VALIDATION OF MEASURING INSTRUMENTS 177 An alternative formula is ZXY-NM.M, (15) T NEIX—NIL ZV NI where Af. is the mean of the X’s and M, the mean of the Y’s. The X’s and Y’s are gross measurements of each indi- vidual in the two variables being compared. There are several graphic methods of computing the cor- relation coefficient. One of these is Galton’s graphic method, described by Rugg (157, p. 245), which requires the com- putation of the median and the quartiles, or the means and the standard deviations. A scatter diagram is drawn in which the interquartile distance, or the sigma distance, is the same for both variables. Correlation is measured by the closeness with which the line connecting the intersec- tion points of the quartiles or standard deviations (and necessarily passing through the median or mean of the scatter diagram) is approximated by either regression line (the line of the means of the arrays). Another graphic method is given by Yule (233, p. 203): The means of rows and columns are plotted on a diagram, and lines fitted to the points by eye, say by shifting about a stretched black thread until it seems to run as near as may be to all the points. If b,, b, be the slopes of these two lines to the vertical and the horizontal respectively, (16) r=vbb, Other short statistical methods of estimating correlation are given by Yule (233, p. 204) and Brown and Thomson (21, p. 129). Sturges (177) gives a formula for finding » for a whole group if 7 for sections of the group is known. The product-moment formula comes into use when the number of cases is about 30 or more and when the measures are in their original form and not expressed as rank order. It takes into account the absolute value and position of every measure in the series. There are several other methods of measuring correlation