- Continuous Normal Data
In most of the standard textbooks, the inferences on one-and two-sample means are discussed when population variance(s) is (are) known or un known, using standard normal and t-distributions. In practice, the population variance(s) is (are) unknown and as such we will discuss the results using only the t-distribution in this book. The t-distribution assumes normal distribution for the underlying data. When the sample size(s) is (are) small, the normal distribution of the data has to be ascertained using the ShapiroWilk test or other tests, as discussed in Chapter 1. When the sample size(s) is (are) large, the sample mean(s) is (are) approximately normally distributed based on the central limit theorem, and as the t-distribution also approximates normal distribution with increased degrees of freedom, the methods discussed in this and the next section are valid without testing the normality assumption of the data. With ordinal data, sometimes we associate numerical values to the categories and analyze the data using the quantitative methods. If the point scale is seven or more, it may be reasonable to use methods of this chapter, but if the scale is two or three points, these methods are inappropriate and one should use methods for discrete data as discussed in Chapter 2.