106 BINOMIAL AND NORMAL DISTRIBUTIONS Ch. 4 



With the foregoing introduction to the method of rectifying 

 curves the same general process will be applied to the normal r.c.f. 

 curve. As noted earlier, one of the questions which may arise in prac- 

 tice is whether or not a given type of numerical measurement does fol- 

 low a normal frequency distribution. Although the graphic proce- 

 dure to be illustrated is definitely not a rigorous test for normality, 

 it may be sufficient for practical purposes. 



The vertical scale to be employed will have what is called a nor- 

 mal r.c.f. scale marked off in whole percentages. The horizontal 

 scale will be an arithmetic (or uniform) scale for the A. used previ- 

 ously in discussions of the standard normal frequency distribution. 

 Figure 4.55 illustrates the process of obtaining the vertical scale in 

 a manner which is analogous to that illustrated earlier for semi-log 

 paper. It was constructed with the aid of Table III by plotting the 

 normal r.c.f. as a percentage (top scale) directly over the cor- 

 responding A, and then interpolating for the "integral r.c.f. per cent" 

 found on the middle scale of Figure 4.55. This middle scale is the 

 one to be used here in studying the approximate normality of fre- 

 quency distributions. 



Figure 4.55. Determination of the scales for a normal-arithmetic graph. 



As is to be expected after the discussion of semi-log graph paper, 

 it is not necessary to go through the work back of Figure 4.55 be- 

 cause graph paper already exists on which we can do this graphing. 

 Figures 4.56^4. and B were constructed on normal-arithmetic paper 

 to illustrate the way the normality or the non-normality of a dis- 

 tribution affects a graph on such paper. Four distributions are 

 employed in these illustrations: 



(a) Truly normal distribution of Table III; 

 (6) ACE scores of Table 2.01; 



(c) the data on farm acreages in Table A (below) ; and 



(d) the definitely non-normal distribution of Table 4.53. 



