On Sat, 31 May 2008 08:15:38 -0700, Jim Clark wrote: >>> "Mike Palij" <[EMAIL PROTECTED]> 31-May-08 7:19:05 AM wrote: >>> >>Consider the two colleges "College S" and "College C": >>[NOTE: Deleted portion on College S reinserted below:] >>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)
Comment: The choice of frequencies for the grades above is not accidental, indeed, a Google search of "grade inflation" and the names of the Ivy League schools, one will see that it had become de facto policy at a number of schools NOT to give D or F grades and even limit the number of C grades. See for example: http://media.www.dailynorthwestern.com/media/storage/paper853/news/2001/05/03/UndefinedSection/Doctoring.The.Grade-1906657.shtml or http://tinyurl.com/6now78 What would correction for restriction of range mean if in fact the only values GPAs can take are in the range 2-4, with 3-4 predominating? Obviously, students accepted with SATs less than 1200 accepted to these schools should do no worse than a "C" regardless of how poorly they do (NOTE: Stanford has a policy for decades of not giving "F" grades, so some places have institutional forces operating to keep grades above a certain point, thus, affecting correlations using those grades). Palij continued: >>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% >> >>... >>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? Jim Clark writes in response: >No, if the distribution of the added students includes more gpas of 0 and 1, >and fewer gpas of 3 and 4 (e.g., below), then the SD of the combined >distribution will be greater. Clearly, this would not be true for the Ivy League schools identified above since there would be no increase in grades in the range 0-3. >Hypothetical distribution for SAT < 1200 > >Grade____% of Student >4.00(A)____5% >3.00(B)____15% >2.00(C)____35% >1.00(D)____30% >0.00(F)____15% > >SD depends on the proportion of observations at each level, not simply >on whether or not any students occur at that level. If you assume that GPA is normally distributed, then the percentages of grades below a grade of 2.00 (C) should be mirror images of the percentages of grades above it. The percentage of 0.00 (F) grades should be roughly equivalent to the percentage of 4.00 (A) grades. You seem to be implying that expanding the range of SAT scores will inflate the lower grades more than the upper grades but this just doesn't make any sense unless one assumes that the distribution of GPAs is something different. What distribution do you have in mind? Also, note the following, assume that SAT and GPA are bivariate normal distributions and perfectly correlated. In this situation, persons with SAT > 1200 will only get grades of B and above. Expanding the range of SAT will then fill in the other grade levels (e.g., combined SAT=100, GPA=2, etc.) and we would expect to see a normal distribution of GPAs. Even in this situation where SAT perfectly predicts GPS, there should be no inflation of grades at the lower end (i.e., they should be mirror image of the percentages of the higher grades). Because the correlation is not perfect and in some situations there may be no significant correlation between SAT and GPS, the real question is what is the population distribution for the GPAs. Bivariate normality for SAT and GPAs is a standard assumption because one can't determine whether the sample correlation is statistically significantly different from zero. Do you disagree with this assumption? -Mike Palij New York University [EMAIL PROTECTED] --- To make changes to your subscription contact: Bill Southerly ([EMAIL PROTECTED])
