Educational guidance : an experimental study in the analysis and prediction of ability of high school pupils / by Truman Lee Kelley.

Truman Lee Kelley

Date:: 1914

Credit: Educational guidance : an experimental study in the analysis and prediction of ability of high school pupils / by Truman Lee Kelley. Source: Wellcome Collection.

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$From the accompanying data: H. . = .450 I. a. - .024 a. ^Con Cons.+ .305 —5— Emo. i. ^Emo. i. -.287-^ Exp. ‘Exp. I. a. Cons. H .381 .290 I. a. .61 Cons. Emo. i. Exp. Emo. i. .390 .61 .66 Exp. (t’s .245 .82 .55 .59 ‘l.a. ‘Confl. ‘Emo. i. ‘Exp. rjj Ti^ = . 46 (Population = 68) t. e. Grading op the Algebra Test Having the gradings for the various problems in the algebra test, it is impossible to say, a 'priori, with any assurance, which are the most significant and which are the least so. The common procedure in a case like this is to call them all of equal importance and add or average. Whether such a procedure results in getting out of the data all that is in them or not, is a fit subject for in- vestigation. The question is simply this—does the magnitude (grade of prob. 1+ grade of prob. 2 • • • + grade of prob. 14) correllate as highly with the algebra grade received at the end of the school year, as the magnitude (Ci X grade of prob. 1+C2Xgrade of prob. 2+ • • • Cu Xgrade of prob. 14) where C\, C2, • • • Cu have the best values possible. Of course the second magnitude would result in the higher correlation, or, what amounts to the same thing, the stand- ard deviation of the residuals in the second case is smaller than the standard deviation of the residuals in the former case. Using the notation given by Yule, this is to say that ‘a. 1, 2, 3, 4,5, 6, 7. 8. 9, 10, 11, 12, 13, 14 ^ ‘a. 1+2+3+4+5+6+7+8+9+10+11+12+13+14 (A = grade in algebra course, 1 = grade of first problem, etc.) It is manifestly impractical to attempt to calculate cr^ 2,3,4,5, 6, 7, 8,9,10,11,12,13,14, approximation to this may be obtained if the problems 1, 2, • • • 14 that have about the same standard deviations, and that are correlated to about the same extent with A, and are correlated with each other to approximately an equal extent, are grouped, thus reducing the variables to such a number that the calculation is feasible. In attempting to fulfill these conditions, problems 1-4, 8-11, were grouped, as were also problems 6, 13, 14, giving groups A’, B', C', respectively. The question then is to determine ‘a A'+B'+C'- Formulae giving these expressions (derived in the next section) are as follows: A'B'C 'a. A+B’+C 7 — O' 1 1 — '^r^A'B' +2 ] 1 - 2cr A' ~^^^‘’’a'B'^A'^B'$