value.

Two details that save a whole round of review. Say whether the test was two-tailed — it is by default, but writing it down removes a query — and never compress the p value to “< .05”. A p = .049 and a p = .003 do not say the same thing, however similar their asterisks look. If you already have the output and what you need is the string with the italics and decimals in the right places, the APA 7 results formatter assembles it for you.

Independent samples: describe first, test second

Lead with the means. “Participants in the self-compassion condition reported lower perceived stress (M = 18.94, SD = 5.62, n = 52) than participants in the active control condition (M = 22.10, SD = 6.05, n = 50).” The comparison comes after: t(100) = 2.73, p = .007. That order is not a stylistic preference. The means are the finding; the t is the evidence that the gap between them is not sampling noise. A paragraph that opens with the statistic and buries the means in a table makes the reader work for nothing.

The piece that most often goes missing is the mean difference with its confidence interval in the original units: 3.16 points, 95% CI [0.87, 5.45]. APA 7 asks for an interval around your primary estimate, and the primary estimate here is that raw difference rather than its standardized version. Three points on a stress scale mean something to anyone who has used it; 0.54 has to be translated first. If that interval excludes zero, you already know what the p value is going to say.

The effect size for this version is Cohen's d with the pooled standard deviation in the denominator: here the pooled SD is 5.83, and 3.16 divided by 5.83 gives d = 0.54, 95% CI [0.15, 0.94]. That interval is the most informative thing in the paragraph and the first thing to get cut. It runs from below the small benchmark up to a large effect, so with 102 participants the honest sentence is that the study places the effect somewhere between negligible and substantial, not that it “was medium”. Cohen's (1988) benchmarks — 0.20, 0.50 and 0.80 — are a convention from that book, not a property of your data. The effect size calculator returns d and its interval from the means, standard deviations and group sizes.

Put the direction in words rather than in the sign. “t(100) = 2.73” does not say who scored higher, and depending on the order your software fed the groups in, the same comparison can print as −2.73 with nothing having changed. Write “the self-compassion group scored significantly lower” and the sign stops mattering. And if you have three groups, this is not solved by running three t tests against a shared control: that is an ANOVA with post hoc comparisons and a correction.

Welch's correction, and why it is now the default many people ask for

The routine most textbooks teach is a two-step ritual: run Levene's test first and, if it comes out significant, switch to the “equal variances not assumed” row. There are two problems with that. Choosing your test on the basis of another test's result changes the error rates of the whole procedure, and Levene's test has little power precisely where it matters most — small, unequal groups, which is exactly when heterogeneity of variance does damage. A non-significant Levene says “no evidence that they differ”, not “they are equal”.

Here is what is at stake, using a shape of data that turns up constantly in clinical work: a diagnosed group of 19 (M = 41.20, SD = 13.80) against a community comparison group of 88 (M = 33.60, SD = 6.40). Student's t gives t(105) = 3.68, p < .001. Welch's t, on exactly the same numbers, gives t(19.70) = 2.35, p = .030. That is not a third-decimal quibble. The degrees of freedom collapse from 105 to under 20 because the small group is the one carrying the large variance, and Student's version had been crediting it with precision it does not have.

Now the other half of the bargain. When the variances really are similar, Welch costs you almost nothing. The data from the previous section, with standard deviations of 5.62 and 6.05, give t(100) = 2.73, p = .007 under Student and t(98.74) = 2.73, p = .007 under Welch: you lose barely more than one degree of freedom and neither the statistic nor the p value moves. That asymmetry — large protection when you need it, negligible cost when you do not — is the argument for using it by default (Ruxton, 2006; Delacre et al., 2017), and it is why t.test() in R applies it without asking while SPSS leaves it sitting in the second row of the table.

It is written exactly like Student's, with two caveats. The degrees of freedom carry decimals and you keep two of them: t(19.70), not t(20). And one sentence in the analysis plan covers it: “all between-group comparisons used Welch's t test, which does not assume homogeneity of variance”. Watch the effect size, because that decision is still open: when variances genuinely differ, a pooled SD is a questionable denominator — it returns d = 0.93 in the clinical example above — and many people prefer Glass's delta, which uses only the comparison group's SD and returns 1.19 on the same data. Pick one, say which, and do not switch halfway down the table. The rest of the assumptions are covered in how to check statistical assumptions.

