How do a do a correlation for SAT test results from my students?

Question

I have an SPSS database with about 2000 students who took English Comp this past academic year. I also have their SAT scores. The correlation between the two is .381, which is significant at the .01 level. But how do use that to predict what a student with an SAT of X will get in English Comp? We are trying to determine if our SAT cut-score for entrance into English is too high or too low.

Answer 1

Yes there is a correlation, but with r=.381, there is also a lot of scatter in your data. Make a scatter plot, and see what the relationship really looks like. Are there students that scored poorly on the SAT but still did well? Do you really want to exclude those students in the future? How about using a regression analysis with SAT and GPA used as predictors? You might want to go to your school's psychology department and ask to speak to a prof who is good with stats - the psychologists have experience with how to statistically interpret test scores.

Answer 2

Look at your current cut-score, and see how much Type 1 and 2 errors it generated...

How many students pass it, yet fail English Comp? That's a Type 1 error. You can reduce this by raising the cut.
How many students fail the SAT, yet succeed English Comp? That's the Type 2 error. You can reduce it by lowering the cut. It's all about striking the right balance between the two.

... But wait! do you even have this information? Since the Type 2's didn't make the SAT cut, how can you have an English comp score for them?

Answer 3

You'll need to make a scatter graph. Make one axis English Comp grades and then make the other axis SAT score. Plot the points for the students. Find a percentage grade for Eng Comp that you find acceptable, and see what students that received that grade got on the SAT. Then drop your expectations one grade so that you can give students with extenuating circumstances a chance to succeed.

As was said above. A math teacher would be a helpful aid in this process, as probably would someone good with computers. 2000 points is a lot to plot by hand.

Answer 4

Run a linear regression on the data with English grade as the y variable and SAT score as the x variable. The slope this regression yields will be the ratio of English grades to SAT scores, biased by the intercept value. the "r" value of the regression (calculated separately) will tell you how well the projection fits tha data |r| > 0.9 is generally considered a good fit.

Answer 5

Consult a math teacher