10: Quantitative Two-Sample Tests
- Page ID
- 45198
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A one-sample parametric test compares the mean against a population value. The population value may come literally from census information, or, more likely, it comes from some applicable theory. The one-sample t-test was presented, along with how to calculate the confidence interval, in the previous chapter.
In this chapter, we also extend to considering two-sample tests, about hypotheses for two groups. The two groups may consist of observations on different subjects, and thus the two groups are independent of each other — an independent sample t-test may be used to test null hypothesis. A common experimental design is to measure individuals two or more times, e.g., observations like body mass index, BMI, recorded on individuals at the start of an exercise program, and again on the same individuals some time after a treatment — a repeated measures design. In this case, the measures are paired and are, thus, not independent, and a paired-sample t-test would be advised.
Two-sample parametric tests are used to answer questions about the mean where the data are collected from two random samples of independent observations, each from an underlying normal distribution. The samples may be independent or paired, in which different hypotheses are tested.
- 10.1: Compare two independent sample means
- Introduction to the two-sample or independent sample t-test, and the applications of comparing multiple sample means from the same population rather than a single mean against a population parameter or specified value.
- 10.2: Digging deeper into t-test plus the Welch test
- Analysis of the independent sample t-test and what it reveals about the broader category of parametric tests. The Welch test as an alternative to the t-test when assumptions for the t-test are violated but the normal assumption still holds.
- 10.3: Paired t-test
- Discussion of scenarios where relationships exist between observations in two samples, and the assumption of independence used for the previously covered two-sample t-tests no longer holds. Use of the paired t-test for analysis of such data.