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t-test

Statistics & analysis

Definition

A test comparing means — of two groups (independent-samples), two related measurements (paired-samples) or one sample against a known value (one-sample) — on a continuous outcome.

All three forms share the same logic: how large is the mean difference relative to the variability in the data? The independent form assumes approximate normality per group and (checked via Levene's test) equal variances; SPSS prints a corrected row when variances differ.

Report the t statistic, degrees of freedom, p-value and Cohen's d — a significant t-test with a trivial effect size is a statistically detectable but practically unimportant difference.

Choosing between the forms depends on how the data were collected, not on what you hope to find. If the same respondents are measured twice — before and after a workshop, for example — the observations are dependent and the paired test is correct; treating them as independent groups throws away that pairing and weakens the test. If the two groups are different people, use the independent-samples test. When you have three or more groups, running several t-tests inflates the false-positive rate, and a one-way ANOVA with post-hoc comparisons is the right tool instead.

When assumptions fail, there are established alternatives. For skewed data or small samples, the Mann–Whitney U test replaces the independent-samples t-test and the Wilcoxon signed-rank test replaces the paired version. With reasonably large groups (around 30 or more each), the t-test is fairly robust to moderate non-normality, so a normality test that is 'significant' in a large sample is not by itself a reason to abandon it. State which assumption checks you ran and what you concluded from them.

Where it's used

  • Comparing job satisfaction between two genders
  • Before/after comparison of a training intervention
  • Testing a sample mean against a scale midpoint or benchmark

Software used

SPSSRPythonJASPjamovi

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