I just found a good answer to this question in another thread in the forum here, therefore, I think this question could be closed. Thanks so much for your help and the clarification about the underlying continuous.
I know that the biserial correlation coefficient (rb) is used when we want to correlate a continuous variables (say, number of activities identified) with a dichotomous categorical variable that has an underlying a continuous dichotomy. By this I mean, for instance, the education level of parents divided in two categories (low / high), each of which contains the following "subcategories":
1) LOW educational level: 6 categories ranging from 1 (never attended school) to 6 (vocational school not finished).
2) HIGH educational level: 4 categories ranging from 7 (vocational school finished) to 10 (graduate degree).
I know I can dummy code these categories, but if I were to, I would end up with 9 new predictors (to be added to the other 10 predictors of the regression). Though I have a large sample (n = 2,643), I am not sure using all the many dummies would be good.
So, the bottom line is: can I use a dichotomous categorical variable that has an underlying continuous dichotomy in a multiple regression?
I want to discover if the educational level of parents (high/low) is a good predictor of the number of activities identified by their children.
Thank you very much.
EDITION TO THE ORIGINAL QUESTION
I guess I should have given a better example. I have dichotomized a continuous variable (a test score) into:
- high (scores between 100 and 50)
- low (scores between 49 and 0)
The reason why I am not using the actual scores is because more than half the sample did not provide their test score results. Based on another category (the type of higher education institution attended), I can estimate their test score to be high or low: a high is a requirement to enter one specific type of institution, so if the student attends that institution, he must have had a high score (above 50) in the test. I hope here the "underlying continuous" is clearer.