SUPPLEMENTS—GOODNESS OF FIT. { 
being given in the second column. Taking the two groups at the 
bottom of the table together and testing goodness of fit, x? is 
found to be 4°11, »” is 5, and P is 0-39. 
TABLE D.— Theoretical Distribution of Totals of x2 (calculated from Independ- 
ence-values) for Pairs of Tables with 4 Rows and 4 Columns, compared with 
the Actual Distribution given by Experimental Tables. 
fant two Expectation. ~~ Observation. 
0-10 68 8 
10-15 270 27 
15-20 329 31 
20-25 20-8 27 
25-30 88 
30- 37 
Total . 
The general theorem that n” must be taken equal to the number 
of algebraically independent frequencies increased by unity applies 
not only to association and contingency tables, but to all cases in 
which the frequencies observed are connected with those expected 
by a number of linear relations, beyond their restriction to the 
same total frequency (Fisher, ref. 76). Thus, if a frequency 
curve has been fitted by the mean and standard deviation, n’ 
should be taken as 2 less than the number of classes: if it has 
been fitted by the first four moments, n’ should be taken as four 
less than the number of classes, 
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