Question

Why is it crucial to know the level of measurement (nominal, ordinal, metric) when conducting significance testing? What flaw is evident with SPSS in this regard?

Answer 1

1) Nominal scales are used for labeling variables, without any quantitative value. A variable can be treated as nominal when its values represent categories with no intrinsic ranking; for example, Gender. One cannot rank Gender as male/female is superior.

2) Ordinal variables are same as Nominal but the measurements have a significant defining order. Example: Grades obtained by students in a test. In general A is superior to B and B is better than C and so on. Which is to say that there is a definitive order to the data.

3) Metric has two sub categories namely, Ratio and Interval. Unlike Ordinal and Nominal measurements they are quantitative in nature. Ratio has a fixed origin(zero exists) and fixed distance whereas Interval only has a fixed distance.

We need to know exactly what level of measurement is appropriate for our data in order to conduct appropriate statistical tests. Chi-square tests of independence are to be used for nominal level data. For continuous metric variables Anova is appropriate. Nominal variable can only be counted so we cannot find mean or standard deviation ; Ordinal variable can be counted but since order exists we can find the median. Interval and ratio are quantitative variables. most quantitative analysis can be conducted on these.

Statistical measurements only make sense when used appropriately. If we consider rank obtained by students in an exam. They are noted as 1,2,3,..,20. This is an ordinal measurement since observations are categories with some value attached to them(rank 1 is better than rank 2) but not metric because rank 1 does not imply he is 20 times better than rank 20. Suppose if we treated this ordinal data as metric and found the mean for hypothesis testing. Mean would 9.6. But a rank of 9.6 does not exist and does not make sense. Because we did not know the level of measurement or used it incorrectly our test would result in result with statistical value.

In SPSS if your ordinal data is in form of numbers such as rank, gender coded as 1 or 0 and you do not specify the variable as Ordinal while entering, than SPSS treats them as Metric.