![]() These two tests (Student’s t-test and Wilcoxon test) have the same final goal, that is, compare two samples in order to determine whether the two populations from which they were drawn are different or not. This article being already quite long and complete, the Wilcoxon test is covered in a separate article, together with some illustrations on when to use one test or the other. However, in some cases, the mean is not appropriate to compare two samples so the median is used to compare them via the Wilcoxon test. In the case of the Student’s t-test, the mean is used to compare the two samples. To compare two samples, it is usual to compare a measure of central tendency computed for each sample. Note that this statistical tool belongs to the branch of inferential statistics because conclusions drawn from the study of the samples are generalized to the population, even though we do not have the data on the entire population. On the contrary, if the two samples are rather similar, we cannot reject the hypothesis that the two populations are similar, so there is no sufficient evidence in the data at hand to conclude that the two populations from which the samples are drawn are different. The reasoning behind this statistical test is that if your two samples are markedly different from each other, it can be assumed that the two populations from which the samples are drawn are different. In other words, a Student’s t-test for two samples allows to determine whether the two populations from which your two samples are drawn are different (with the two samples being measured on a quantitative continuous variable). 1 The Student’s t-test for two samples is used to test whether two groups (two populations) are different in terms of a quantitative variable, based on the comparison of two samples drawn from these two groups. One of the most important test within the branch of inferential statistics is the Student’s t-test. Combination of plot and statistical test.A note on p-value and significance level \(\alpha\).Scenario 5: Paired samples where the variance of the differences is unknown.Scenario 4: Paired samples where the variance of the differences is known.Scenario 3: Independent samples with 2 unequal and unknown variances.Scenario 2: Independent samples with 2 equal but unknown variances.Scenario 1: Independent samples with 2 known variances. ![]() ![]() How to compute Student’s t-test by hand?.Different versions of the Student’s t-test.
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