10 – Inferences, Quantitative: Two Sample tests

Testing differences in averages: From one group to two

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 consider two samples, 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. This is called a crossed design or between-subjects design –where each group has its own unique set of observations, and no relationship exists between the observations in the two groups. We discuss crossed experimental designs in Chapter 14.1.

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. If the repeated measures occur at different times, then the design is also longitudinal design or within-subjects design. Paired data are examples of nested design — the data points are clustered within individual units. We discuss nested experimental designs in Chapter 14.5.

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.

Chapter 10 contents