Research Design and Statistical Consulting
George M. Diekhoff, Ph.D.

# Why a Dichotomously-Scored Nominal Scale Variable is Really a Ratio Scale Variable

Why is it that a dichotomously-scored (two-category) nominal scale variable can be used as a predictor in statistical procedures like multiple regression and discriminant analysis? (Yes, discriminant analysis too, notwithstanding statements from lots of authors that this method requires continuous predictor variables, i.e., interval or ratio scale variables.) It’s because a dichotomously-scored nominal scale variable (often called a binary variable, because the only two scores are 0 and 1) is actually a ratio scale variable. How can it be that what appears to be a 2-category nominal variable is actually a ratio scale variable? Here’s your answer. A ratio variable is one in which a score of 0 = none of the attribute and each successive score point,–1, 2, 3, …–represents one more fixed-sized unit of the attribute being measured. Now let’s take the dichotomous variable, “Military Veteran,” with two categories coded no = 0 and yes= 1. Someone with no military service is scored 0 because they possess none of the attribute being measured. Someone with military service is scored 1 because they possess one unit of military service. There don’t happen to be any cases scored 2, 3, 4 or higher because we don’t need those values. We just need 0 for none and 1 to represent those individuals with one “fixed size unit” of military service. But lack of need for scores above 1 doesn’t somehow disqualify a binary variable from being ratio scale. Any dichotomous variable can therefore be treated as a nominal variable or as a ratio variable, whichever is more convenient at the moment.

s