What does a one-sample t-test compare?

A single sample's mean against one specific, pre-specified value - a published figure, a clinical threshold, or a target set in advance. It is the third member of the t-test family, alongside the independent-samples and paired-samples versions.

What assumption does a one-sample t-test make about the reference value?

That it is a known, fixed constant with no uncertainty of its own. That is reasonable for a defined clinical threshold, but shakier when the comparator is another study's sample mean, which carries its own confidence interval that never enters the calculation.

What is the nonparametric alternative to a one-sample t-test?

The sign test or the Wilcoxon signed-rank test, both built for the one-sample situation. They are worth reaching for when the departure from normality is severe and the sample is small; the t-test tolerates moderate departures well.

The One-Sample t-Test, Reported Properly

Comparing a case series mean against a published figure is an inferential claim, and it hides an assumption about someone else's data.

The comparison everyone runs, rarely as a test

Open a case series in almost any surgical journal and you will find a sentence like this in the discussion: “Our mean operative time of 92 minutes was comparable to previously reported values.” No test is named. No P value appears. The comparison reads as narrative colour, something closer to a caveat than a result. But the moment an author decides that 92 minutes is or is not meaningfully different from a number in someone else’s paper, they have made a statistical judgment, and the test built for exactly that judgment already exists: the one-sample t-test, which asks whether a sample mean differs from a single hypothesised or a priori value.¹^,²

It is the least discussed of the three t-tests. The independent-samples version compares two groups; the paired version compares two measurements on the same subjects; the one-sample version compares a single group’s mean to a constant.¹ That constant does not have to come from another study — it can be a clinical threshold, a device specification, or a target set in advance — but in case series and single-arm cohorts, it is overwhelmingly a number lifted from the published literature. Reviewers of medical manuscripts have flagged exactly this gap: methods sections routinely select the wrong test, or fail to name one at all, when the comparison in question is this specific, this simple, and this checkable.³

What the test assumes, and the assumption nobody states

Like the other members of the t-test family, the one-sample version assumes the observations are independent of one another and that the underlying data are reasonably close to normally distributed, or that the sample is large enough that the distribution of the mean approaches normality regardless.³ The t-test tolerates moderate departures from normality well; when the violation is severe and the sample small, the sign test or the Wilcoxon signed-rank test are the nonparametric alternatives, built for exactly this one-sample situation rather than borrowed from the paired-data case.⁴

The assumption that matters most here is not about your data at all. Every formulation of the one-sample t-test treats the comparison figure as a known, fixed constant with no uncertainty of its own.²^,⁵ That is a reasonable simplification when the comparator is a defined clinical threshold. It is a much shakier one when “the published value” is itself a single study’s sample mean, with a confidence interval that never makes it into your discussion section. Treating someone else’s point estimate as gospel and your own as the only thing with sampling error is an asymmetry worth naming in your limitations, not quietly assuming away.

A worked example

The following is illustrative, constructed for demonstration and not drawn from a real dataset. Suppose a single-centre series reports laparoscopic cholecystectomy operative times for 58 consecutive patients, with a sample mean of 71.4 minutes and a standard deviation of 14.2 minutes. The authors want to compare this against a reference figure of 78 minutes cited in a prior series. A one-sample t-test against a test value of 78 returns a mean difference of −6.6 minutes (95% CI, −10.3 to −2.9), t(57) = −3.54, P < .001. Written up in AMA format: “Mean operative time (71.4 [SD, 14.2] minutes) was significantly shorter than the reference value of 78 minutes reported by [source] (mean difference, −6.6 minutes; 95% CI, −10.3 to −2.9; t₅₇ = −3.54; P < .001).” That sentence, not “comparable to previously reported values,” is what a reviewer can actually check.

How to run it — SPSS vs StatsPlease

In IBM SPSS Statistics (documentation current to version 32), the path is Analyze ▸ Compare Means ▸ One-Sample T Test. The variable or variables to be tested go in the “Test Variable(s)” box, and the reference figure — the published value, the threshold, whatever number the comparison is against — goes in the “Test Value” field; the confidence level for the difference defaults to 95% but is adjustable under Options. SPSS returns two tables: “One-Sample Statistics,” with the mean, standard deviation, and standard error for each variable, and “One-Sample Test,” which is where the t statistic, degrees of freedom, significance, and mean difference actually live. The test value used is printed only in that table’s header, not as a column — the most common misread is pasting the table into a manuscript or a sensitivity-analysis log without keeping that header attached, so a second reader has no way of knowing which reference figure the numbers were tested against.

In StatsPlease, the process collapses into upload and read. You upload the dataset (or the relevant column). StatsPlease’s deterministic engine identifies the appropriate test from the variable type and study design, checks the relevant assumptions, computes the result using fixed, non-LLM algorithms, and drafts the Methods/Results sentence in AMA format — the same number a reader would get running the test by hand in SPSS.

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References

Hazra A, Gogtay N. Biostatistics series module 3: comparing groups (numerical variables). Indian J Dermatol. 2016;61(3):251-260.
Ross A, Willson VL. One-sample t-test. In: Basic and Advanced Statistical Tests: Writing Results Sections and Creating Tables and Figures. Rotterdam: Sense Publishers; 2017:9-12.
Liang G, Fu W, Wang K. Analysis of t-test misuses and SPSS operations in medical research papers. Burns Trauma. 2019;7:31.
Krzywinski M, Altman N. Points of significance: nonparametric tests. Nat Methods. 2014;11(5):467-468.
Al-Kassab M. The use of one sample t-test in the real data. J Adv Math. 2022;21:134-138.

The line “comparable to the published literature” is a claim your data can either support or contradict — it just needs the test run.

StatsPlease's deterministic engine takes your uploaded outcome column and a stated reference value, runs the one-sample t-test (or its nonparametric alternative if your data call for it), and returns the t statistic, degrees of freedom, mean difference, confidence interval, and P value, along with the AMA-format sentence for your results section — the same numbers you would get running the test by hand in SPSS.

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