Re: Measure of Association Question.
On Fri, 28 Dec 2001, Petrus Nel wrote: > I require some advice regarding the following: One set of variables is > the grades obtained by students for different high school subjects > (i.e. the symbols candidates obtained such as A, B, C, D, etc. for each > subject). The other set of variables are the scores obtained for a > college level subject (i.e. no symbols, just their percentages > obtained). I want to determine the correlation between their grades > for different high school subjects (A, B, C, D, etc.) and their > percentage scores for a college level subject. Why do you want to? _Nobody_ just wants correlation coefficients: there's always something more that is desired. > The grades obtained for their high school subjects were coded on the > questionnaire as follows - 1=3DA, 2=3DB, 3=3DC, 4=3DD, 5=3DE, 6=3DF. > I`ve entered the data for the grades as 1,2,3, etc. to indicate the > grade (category) and the percentages (as the other variable) into SPSS. > How do I proceed? What follows assumes that the answer to "Why?" implies that correlation coefficients are part of the desiderata, for good reason(s). First, recompute each HS subject grade: e.g., NEWGRADE = 7 - OLDGRADE so that both grades and percentages are coded in the same direction (higher values = better performance); else your correlation coefficients will be negative where the relationship is positive, etc. Second, produce scatterplots of grade vs. percentage, grade vs. grade, and percentqage vs. percentage, for all pairs whose correlations are of interest: so that you can properly interpret correlation coefficients when you get them (and can be prepared to deal with nonlinear relationships, should there be any obvious from the plots). For this purpose one needn't be too fancy: character plots will do, high-resolution plots won't tell you anything more unless there are some rather odd nonlinearities among the relationships. Third, invoke SPSS's CORREL routine to calculate all pairwise zero-order correlation coefficients. Fourth, proceed with whatever your answer to "Why?" implies about subsequent analyses and interpretation. -- DFB. Donald F. Burrill [EMAIL PROTECTED] 184 Nashua Road, Bedford, NH 03110 603-471-7128 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Measure of Association Question.
Good advice on all counts. I'm curious about where you want to take this 'correlation' if found. A college admissions person could use the relationship (in the form of a regression equation), if any, to predict the score on the 'college level subject' for those students who were unable to take such a course in HS, or to predict the performance on the college level subject, once admitted. But correlation & regression eq. do not produce the same end result, especially where the independent variable contains significant measurement variance. Donald Burrill wrote: > On Fri, 28 Dec 2001, Petrus Nel wrote: > > > I require some advice regarding the following: One set of variables is > > the grades obtained by students for different high school subjects > > (i.e. the symbols candidates obtained such as A, B, C, D, etc. for each > > subject). The other set of variables are the scores obtained for a > > college level subject (i.e. no symbols, just their percentages > > obtained). I want to determine the correlation between their grades > > for different high school subjects (A, B, C, D, etc.) and their > > percentage scores for a college level subject. > > Why do you want to? _Nobody_ just wants correlation coefficients: > there's always something more that is desired. > > > The grades obtained for their high school subjects were coded on the > > questionnaire as follows - 1=3DA, 2=3DB, 3=3DC, 4=3DD, 5=3DE, 6=3DF. > > I`ve entered the data for the grades as 1,2,3, etc. to indicate the > > grade (category) and the percentages (as the other variable) into SPSS. > > How do I proceed? > > What follows assumes that the answer to "Why?" implies that correlation > coefficients are part of the desiderata, for good reason(s). > > First, recompute each HS subject grade: e.g., > NEWGRADE = 7 - OLDGRADE > so that both grades and percentages are coded in the same direction > (higher values = better performance); else your correlation coefficients > will be negative where the relationship is positive, etc. Translating letter grades into a number implies that the letters were ordinal categorical data, and further, that they have equal increments (distance between them). Inasmuch as the grades came from a numerical scale, typically with 60 = D, one could argue that this translation is fully valid. HOWEVER As I recall, a correlation analysis assumes the