Student's t-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. When the scaling term is estimated based on the data, the test statistic—under certain conditions—follows a Student's t distribution. The t-test's most common application is to test whether the means of two populations are significantly different. In many cases, a Z-test will yield very similar results to a t-test since the latter converges to the former as the size of the dataset increases.
William Sealy Gosset, who developed the "t-statistic" and published it under the pseudonym of "Student"
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Statistical hypothesis test
A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently support a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a p-value computed from the test statistic. Roughly 100 specialized statistical tests have been defined.
Suppose the data can be realized from an N(0,1) distribution. For example, with a chosen significance level α = 0.05, from the Z-table, a one-tailed critical value of approximately 1.645 can be obtained. The one-tailed critical value Cα ≈ 1.645 corresponds to the chosen significance level. The critical region [Cα, ∞) is realized as the tail of the standard normal distribution.
