One‐ and two‐sample t tests

C omparisons of samples of continuous data are commonplace in biomedical science. Many of these comparisons rely on a powerful observation: most natural phenomena are distributed in a similar way, with data clustered around a central value and tailing off in frequency as they fall further from that point. The bell-shaped curve of the normal distribution and its relative the t distribution is a familiar sight. Both distributions share the advantage that they can be summarized using only the mean and the standard deviation (SD). This thrifty description is the basis of the t tests. Sets of continuous presumably normal data can be compared with only the difference between their means and their relative degree of spread. The t test was first described in 1908 by William Gosset, who developed a set of tests for comparing the mean of a small sample with either an absolute standard or the mean of another sample. Because the tests rely on the t distribution, he called them oneand two-sample t tests. Gosset worked at the Guinness Brewery in Dublin, and company policy regarding trade secrets forced him to publish under the pseudonym “Student.” The tests are now commonly known as Student’s t tests.