data is Normally distributed. Grades usually ain't, and the upper limit of 'A' forces the issue. If you wish to compute confidence intervals, this may come back to haunt you. Nonetheless, good luck on this project, and don't forget Prof. Burrill's next urging, that you look carefully at some scatter plots. Those may tel you as much or more than your calculations. > > > Second, produce scatterplots of grade vs. percentage, grade vs. grade, > and percentqage vs. percentage, for all pairs whose correlations are of > interest: so that you can properly interpret correlation coefficients > when you get them (and can be prepared to deal with nonlinear > relationships, should there be any obvious from the plots). > For this purpose one needn't be too fancy: character plots will do, > high-resolution plots won't tell you anything more unless there are some > rather odd nonlinearities among the relationships. > > Third, invoke SPSS's CORREL routine to calculate all pairwise zero-order > correlation coefficients. > > Fourth, proceed with whatever your answer to "Why?" implies about > subsequent analyses and interpretation. > > -- DFB. > > Donald F. Burrill [EMAIL PROTECTED] > 184 Nashua Road, Bedford, NH 03110 603-471-7128 > > = > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > = -- Jay Warner Principal Scientist Warner Consulting, Inc. North Green Bay Road Racine, WI 53404-1216 USA Ph: (262) 634-9100 FAX: (262) 681-1133 email: [EMAIL PROTECTED] web: http://www.a2q.com The A2Q Method (tm) -- What do you want to improve today? = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Measure of Association Question.
[EMAIL PROTECTED] (Petrus Nel) wrote in message news:<000201c18fe2$f73aeee0$ed9e22c4@oemcomputer>... > I require some advice regarding the following: One set of variables is > the grades obtained by students for different high school subjects (i.e. > the symbols candidates obtained such as A, B, C, D, etc. for each > subject). The other set of variables are the scores obtained for a > college level subject (i.e. no symbols, just their percentages > ... > The grades obtained for their high school subjects were coded on the > questionnaire as follows - 1=A, 2=B, 3=C, 4=D, 5=E, 6=F. > ... > How do I proceed? Simpler answer: First, change the coding to 1=F, 2=E, 3=D, 4=C, 5=B, 6=A. In the US at least there is no 'E'; if so, the correct coding would be 1=F, 2=D, 3=C, 4=B, 5=A. If the latter coding is used, calculate the Spearman rank correlation between the grade in a given high school course and the college score. If the former coding is used, you can use either the Pearson correlation or the Spearman rank correlation; the Pearson correlation would probably be better. More complex answer: The approach above ignores the fact that within each letter grade there is variation--e.g., all students who get a 'B' are not at the same level. Further, there is censoring at the upper end and lower ends of the scale--e.g., no matter how well a person does, the highest grade they can get is an 'A'. The polyserial correlation can account for this. The polyserial correlation estimates what the correlation of grade and score would be if grades were measured on a continuous scale. An assumption is that there is a bivariate normal distribution between (1) the continuous latent variable of which grade is a manifest representation and (2) the percentage score. The polyserial correlation is related to the polychoric correlation. For information about the polychoric correlation, see: http://ourworld.compuserve.com/homepages/jsuebersax/tetra.htm Drasgow F. Polychoric and polyserial correlations. In Kotz L, Johnson NL (Eds.), Encyclopedia of statistical sciences. Vol. 7 (pp. 69-74). New York: Wiley, 1988. I don't know if SPSS will calculate the polyserial correlation--the last I heard it did not. If not, the polyserial correlation can be calculated with the program PRELIS, which is distributed with LISREL. Many universities have copies of LISREL/PRELIS. If you are interested in comparing to see which high school classes best predict college scores, then, as a practical matter, I would expect you would draw the same conclusions regardless of whether you used the Pearson, the Spearman, or the polyserial correlation coefficients. Good luck! John Uebersax, PhD (805) 384-7688 Thousand Oaks, California (805) 383-1726 (fax) email: [EMAIL PROTECTED] Agreement Stats: http://ourworld.compuserve.com/homepages/jsuebersax/agree.htm Latent Structure: http://ourworld.compuserve.com/homepages/jsuebersax Existential Psych: http://members.aol.com/spiritualpsych Diet & Fitness:http://members.aol.com/WeightControl101 = Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =
