A one-sample t-test checks whether the mean of a single sample differs from a known or hypothesized value, for example whether average scores differ from a national benchmark. The write-up is short, but people often forget the test value or the effect size. This guide gives you the exact APA 7 format, a worked example you can copy, and the mistakes reviewers catch.
What you need before you write a single word
An APA 7 write-up of a one-sample t-test needs these values from your output:
- The sample mean (M) and standard deviation (SD).
- The test value you compared against (the hypothesized or population mean).
- The t value.
- The degrees of freedom (df), which is N minus 1.
- The exact p value.
- An effect size, Cohen's d, computed as the difference from the test value divided by the sample SD.
A 95% confidence interval for the mean (or for the difference from the test value) is encouraged in APA 7.
The APA 7 format template
Report the result in running text using this pattern:
A one-sample t-test showed that [variable] (M = X.XX, SD = X.XX) differed significantly from the test value of XX, t(df) = X.XX, p = .XXX, d = X.XX, 95% CI [X.XX, X.XX].
Formatting rules reviewers actually check:
- Italicize M, SD, t, p, d.
- Name the test value explicitly; the reader needs to know what you compared against.
- Put the degrees of freedom (N minus 1) in parentheses after t.
- No leading zero on p. Keep the leading zero on Cohen's d.
- Round to two decimals. If p is below .001, write p < .001.
A worked example
Suppose a sample of 40 students scored on a test where the national mean is 100.
- Sample (n = 40): M = 104.60, SD = 12.30
- Test value: 100
- Result: t(39) = 2.37, p = .023, d = 0.37, 95% CI [100.67, 108.53]
Written up in APA 7, that becomes:
A one-sample t-test showed that students' scores (M = 104.60, SD = 12.30) were significantly higher than the national mean of 100, t(39) = 2.37, p = .023, d = 0.37, 95% CI [100.67, 108.53].
The sentence carries the sample statistics, the comparison value, the test result, the effect size, and the confidence interval.
Mistakes reviewers catch
- Omitting the test value. A one-sample test is meaningless without stating what the mean was compared against.
- No effect size. Report Cohen's d, the difference from the test value divided by the sample SD.
- Reporting the CI for the wrong quantity. State whether it is the CI for the sample mean or for the difference from the test value.
- Writing p = .000. Report p < .001.
- A leading zero on p. APA drops it.
- Using the wrong test. To compare two related measurements use a paired t-test; to compare two separate groups use an independent t-test.
Before you report: did the test's assumptions hold?
A one-sample t-test assumes:
- Independent observations.
- Approximate normality of the variable (or a large enough sample for the central limit theorem to apply).
If the variable is badly non-normal in a small sample, the Wilcoxon signed-rank test against a hypothesized median is a non-parametric alternative.
Let KyroStat do the write-up for you
Getting the test value, effect size, and confidence interval right is where errors creep in. KyroStat runs the one-sample t-test on your data, checks normality, and hands you the finished APA 7 sentence, the effect size, and the underlying Python or R code. Upload your spreadsheet, and the report is done in seconds.
Frequently asked questions
What is a one-sample t-test used for? To test whether the mean of a single sample differs from a known or hypothesized value, such as a population mean or a benchmark.
What degrees of freedom does it use? N minus 1. With 40 participants, df = 39.
Which effect size should I report? Cohen's d: the difference between the sample mean and the test value, divided by the sample standard deviation.
My p value shows as .000. What do I write? Report p < .001. A p value is never exactly zero.