ABSTRACT
Statistical inferential methods are different for qualitative variables than for quantitative variables. This is analogous to different methods of assessment of cardiovascular diseases than for gastrointestinal tract diseases. Those variables can be considered qualitative that are concerned with proportions of subjects in different categories. A variable such as birth weight is in fact quantitative but is treated as qualitative when the interest is in knowing the percentage of newborns with weight <2500 g, 2500-3499 g, and 3500 g. The actual scale can be metric but the variable becomes qualitative when such categories are formed. There is a rider though. The number of such categories must be small. If, instead of three broad categories, the birth weight is divided into a large number of 100 g categories such as <2000, 2000-2099, 2100-2199, etc., the interest would rarely be in a proportion of births in these categories. It would then be in parameters such as mean or median birth weight. The methods to draw inferences from mean are presented in Chapter 15. Although 100 g categories of birth weight also give rise to categorical data just
as the broad categories do, the statistical methods of analysis of data in these two setups are different. This text therefore avoids using the term ‘‘analysis of categorical data’’ that many other texts do. For the methods described in this chapter, categories are not a prerequisite either. A metric variable such as parity with values 0, 1, 2, and 3þ has no conventional kind of categories (except the last with parity 3þ) but is covered by the methods described in this chapter as long as the interest is in the proportion of subjects with different parity. As you will shortly see, the statistical methods for inference from proportions are distribution free, generally called nonparametric. There is no requirement that the values follow a particular distribution such as a Gaussian distribution. Outliers also do not affect these methods. The statistical inference primarily discussed in this chapter is the test of signifi-
cance. However, the corresponding CI is also explained when not covered in the previous chapter. As already outlined for testing of hypothesis in Chapter 12, the procedure is to set up a null hypothesis and check whether the sample provides enough evidence against it for its rejection. A large number of statistical tests are available for different situations even when restricted to proportions. It is not possible to describe all of them in this text. The attempt is to include the methods that are commonly used in health and medicine.
