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