A test of whether a mean differs from a given value, or whether two means differ, when the population standard deviation is unknown and estimated from the sample. The statistic is the difference divided by its standard error, which follows a t distribution under the null hypothesis.
Card 1 of 244. Answer: A test of whether a mean differs from a given value, or whether two means differ, when the population standard deviation is unknown and estimated from the sample. The statistic is the difference divided by its standard error, which follows a t distribution under the null hypothesis.
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There are three common versions: the one-sample t-test compares a mean with a fixed value, the two-sample t-test compares two independent groups, and the paired t-test compares two measurements on the same units. For two groups, Welch's version, which doesn't assume equal variances, is the safer default over Student's original. The test assumes independent observations and roughly normal sample means, which large samples provide through the central limit theorem.
Example: two page designs are each shown to 25 users, with mean session lengths of 5.2 and 4.4 minutes and standard deviations of 1.5 and 1.3. Welch's t = 0.8 / √(1.5²/25 + 1.3²/25) = 0.8 / 0.397 ≈ 2.02, with about 47 degrees of freedom, so p ≈ 0.050. That is right on the line, which is a reason to report the confidence interval for the difference, not just "significant".
William Sealy Gosset developed it while working at the Guinness brewery and published it in 1908 under the name "Student". Interview follow-ups: use the paired test for before-and-after data on the same users, consider the Mann-Whitney U test for small samples with heavy skew or outliers, and use ANOVA or a multiple-testing correction instead of many pairwise t-tests.
