the Calculation of Errors. 



107 





1. 



3. 



4. 



Positive 

 deviation. 



Negative 

 deviation, j 



" subject." 



" subject." 





•80 

 •87 



•80 



•82 



•75 



•81 

 •93 



•83 



•87 

 •80 







•86 



•87 



Each of these results is based upon two sets of 1 50 obser- 

 vations ; but these sets are not independent. For instance, the 

 basis of the " positive deviations " (column 1) consists of 150 



observations (for e. g., p 12 ) of the form -, and 150 of the form 



X 



— ; taking the average of the two values (of p 12 ) respectively 



if 



determined from the two sets of 150 observations. Now the 

 error under head (a) affecting the sum of these is, — if e 1 is put 

 for the error of the abscissa of the Median, and e 2 for that of 

 its ordinate — 



\/l 



(e 2 minus e,) plus \J - (e 1 minus e 2 ) 

 w n 



that is, zero. The result therefore is affected only with the 

 error (/3) , that is, 



v 



"(1-P12*). 



or, putting p = -8, and ti = 300, -06. This result again has to 

 be diminished by about ten per cent. ; considering that in 

 the calculation the corrected method ((i.)) was employed* 

 Similar remarks apply to the " negative deviation "— the 

 results in the second column of the table. The probable error 

 of the difference between these two results is 



•06 x *9 x s/2 x -477, or -04 nearly. 

 Similarly the basis of the results in the third column is 

 one set of 150 positive observations and another set of 150 

 negative observations. The errors under head (a) which 

 affect each of these sets cut each other out ; and accordingly 

 the probable error of the difference between an entry in 

 column 3 and the corresponding entry in column 4 is the 



* Above, p. 101. 



