Читать книгу Applied Univariate, Bivariate, and Multivariate Statistics - Daniel J. Denis - Страница 36

Recall that in our discussion of the so‐called “soft” versus “hard” sciences in Chapter 1, we concluded that a key principal difference between the two is not necessarily one of different statistical or analytical methods used in drawing conclusions, but rather in the actual material that is subjected to measurement. Though this book is not about measurement per se, we nonetheless wish to review the scales of measurement as first proposed by S.S. Stevens in 1946 (Stevens, 1946).

Table 2.3 Contingency Table for 2 × 2 Diagnostic Design

	Diagnosis Yes	Diagnosis No	Total
Disease Yes	20	10	30
Disease No	5	15	20
Total	25	25	50

Before we discuss these scales, it would do well to remind ourselves just what is measurement in the first place. We propose the following workable definition:

Measurement is the systematic assignment of numbers to observations according to a well‐defined set of rules.

The job of the “rules” is to make good sense of the measurement process. For instance, if we simply assigned numbers to observations without a set of rules to govern the assignment, then even if I weigh more than you, I could be assigned 150 lbs and you 180 lbs. The requirement of having rules of measurement avoids such meaningless and contradictory assignments. If I weigh more than you, rules of measurement imply that my weight measurement will be larger than yours within the margin of measurement error.