![]() ![]() In fact, as the sample size in the two groups gets large, the t-test is valid (i.e. that if the null hypothesis is true, it will falsely reject the null 5% of the time (I’m assuming we are using the usual significance level). In particular, we would worry that the t-test will not perform as it should – i.e. On the face of it then, we would worry if, upon inspection of our data, say using histograms, we were to find that our data looked non-normal. So, as constructed, the two-sample t-test assumes normality of the variable X in the two groups. ![]() Since often variances can differ between the two groups being tested, it is generally advisable to allow for this possibility. that in the first group, the variable of interest X is distributed and in the second group as. Ī simple extension allows for the variances to be different in the two groups, i.e. That is, the variance is assumed to be the same in both groups, and the variable is normally distributed around the group mean. In its simplest form, it assumes that in the population, the variable/quantity of interest X follows a normal distribution in the first group and is in the second group. The two-sample t-test allows us to test the null hypothesis that the population means of two groups are equal, based on samples from each of the two groups. The t-test is one of the most commonly used tests in statistics. ![]()
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