PROBABLE SIGNIFICANCE OF STATISTICAL CONSTANTS. 87 



parable series of measurements. These means differ by a 

 certain amount. The difference is found to be, let us say, 3.2 

 times as large as the probable error of the difference. Is one 

 mean significantly larger than the other? Or, put in another 

 way, what is the probability 'that the difference arose purely as 

 a result of random sampling (as a result solely of chance) ? 

 Under the argument 3.2 in the table we find the probability of 

 the occurrence of a -deviation as great or greater than this to 

 be 3.09. This means that in every 100 trials a deviation of this 

 size or greater would be expected to occur, as result of chance 

 alone, (the error of random sampling), 3.09 times. Or, from 

 the next column, the odds against the occurrence of a diiference 

 as great or greater than this in proportion to its probable error, 

 are 31.36 to i, if chance alone were operative in the determina- 

 tion of the event. If one wants to call this "certainty" he has 

 a perfect right to do so. The table merely defines quantitatively 

 his particular conception of certainty. 



It will be noted that after the ratio, deviation-*- P. E., passes 

 3.0 the odds against the deviation increase rapidly, reaching a 

 magnitude at 8.0 which is, practically speaking, beyond any 

 real power -of conception. We have started the table at i.o, 

 because this is the point where the chances are even. A devia- 

 tion as large as the probable error is as likely to occur as not, 

 and vice versa. 



