CLASSIFYING MEASUREMENTS
Whether you use a ready-made measure or create your own, you always need to know what class of measurement you have made. How you classify a measurement will have an impact on the kinds of numerical analyses you can perform on the data later on. Stevens (1946) proposed that all measurements can be classified as being of one of four types. This system has become dominant within psychology and no methods textbook would be complete without describing it.
Categorical measures:
Categorical measurements (variables), also called nominal measurements, reflect
qualitative differences rather than quantitative ones. Common examples include categories such as yes/no, pass/fail, male/female or Conservative/Liberal/
Labour. When setting up a categorical measurement system the only requirements
are those of mutual exclusivity and exhaustiveness. Mutual exclusivity means that each observation (person, case, score) cannot fall into more than one category; one cannot, for example, both pass and fail a test at the same time.
Exhaustiveness simply means that your category system should have enough categories for all the observations. For biological sex, there should be no observations (in this case people) who are neither male nor female.
Ordinal level measures:
Ordinal measurement is the next level of measurement in terms of complexity. As before, the assumptions of mutual exclusivity and exhaustiveness apply and cases are still assigned to categories. The big difference is that now the categories themselves can be rank-ordered with reference to some external criterion such that being in one category can be regarded as having more or less of some underlying quality than being in another category. A lecturer might be asked to rank order their students in terms of general ability at statistics.
They could put each student into one of five categories: excellent, good, average, poor, appallingly bad.
Clare might fall into the ‘excellent’ category and Jane into the ‘good’ category.
Clare is better at statistics than Jane, but what we do not know is just how much better Clare is than Jane. The rankings reflect more or less of something but not how much more or less.
Most psychological test scores should strictly be regarded as ordinal measures.
For instance, one of the subscales of the well-known Eysenck Personality Questionnaire (Eysenck & Eysenck, 1975) is designed to measure extroversion. As this measure, and many like it, infer levels of extroversion from responses to items about behavioral propensities, it does not measure extroversion in any direct sense. Years of validation studies have shown how high scorers will tend to behave in a more extroverted manner in the future, but all the test can do is
rank-order people in terms of extroversion. If two people differ by three points on the scale we cannot say how much more extroverted the higher-scoring person is, just that they are more extroverted. Here the scale intervals do not map directly on to some psychological reality in the same way that the length of a stick can be measured in centimeters using a ruler. The fundamental unit of measurement is not known.
Since many mental constructs within psychology cannot be observed directly, most measures tend to be ordinal. Attitudes, intentions, opinions, personality characteristics, psychological well-being, depression, etc. are all constructs which are thought to vary in degree between individuals but tend only to allow indirect ordinal measurements.
Interval level measures:
Like an ordinal scale, the numbers associated with interval measurement reflect more or less of some underlying dimension. The key distinction is that with interval level measures, numerically equal distances on the scale reflect equal differences in the underlying dimension. For example, the 2°C difference in temperature between 38°C and 40°C is the same as the 2°C difference between 5°C and 7°C.
Ratio scale measures:
Ratio scale measurement differs from interval measurement only in that it implies the existence of a potential absolute zero value. Good examples of ratio scales are length, time and number of correct answers on a test. It is possible to have zero (no) length, for something to take no time, or for someone to get no answers correct on a test. An important corollary of having an absolute zero is that, for example, someone who gets four questions right has got twice as many questions right as someone who got only two right. The ratio of scores to one another now carries some sensible meaning which was not the case for the interval scale.
The difference between interval and ratio scales is best explained with an example. Suppose we measure reaction times to dangers in a driving simulator. This could be measured in seconds and would be a ratio scale measurement, as 0 seconds is a possible (if a little unlikely) score and someone who takes 2 seconds are taking twice as long to react as someone who takes 1 second. If, on average, people take 800 milliseconds (0.8 seconds) to react we could just look at the difference between the observed reaction time and this average level of performance. In this case, the level of measurement is only on an interval scale.
Our first person scores 1200 ms (i.e. takes 2 seconds, 1200 ms longer than the average of 800 ms) and the second person scores 200 ms (i.e. takes 1 second,
200 ms more than the average). However, the first person did not take 6 times as
long (1200 ms divided by 200 ms) as the second. They did take 1000 ms longer, so the interval remains meaningful but the ratio element does not.
True psychological ratio scale measures are quite rare, though there is often confusion about this when it comes to taking scores from scales made up of individual problem items in tests. We might, for instance, measure the number of
simple arithmetic problems that people can get right.We test people on 50 items and simply count the number correct. The number correct is a ratio scale measure since four right is twice as many as two right, and it is possible to get none right at all (absolute zero). As long as we consider our measure to be only an indication of the number correct there is no problem and we can treat them as ratio scale measures.
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