86 MAIXE AGRICULTURAL. iiXPERIMENT STATION. I914. 



Gaussian curve it is a simple matter to determine from any- 

 table of the probability integral the precise portion of the area 

 of a normal curve lying outside any original absicissal limits, 

 or in other words, the probability of the occurrence of a devia- 

 tion as great as or greater than the assigned deviation. To say 

 that a deviation as great or greater than three times the prob- 

 able error is "certainly significant" means, strictly speakings 

 that the area of the normal curve beyond 3 P. E. on either side 

 of the central ordinate is negligibly small. As a matter of fact 

 this is not true, unless one chooses to regard 4.3 per cent, as a 

 negligible fraction of a quantity. There are certainly many 

 common affairs of life in which it would mean disaster to "neg- 

 lect" a deviation of four percent of the total quantit}^ involved. 



It seems likely that it may be useful to statistical workers to 

 have at hand a small table which will set forth for a series of 

 ratios between a statistical r'eviation and the "probable error""*" 

 of the error distribution, first the probability that a deviation 

 as great as or greater than the given one will occur, and second 

 the odds against the occurrence. of such a deviation. Such a 

 table is appended hereto. In calculating it we have used Shep- 

 pard's '' tables of the probability integral, changing from argu- 

 ments in terms of standard deviation to arguments in terms of 

 probable error. The probabilities have been expressed on a 

 percentage basis, on the ground that they will probably in this 

 way make a more direct appeal to the average mind, -since we 

 are more accustomed to thinking in terms of parts per 100 than 

 per any other number. 



A single example will indicate how the table is to be used. 

 Suppose one has determined the mean of each of two com- 



* As many statistical writers have pointed, out, the convention of 

 using the "probable error" rather than the standard deviation of a dis- 

 tribution as a measure of its "scatter" is unfortunate. Yule (Introduc- 

 tion to the Theory of Statistics) has made recently a strong plea for 

 the use of the "standard error." It however seems likely that the prob- 

 able error is too strongly entrenched in the common usage now to be 

 dislodged. 



tBiometrika Vol. II, pp. 174-190. 



