The essentials of mental measurement . resents the law ofchange of mean y-value with increase of a; and gives the most probable * The true oentroid ordinate is slightly nearer the denser part of the scatter diagram,here slightly towards the right of PM. The correction is made later by means of Sheppardsformulae (see above, p. 84). •f The means have been placed on the straight line for the sake of convenience ofexposition. Actually, they will occur irregularly on either side of it, and AB will be thebest fitting straight line, determined by an application of the Method of Least next
The essentials of mental measurement . resents the law ofchange of mean y-value with increase of a; and gives the most probable * The true oentroid ordinate is slightly nearer the denser part of the scatter diagram,here slightly towards the right of PM. The correction is made later by means of Sheppardsformulae (see above, p. 84). •f The means have been placed on the straight line for the sake of convenience ofexposition. Actually, they will occur irregularly on either side of it, and AB will be thebest fitting straight line, determined by an application of the Method of Least next chapter. 7—2 100 CORRELATION [PT, II value of y for any particular value of x. If the line is straight or ap-proximately straight the regression is said to be linear, and theequation to the line is y-y = r^ (x- x), where x, y are the mean values of all the xs and ya respectively (notthe means of the arrays just mentioned), ctj, (t^ are the standarddeviations of the xs and «/s respectively, and r is the coefficient meeh. memory Kg. 16 Thus if 20 is the mean value of the mechanical memory of the group,30 „ „ „ „ general intelligence of the group, 4 „ „ standard deviation for mechanical memory (ct^),7 „ „ „ „ „ general intelligence (a^), and, finally, -6 is the value of r; then the most probable measure of thegeneral intelligence of a child whose mechanical meinory is representedby, say, the value 14, is given by the equation 2/ - 30 = -6 X f (14 - 20), CH. V] INTRODUCTION TO CORRELATION 101 whence y = 237. This value is the average of an array of possiblevalues, whose standard deviation = 5-6. It will be proved in the next chapter that where x and y are deviations from the mean (not absolute values asassumed above), and S ( ) indicates summation, S (xy) = x^y^ + x^^ + x^y^-\r ... + Xj^y^^, where N is the total number of cases (children measured). It is important to note that by starting from y instead of from x,alid determining the
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