342 Method of estimating Bacterial Density 



To test the first point, each hne of Table XI is treated as a 2 x 3 

 contingency table, and the value of -j^ calculated from it. It has been 

 shown (Fisher, 1922(0)) that as in such a table there are two degrees of 

 freedom, x" '^^'ill be distributed, if there is no association, as in Elderton's 

 Tables when n = 3. To show that at no period is there significant 

 association, the values of x^ for the 10 periods are added, and the resulting 

 quantity should be distributed as in Elderton's Tables when w' = 21. 

 Since in two consecutive periods no exceptionally variable sets occurred, 

 these periods have been omitted, and n' is taken to be 17. It will be seen 

 from the table that all the values of x^ are less than 2, except in two 

 periods in which only a single exceptionally variable set occurred. Such 

 cases are evidently beyond the range of effective application of the x^ 

 test, but even including these high values, P = -266, and therefore there 

 is no significant departure from the rule that sets of three, four and five 

 plates show equal proportions of exceptions in all sections of the period 

 of observations. 



This fact confirms the justness of the criterion by which the exceptions 

 have been identified, for any error in the method of identification would 

 naturally show itself in the proportion of cases regarded as exceptions; 

 in the second place it indicates that the cause of exceptional variabiHty 

 is not connected with the causes which lead to the rejection of individual 

 plates (contamination, development of fungi or overgrowth by B. 

 dendroides) , and in the third place it shows that the exceptions are not 

 caused by the exceptional deviation of a single plate, for in this case the 

 proportion of 5-plate sets Avould necessarily be highest. The third 

 conclusion is borne out by an examination of the numbers counted on 

 individual plates, and both it and the second conclusion are more 

 decisively drawn from the contingency table by ignoring the period of 

 occurrences. 



Table XII 



The numbers in the smaller groups are here sufficient to make a 

 satisfactory test, and the value of P, -739, shows distinctly that there is 



