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THE AMERICAN NATURALIST [Vol. XLII 



enee in the results of the parallel sets of experiments is real, 

 thai is. is due to the changing of condition a to ^/ and not merely 

 a chance result of random sampling.' On account of the sta- 

 tistical smallness of such experimental series, coupled with the 

 fact that the results usually deviate widely from the normal dis- 

 tribution of errors, the usual theory of the probable error of a 

 class frequency or of a mean fails to give an adequate answer 

 to the problem. "Student*' has done the great service of pro- 

 viding formulas to cover the case. lie furthermore gives a table 

 of probabilities for series involving four to ten experiments, in- 

 clusive, wherefrom the answer to such a question as that pro- 

 pounded above may be read off at once when the experimental 

 data are at hand. In the original paper concrete illustrations 

 of the use of the table are given, based on published experimental 

 data in the fields of physiology and of agriculture. No par- 

 ticular mathematical knowledge or skill is necessary to use this 

 table and its importance to the experimental worker is obvious. 



On this same topic of probable error Pearson and Lee 4 have 

 recently made an important contribution. While the investiga- 

 tion itself is of a complex mathematical character, the essential 

 point is this: Suppose a number of bodily characters (say six to 

 eight) to be measured in a large sample of a population. There 

 are likely to be a very few individuals out of the whole sample 

 that differ rather widely from all the other individuals. "What 

 is the probability that such outlying individuals do not really 

 (>. €., biologically or genetically) belong to the population from 

 which the sample is drawn, but only happen to get into the 

 sample by accident.' The solution to this problem is what 



Along with these investigations on probable errors is to be 

 included a recent paper of Pearson's 5 on the relation of past 

 experience to future expectation. The nature of the problem 

 discussed may be indicated by an example. Suppose that a 

 sample of 100 individuals out of a population be examined and 

 2 per cent, of these individuals be found to be suffering from 

 some particular disease. "What percentage of a second sample of 

 100 may reasonably be expected to show the disease? The 



