Is it okay to use dichotomous variables in procedures like regression or path analysis which assume interval data?
If one assumes the dichotomy collapses an underlying interval variable, there will be more distortion with dichotomization than with an ordinal simplification. Dichotomization of continuous variables attenuates the resulting correlations. Moreover, the cutting points used in the dichotomization will affect the degree of attenuation. If the underlying correlations are high (over .7), the cutting points will have a non-trivial effect. Note also that categorical variables with similar splits will necessarily tend to correlate with each other, regardless of their content (see Gorsuch, 1983). This is particularly apt to occur when dichotomies are used. The correlation will reflect similarity of “difficulty” for items in a testing context; hence such correlated variables are called difficulty factors. The researcher should examine the factor loadings of categorical variables with care to assess whether common loading reflects a difficulty factor or substantive correlation. Nonetheless, it is
