![]() So, what do we mean by independent samples or independent data, and how do we go about verifying it? Independence is a mathematical idea, an abstraction from probability theory. It often involves considerable creative thinking and tedious legwork. ![]() Checking for independence is the difference between doing statistics and carrying out a mathematical or maybe just a mechanical exercise. Independence, on the other hand can be a show stopper. The whole test depends on it, but this assumption is baked into the software that will run the test. is very important, but it is relatively easy to check, and the t-test is robust enough to deal with some deviation from normality. There are other tests and workarounds for the situations where 4. However in my opinion, from the point of view of statistical practice, assumption 2. ( of the MIT Open Courseware notes Null Hypothesis Significance Testing II contains an elegantly concise mathematical description of the t-test.)Īll of the above assumptions must hold, or be pretty close to holding for the test to give an accurate result. On the other hand, if the test statistic does fall in the rejection region, then we reject the \(H_0\) and conclude that our data along with the the bundle of assumptions we made in setting up the test, and the “steel trap” logic of the t-test itself provide some evidence that the population means are different. If we compute the test statistic and its value does not fall in the rejection region, then we do not reject \(H_0\) and we conclude that we have found nothing. This region depends on the particular circumstances of the test, and is selected to balance the error of rejecting \(H_0\) when it is true against the error of not rejecting \(H_0\) when it is false. Next, a test statistic that includes the difference between the two sample means is calculated, and a decision is made to establish a “rejection region” for the test statistic. The variances of the two samples are equal (This is the simplest test.).The formal test of the null hypothesis, \(H_0\), that the means of the underlying populations from which the samples are drawn are equal, proceeds making some assumptions: Typically, we have independent samples for some numeric variable of interest (say the concentration of a drug in the blood stream) from two different groups, and we would like to know whether it is likely that two groups differ with respect to this variable.
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