All you want to know about discrete variables

Todd Murphy inquired:

Q. 1) I'm planning to test how race affects attitude toward abortion, seeing if the gap between whites and black is closing. I would be controlling for religiosity, gender, and socioeconomic status (income and education level). All of these are discrete variables, which according to our class today means I cannot use regression.

A. Not quite. The dictionary definition of "discrete" is "separate and distinct." So a discrete variable, as contrasted with a continuous variable, has distinct categories. A discrete variable with only two categories is a dichotomy. If it has more than two, it is a polychotomy.

Discrete variables also are of two types: unorderable (also called nominal variables) and orderable (also called ordinal).

A dichotomy (such as gender) can always be interpreted as ordinal. (For example, one respondent has more "femaleness" than another.) So a dichotomy can be used in regression analysis, but only as a independent variable. As an independent variable, a dichotomy can be best interpreted when converted into a dummy variable--coded 0 (no femaleness) or 1 (has femaleness). Recall that I used south in exactly this way in my regression analysis of how states votes for Reagan in 1984.

Moreover, ordered polychotomies (ordinal variables) can be used in regression analysis provided that you assume (as is usually done) that there are equal intervals between the discrete categories. This assumption allows you to compute a mean, from which all blessings (i.e., squared deviations) flow.

Q. However, in the research paper handout you mention using "thermometer" variables for regression analysis. Aren't these thermometer variables also discrete? It seems that even in your example today "South" and "Non-South" are discrete even after you convert them to dummy variables (1 and 0). Did you mean that we cannot use nominal variables?

A. Yes, the thermometer variables are discrete, but they are orderable, which makes them suitable for regression analysis, either as independent or dependent variables. The key attribute is ordinality (magnitude).

 Q. 2) If I cannot use multiple regression, can I use Crosstabs or Chi-square instead? In other words will it affect my grade if I stick with what I have and use these methods or should I change my question so that I can use multiple regression? For example, I could investigate how abortion attitudes affect voting and convert all the independent variables to dummy variables.

A. You could use CROSSTABS, but you won't learn as much. Use regression instead.