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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$where Sri2ri3r23 =ri2ri3ro3+ri2rur24+ri3ri4rs4 =r\2+r\z-\-r'^iA Sr^i 2r2 3 4 = r2i2r^ 3 4+r^i zr\4+r\\r\3 2ri2ri sr24r 3 4 = ri2ri 3r24r 3 4+ri2ri 4r23r 34+n sn 4r23r24 Sr*23 = rhi -\-rh\+r^zA cr\ .2+3=o-^i (1 - r^i .2+3) = (J\ {rn(Ti<T'i-\-nz(yx(Tz)^ (j\ ((7^2 “f <7^3 “1“2723(72(7$) ] (712(72+713(73)^ (7^2 + <7^3 + 2723 (72 (73 Similarly, -2+3+4= O’*! = (7 (712(72+713(73+714(74)^ <723 +(7^3 +(7^4 + 2 (723(72(73 +724(72(74 +734(73(74) (S7i2(72)=^ S (7^2+ 22723(72(73 It may be easily shown that this last formula is general and holds good for any number of variables. It was attempted to derive a formula for (7j 2345^ but paper and patience were exhausted before it was accomplished. The law governing the coefficents of the terms of the formula for (7j 234 is not sufficiently clear to enable the author to state a general formula applicable to residuals of higher order. Grading of Geometry Test The plan adopted in connection with the algebra test is used in combining the parts of the geometry test. The following table of coefficients of correla- tion (calculated by per cent of unlike signs method) supplies the necessary data: G E' F' G' H' E' .25 F' -.06 .13 G' .22 .19 .06 W .40 .13 .09 .45 Estimated <r’s 3.3 7.4 4.0 9.0 = problem 1; i^' = problems 2, 4, 5, 6; G' = problem 7; = problems 8, 9,10. Problem 3 turned out to be too easy for the group in question, some 98 per cent making a perfect score, so its grading is not used. The surprise in this table is the small negative correlation between G and F'. Because of this small correlation F' is also discarded. For the balance of the data the advantage of the regression method over the average method is negligible, as the following standard deviations show: ^'G. E'G'H' =• 800(7^(5 (7q =.894(7q £'+G+H'~^^G ^G. W+G'-\-W =-^04(j-q ^G. £'+F+G+H' ^ ^G Accordignly the sole measure of the geometry test is taken as the average of E', G\ H'\ =i.e. Gt F'+G'+/7'-mean. 7 3$