Chapter 10 Two Samples
Given a choice between two theories, take the one which is funnier.
– Blore's Razor
10.1 Introduction
A two-sample inference is one of the most common statistical procedures used in practice. For example, a colloquial use of “t-test” usually refers to the comparison of means from two independent normal populations rather than a single-sample t-test. In this chapter we will test the equality of two normal means for independent and dependent (paired) populations as well as the equality of two variances and proportions. In the context of comparing proportions, we will discuss the risk and odds ratios. In testing the equality of means in independent normal populations, we will distinguish two cases: (i) when the underlying population variances are the same and (ii) when no assumption about the variances is made. In this second case the population variances may be different, or even equal, but simply no assumption about their equality enters the test. Each of the tests involves the difference or ratio of the parameters (means, proportions, variances), and for each difference/ratio ...
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