Clinical Trials

❘❙❚■ Chapter 19 | Comparison of MeansTo address these questions, we can perform the statistical significant testsintroduced below [2–4]. As described in Chapter 18, statistical inference concernsthe problem of generalizing findings from a sample to the population from whichit was drawn.One-sample t-testTo address Question 1, we need to perform a one-sample t-test. This tests the nullhypothesis that the mean of a population (μ) from which the sample is drawn isequal to a constant (μ 0). Therefore, the hypotheses are expressed as:H 0: μ = μ 0vs (1)H a: μ ≠ μ 0The statistic (t) for testing the above hypotheses is given by:t =X – μ 0SE(X) (2)SE(X) = S / √nwhere:• X is the sample mean• S is the standard deviation• n is the sample size• SE(X) is the standard error of the sample mean (X)Under the null hypothesis, the test statistic in equation (2) is distributed as thet-distribution (or Student distribution) with n – 1 degrees of freedom [5].Degrees of freedomNote that there is a different t-distribution for each sample size, and we have tospecify the degrees of freedom for each distribution (see reference [4] for moreabout degrees of freedom).The t-density distribution curves are symmetric and bell-shaped, like the standardnormal distribution, and peak at 0. However, the spread is wider than that of the200