Paired samples: the d you choose changes the number

The comparison of two measurements from the same person is reported with both time points described and the difference in the middle. “Insomnia severity fell from baseline (M = 15.28, SD = 4.16) to post-treatment (M = 12.55, SD = 4.02) across the 40 participants with complete data, t(39) = 5.57, p < .001; mean difference = 2.73 points, 95% CI [1.74, 3.72].” Note that the interval sits on the difference, not on either mean separately: the difference is what you tested.

The number almost nobody prints is the standard deviation of the differences, which here is 3.10. It is not a curiosity; it is the denominator of the test and of everything that follows, and it depends on how strongly the two measurements correlate (here r = .71). With the same 2.73-point mean change, a weaker baseline-to-follow-up correlation would have produced a much smaller t. Reporting that SD and that correlation is what lets somebody recompute your result or feed it into a meta-analysis.

Which brings us to the question that generates the most reviewer comments: which d do you report? d_z divides the mean difference by the SD of the differences — 2.73 / 3.10 = 0.88, 95% CI [0.52, 1.25]. d_av divides it by the average of the two original standard deviations — 2.73 / 4.09 = 0.67. These are the same effect described two ways, and the gap between 0.88 and 0.67 is not trivial. Because d_z absorbs the correlation between measurements, it is not comparable with a d from a between-groups design; if you plan to sit your effect next to between-groups studies, d_av is the one that belongs there (Lakens, 2013). Write the subscript, every time. The pre-post effect size calculator returns both so you can see the distance between them.

A last word on pairs. Participants missing either measurement drop out of the analysis, and that has to be visible: if you recruited 44 and analyzed 40, say so in the same sentence. And a paired t test in a single-arm study does not show that your intervention worked, only that scores changed; without a comparison group, regression to the mean and the simple passage of time are still on the table, and it reads far better when you say that before a reviewer does.

One sample: half the report is what you compared against

The one-sample version tests your mean against a fixed value. “Trainees scored above the published reference mean on emotional exhaustion (M = 3.42, SD = 0.86, n = 74), t(73) = 4.20, p < .001, d = 0.49, 95% CI [0.25, 0.73].” The degrees of freedom are n − 1 and the denominator of d is your own sample's SD, with nothing pooled and no correction to argue about. It is the simplest of the three.

The comparison value is half the report and it usually arrives with no surname attached. A normative mean comes from a specific standardization sample, in a specific country, in a specific year: name it and cite it. Testing against the theoretical midpoint of a Likert scale is a different move and a much weaker one — a mean above 3 on a 1-to-5 scale means little unless somebody has shown that 3 is a meaningful threshold. If you do it anyway, justify it in a sentence instead of letting it pass unremarked.

When the metric is interpretable, the confidence interval around the mean tells the reader more than d does: [3.22, 3.62] shows the sample sitting above the reference value while still inside what the scale treats as an ordinary range. Be careful with the wording of the claim, too. The test treats the reference value as an exact number when it actually came from another sample with its own error. “Above the published reference mean” is what you demonstrated; “above the population” is more than you demonstrated.

All three write-ups, ready to paste

Independent samples. “Participants in the self-compassion condition reported lower perceived stress (M = 18.94, SD = 5.62, n = 52) than those in the active control condition (M = 22.10, SD = 6.05, n = 50). Welch's t test confirmed the difference, t(98.74) = 2.73, p = .007; mean difference = 3.16 points, 95% CI [0.87, 5.45], d = 0.54, 95% CI [0.15, 0.94].”

Paired samples. “Insomnia severity fell from baseline (M = 15.28, SD = 4.16) to post-treatment (M = 12.55, SD = 4.02) across the 40 participants with both measurements, t(39) = 5.57, p < .001; mean difference = 2.73 points, 95% CI [1.74, 3.72], d_z = 0.88, 95% CI [0.52, 1.25]. The two time points correlated at r = .71.”

