Scales of Measurement
“Scales of measurement” refers to how your variables are measured. For example, age is a continuous variable because there is no separation between one moment and the next as a person ages. But number of children in a family and gender are categorical variables because there is that separation. After all, no family has 1.5 children. Its either 1 child or 2 (or more, of course), and gender is self-explanatory.
We also have subtypes of these two broader types of variables. When measuring categorical variables, we have either nominal or ordinal scales of measurement. Nominal variables are simply categories with names, that cannot be split into fractions, and they have no order to them. Gender is a nominal variable, and so is ethnicity. These are commonly found demographic questions on a questionnaire. Ordinal variables are also categories with names, that cannot be split into fractions, but they have a particular order. Year in school would be an ordinal variable, as one must complete the 8th grade before beginning the 9th grade. Studies that explore consumer preferences use ordinal measurement, also known as ranking, when they ask people to rate how well they like certain products. For example, out of these three colas which one is your favorite? Which is your second choice, and which is your third?
When measuring continuous variables, we have either interval or ratio scales of measurement. An interval measurement occurs in a certain order, but we find no separation between the choices and you might find negative values. For example, temperature measured in degrees Fahrenheit is an interval variable as it can be split into fractions (it could be 22 ½ degrees outside) and it can have negative values (it could be -22 degrees outside). A ratio variable can also be split into fractions, but it cannot have negative values. For example, your neighbor cannot mow his/her lawn -1 time a week. The lowest value of mowing is 0 times per week, and this is known as a true zero point (meaning a total lack of).
So who cares, right? Well, you do when it comes to choosing the best type of analysis for your data. Among other things, the way your variables are measured influences the type of analysis you will choose. If part of your goal is to find out whether two variables are related, there is more than one way to arrive at this answer. Here is what I mean. What if our fictitious dentist wants to know whether the friendliness of his receptionist is related to the level of anxiety his new patients experience. Both “friendliness” and “anxiety” are continuous ratio variables, so this would require a Pearson’s r correlation. But what if instead this dentist wants to know if light or dark colored uniforms influence how professional the patients perceive his staff to be. Color of uniform is a nominal variable, while level of professionalism is a ratio variable. This situation would still require a correlation, but a different type. In this case, since one variable (color) is dichotomous, and the other is continuous, we would conduct the point-biserial correlation.
Regardless of your research situation, knowing the scale of measurement for your research variables is an important consideration in deciding what the best analysis would be to answer your research question.