I have a list of marks scored by students in Science (X, between 0 to 100%) and whether they went to college to or not (Y).
High marks in science showed a higher concentration of college admits and low marks had the second best hit rate (students went for Arts degree, etc). Scores in the intermediate range had a lower hit rate. Most students have lower scores in Science.
I divided my sample into
5 bins: 0-10, 10-20, 20-80, 80-90, 90-100.
Found Chi-Sq to be significant.
I transformed these bins into dummy categorical variables and then calculated LR coeff which were significant for 80-90, 90-100(+ives), and 0-10(-ive). I concluded that when scores are higher, the odds of getting admissions are high. When scores are low, it is unlikely that the student would go to college.
Q1. Should I instead use marks as
continuous variable? My main hypothesis is: highest marks result in college admissions, while the lowest marks imply no college admission.
Q2. The data was linear before. However, what if the data was shown in the chart below, do you think categorizing it made more sense? Event hit rates are higher for a particular range and then trail off. Categorizing it in bins helps as I just to have to analyze the performance of that bin (main focus of the study). May be using dummy variables removes the affect of non-linear relationships?