One sample. “The sample mean exceeded the published reference value (M = 3.42, SD = 0.86, 95% CI [3.22, 3.62], n = 74), t(73) = 4.20, p < .001, d = 0.49, 95% CI [0.25, 0.73].”

And the methods sentence that covers all three: “All tests were two-tailed with alpha set at .05. Between-group comparisons used Welch's t test, which does not assume homogeneity of variance; within-person comparisons used the paired-samples t test. Effect sizes are reported as Cohen's d with a pooled standard deviation for between-group comparisons and as d_z for within-person comparisons, each with a 95% confidence interval.” Once that sentence exists, no reviewer has to guess where any number in your table came from.

Already drafted it? Paste your Results section into Review one section and you get the first objection a reviewer would raise, quoting the exact sentence from your text. Free, no sign-up.

If you checked normality before the t, the Shapiro-Wilk test guide explains how to read W and p, and why a significant result with a large sample is not a reason to abandon the test.

Missing the effect size and only have the t? With both group sizes you can convert t to Cohen’s d exactly, or t to r if your meta-analysis pools correlations.

Frequently asked questions

How do you report a t test in APA 7?

With the statistic and its degrees of freedom in parentheses, the exact p value and an effect size with an interval: t(100) = 2.73, p = .007, d = 0.54, 95% CI [0.15, 0.94]. In front of that go the means, standard deviations and n for each group or time point, together with the mean difference and its own confidence interval in the original units. Finish with a sentence saying which way the difference runs, because the statistic alone does not say.

Why do my degrees of freedom have decimals?

Because your software applied Welch's correction, which adjusts the degrees of freedom when the two groups have unequal variances. It is not an output error and it is not a number to round to a whole one: report two decimals, t(19.70) = 2.35, and state in your methods that you used Welch's t test. In SPSS it is the second row of the output table; in R it is what t.test() does unless you tell it otherwise.

Does t take a leading zero in APA style?

Yes, whenever it has one. The leading zero belongs to statistics that can exceed 1, and t, M, SD and Cohen's d all can: you write t(45) = 0.87 and d = 0.54. A p value cannot exceed 1, so it never takes one: p = .007, not 0.007. This is the single most common formatting slip in the whole Results section.

Which Cohen's d should I report for a paired-samples t test?

It depends on what you want to compare it with, and the important part is saying which one you used. d_z divides the mean difference by the standard deviation of the differences and is what most software returns; d_av divides it by the average of the pre-test and post-test standard deviations. The same data can give 0.88 and 0.67. If you intend to place your effect alongside between-groups studies or send it to a meta-analysis, d_av is the comparable one — d_z depends on the correlation between measurements and does not belong in that comparison.

Do I need to run Levene's test before a t test?

Fewer and fewer people do, and there are reasons. Choosing your test on the strength of another test's result distorts the error rates of the whole procedure, and Levene's test has little power exactly where variance heterogeneity does the most damage: small, unequal groups. The alternative recommended by Ruxton (2006) and Delacre et al. (2017) is to use Welch's test as standard — when variances are similar it changes essentially nothing, and when they are not it saves you from a false positive.

My data are not normally distributed. Should I use a t test or Mann-Whitney?

Start by remembering that the assumption concerns the sampling distribution of the mean, not the raw variable, and that with reasonable sample sizes the t test tolerates a fair amount of skew. With 20 participants per group, heavy skew or clear outliers, a Mann-Whitney U test or a robust t test on trimmed means are both defensible. What is not defensible is running both and publishing whichever came out significant: that choice is made before you look at the p value and justified in the methods.

With t and its degrees of freedom, the exact p value, the mean difference and its interval, an effect size that says which one it is, and the means and standard deviations behind all of it, your t test is properly reported in all three versions. If you are weighing Student against Welch with your own data in front of you, or a t test against a rank test, that is what my statistical consulting is for.