XXVI 



Tables for Statisticians and Biometricians 



[I 



We are now in a position to draw our graph, see Diagram (p. xxv), if we deter- 

 mine our divisions between " Very Good " and " Normal " and between " Normal " 

 and "Poor" on the vertical scale. But these are given by A/(T X and a'/<r x respectively. 

 Usually it will be best to use the adjusted values 1/3799 and '6606, but for the 

 actual drawing of the graph, small differences such as '0077 are of little importance. 

 In order to form the graph we take any two lines, one vertical and the other 

 horizontal, to represent our means ; choose any vertical unit to represent a x and 

 any horizontal unit to represent cr v , these may be the same or different to suit 

 convenience. Then all the horizontal partitional lengths are given by (&) in terms 

 of a-y , and the vertical partitional lengths by x/<r x and x' jcr x *. The abscissae of the 

 array means are provided by (n) and the array means themselves by either (g) or 

 (h), as measured from the upper or lower boundary of h. As to the graph itself, 

 it will make little difference whether we use (e) or (/) with the marginal mean 

 instead of (g) or (h) with their adjusted mean respectively. 



We are now in a position to find the regression line, and its slope. We indicate 

 the process below using first (e) and its adjusted mean. We have to remember 

 that all the quantities like x a /a- x in (e) are measured downwards from the upper 

 partition of h, the "Normal" range. Hence x^x T3799 will really be & positive 

 quantity, i.e. a quantity measured upwards. 



Here r' is the unconnected correlation, and therefore the slope of the best fitting 

 line to the four points is 



r'a-xfcTy = 2426cr a; /<7, / . 



We can ascertain this as <r x and cr y are arbitrary lengths we have chosen, and 

 draw our regression line on the graph, r' is the uncorrected correlation, which 

 has to be adjusted by the class-index correction, i.e. r = r'/r z V!Cy ; see Biometrika, 

 Vol. ix. p. 119. 



* Care must be exercised if, as usual, there are more than three vertical broad categories in com- 

 bining them so as to form three suitable ones only. There must always be contents for each array in the 

 three categories. Should this fail with high correlation in an extreme array, we must select for this 

 array another threefold division giving h' instead of h. Then h' must be reduced to h and ultimately 

 to ff x , by aid of the a;-marginal totals. 



t To obtain r' correct to three or four figures, we must take more decimals in (p) than we have in (i). 



