On Fri, 30 May 2008 23:20:35 -0700, Jim Clark wrote: >Hi >Mike you seem to be claiming that if we let all the students with >SATs < 1200 into university this would NOT produce any increase >in the variability in GPAs? Given good reason to think that these >students would score on average at a lower level than students >with SATs > 1200, I fail to see how the standard deviation for >GPAs would stay the same. Or do you believe that scores < 1200 ?on the SAT would be associated with GPAs lat the same average >level as people with SAT scores > 1200?
Consider the two colleges "College S" and "College C": College S only selects people with a combined SAT > 1200. A frequency distribution of GPAs at College S looks like the following: Grade____% of Student 4.00(A)____45% 3.00(B)____50% 2.00(C)____05% 1.00(D)____00% 0.00(F)____00% (Assume that College S has a policy which allows students up to the 12th week of a 15th week semester to drop a course without it impacting one's GPA) College C only selects people with a combined SAT > 1200. and its frequency distribution of GPAs looks like thefollowing: Grade____% of Student 4.00(A)____15% 3.00(B)____30% 2.00(C)____35% 1.00(D)____15% 0.00(F)____05% The SD for College S has to be smaller than that for College C because it has restriction of range. For College S, if persons with SAT <1200 were allowed in, the GPA variance is likely to increase (or if the "12 weeek drop rule" is eliminated). For College C, since all values/grades in the range of possible values are being used, the addition of persons with SAT <1200 cannot increase the variance of GPAs unless they come from a non-normal population of GPA scores (e.g., a U-shaped distribution would change the variance above because the U distribution would include more extreme GPA values which would inflate the variance). Indeed, since the entrie range of values of GPAs are already in use, what HAS to happen to the variance of GPAs if we add more students? Variance(GPA) = Sum of Squares(GPA)/[N(Subjects) - 1] For College C, as the denominator increases, what happens to the variance of GPAs? It has to decrease. In contrast, For College S, if students with SAT <1200 are included and the range of GPAs increases, then the variance has to increase. >Or perhaps that faculty would modify their standards >so that everyone fell into the same distribution as at present ... hardly a >compelling argument for not using SATs. I'm not sure I understand your point [however, if one wants to argue that College S suffers from severe grade inflation, I'd agreed and say that they should do something about it] but I'm not arguing for either the use or non-use of SATs. In some cases SATs might be useful (what does one make of the student who has a combined SAT=1600 but a HS-GPA= D? What does one make of a student who has a combined SAT=700 but a HS-GPA= A?). Rather, I'm curious about the process of "correcting" correlation coefficients. I can understand the rationale if both X and Y are restricted (as seems to be the case with College S above) but it seems to me that the standard correction might be problematic when only one variable has range restriction, as in the case of College C. -Mike Palij New York University [EMAIL PROTECTED] --- To make changes to your subscription contact: Bill Southerly ([EMAIL PROTECTED])
