Transforming Truncated Data - Possible? Suggested?

I have now spent countless hours/days looking in statistics texts and performing online searches to determine the appropriate way to treat my current data scenario. And, I have found no answers.:confused:
I am using "high school GPA" data as collected by a university as an independent variable in my dissertation research. At this particular institution, any GPAs above 4.0 (due to advanced placement credit, etc.) that are reported to the institution are truncated in the system to 4.0. Therefore, the distribution of the data now available to me has a significant ceiling effect and deviates from a normal curve. I will use this data in correlational analyses with student-performance in a specific course and with interval-level demographic data. I am interested in the significance of these correlations, so I really should have normally distributed data. Also, all the other independent variables I am using are normally distributed. I need to know what type of transformation would be appropriate for this situation. Or, is there another way (other than transforming the distribution) that I should be handling these analyses?
Any suggestions would be greatly appreciated.:yup:


Super Moderator
I'm not sure that transformation would be useful here. One option could be to use a correlation coefficient that doesn't assume bivariate normality - e.g. a rank-based coefficient like Spearman's rho or Kendall's tau. You could also perhaps use a Pearson's correlation but examine significance via bootstrapping.

There are regression models that are specifically designed for a censored* DV such as the tobit model, but I'm not sure how helpful that is given the variable of concern here is an IV.

*I think that what you actually have here is a censored rather than a truncated variable, but I'm not absolutely sure.