Читать книгу The Tao of Statistics - Dana K. Keller - Страница 15

 With distances unsure

 Blindly even steps

 Arrive at cracks

Ordinal measurement is common for opinion polls. We can distinguish between levels of agreement but cannot be sure that the psychological distance between pairs of adjoining response choices are equivalent. For example, the psychological distance between “strongly disagree” and “moderately disagree” might not be the same as the distance between “neutral” and “moderately agree.” In these cases, an arithmetic average (the mean) might not yield an interpretable answer.

The high school principal has ordinal scales from some student surveys that he has already conducted, and of which he might generate more. Although the case could be made that course grades really are ordinal, they have been and continue to be used as interval (the next topic) since their creation. The debate is whether the difference in knowledge of a topic between two students scoring, say, 20 and 60 points on a test is the same as that between students scoring 60 points and 100 points.

Along with actual medical data, the director of public health has results for perception surveys on the services received by the state’s medical assistance recipients. She also has another survey to be implemented fairly soon, a state requirement of her department. Most of her medical data, however, are either nominal or ratio, at least in how they are handled.

For statistics appropriate to ordinal data, both the high school principal and the director of public health will use frequency counts for the responses to each of their surveys’ items and a form of chi-square (described a bit later) for statistical significance tests. They both will use medians and modes (also discussed later) to describe these central tendencies. Recognizing ordinal data for what they are can save many later headaches. Statisticians using ordinal data with statistics requiring interval data sometimes pay a harsh price in terms of their reputation.