TYPES OF DATA

It must be remembered that behind every statistical methodology there are formal mathematical definitions and proofs. Although it may sometimes seem that a simple intuitive approach is sufficient to understand what is happening, mathematical statistics can be misleading and unforgiving. The mathematical proofs and calculations that are behind our statistical tables and computation programs make strict distinctions among the several types of data ( Table 23-1 ).

One type of data, termed interval data, are simple continuous numerical measurements (e.g., 1.2, 33.4). Often, we describe discrete numerical measurements, such as counts or integral quantities in the same categorization. This approach is occasionally misleading: the claim that a "typical family has 2.3 children" is meaningful in a crude way, even though the quantification of children is obviously not a continuous numerical fraction. In practical use, both continuous and discrete data can be handled by techniques similar to those used for interval data.

The other major grouping of data is categorical data. One type of categorical data is ordinal data, which refers to the ordering or ranking of subjects (e.g., 1st, 3rd, 10th). It is important to be careful to resist the temptation to regard the number of the ranking as an interval number, that is, to confuse "first" with the number "1," and so on. Such grouping does not usually have much meaning in reality and is false to the mathematics if an attempt is then made to manipulate the number as though it were an interval value.

Another similar category is binary data (e.g., up versus down, greater versus lesser). The most general grouping is the simple category (e.g., red, green, blue; cancer, diabetes, ulcer). When using simple or binary categories it is incorrect to attach numbers to the groups and try to get numerical results—the mathematics are not appropriate and the results are not likely to mean much. Specific statistical techniques for categorical data are necessary.