R. A. Fisher, H. G. Thornton, and W. A. Mackenzie 349 



Table XVII 



In all these groups where medium A is used the variance is distinctly 

 subnormal after 7 days, but is apparently normal after 12 days. With 

 medium B, the variance is normal at both counts. Now the sets of 9 and 

 of 20 plates were parallel dilutions of the same sample, and the mean 

 count from medium A was only 75 per cent, of that obtained on medium 

 B. The abnormahty of medium A was afterwards traced to the tempera- 

 ture at which it was filtered, a technical detail w^hich has an important 

 bearing on the abihty of the medium to support bacterial growth 

 (Thornton, 1922(11)). 



In the comparison given by Thornton (ii) of the two batches of 

 medium, identical save that one was filtered at 50° C. and the other at 

 100° C, 10 plates being prepared from each, the former gave a mean 

 count 79 per cent, of the latter; in this case also the defective medium 

 showed subnormal variance giving a value x~= 3-2 (after eight days), 

 whereas the normal medium gave a value 10-3. The former would only 

 occur once in 22 trials by chance, and therefore represents clearly a 

 subnormal condition. 



Whatever the biological explanation of subnormal variance may be, 

 it is therefore sometimes indicative of a serious error in the value of the 

 mean. In this respect it is a danger signal which cannot be disregarded. 

 When a set of plates shows excessive variability no one will be tempted 

 to lay too much stress upon their mean ; it is obvious in such cases that 

 there is a large probable error, and it has been seen (Section 8), that 

 there will usually be also a considerable systematic error in such cases. 

 A set of plates with abnormally low variance on the other hand, may 

 appear to be particularly good data, although, as w^e have just seen, this 

 tvpe of abnormality is also indicative of large systematic errors. It is 

 therefore of practical importance that such departures from the Poisson 

 distribution should be detected, whenever they occur. Since subnormal 



