The only modification needed when the parameters 

 are estimated from the sample itself is a reduction in the 

 number of degrees of freedom by one for each parameter 

 that is estimated from the sample. For example, if a 

 gaussian distribution is assumed and the mean and standard 

 deviation are estimated from the sample, then the number 

 of degrees of freedom are (^-l)-2, where k is the number 

 of groups. 



CUMULATIVE PROBABILITY PLOTS 



The use of cumulative probability paper was also in- 

 vestigated. On this type of plot a gaussian distribution is 

 represented by a straight line. The data are normalized 

 and plotted, and deviations from a gaussian distribution are 

 seen as departures from a straight line. The data are the 

 p. (£ . ) used for the method of moments where £ . is the mid- 

 point of Ax. = x -x . . The points plotted are the normalized 

 cumulative sums, i.e., the first point is 





the second point is 



22, etc. 



S W 



The range used is from x - -3. 00 to x - +3. 00 so 

 that a gaussian curve resembles figure 8. The curve de- 

 viates from a straight line at the ends because of the small 

 amount of area (0. 27 per cent) outside three standard de- 

 viations. This curve should be used for comparison with 

 the data instead of the straight line. 



24 



