XVIII X X I Introduction 



CM I 



<T -067 is the chance of an individual over 0"70; taking both limit* the chance JH 



|:>, :ind \v- expect 1'82 individual*. Thus we cannot r.-j.-ci tin- observation at r'Ol. 



'I'll.- ri.nelusions to be drawn frriin in. 'tlicd (>are thai - I" 10 >hmld | M - i 

 but it is doubtful if rejection of + 1"'01 is justifiable. 



09) We now turn to Chauvenet's criterion, and find 



20 



a * = 30' or 



Hence k<r = 2'13<r nearly (by Part I, Table II), and accordingly all values 

 >1"-13 (for a = 0"-532G) arc to be rejected. Thus - 1"'40 is thrown out as 

 anomalous. 



In the next place we have to consider the observation 4- 1"'01. We have now 



27 

 n = 14, and a k = ^ , or | (1 4- *) = '9821. This leads to 



^o 



ka = 210o- = 2-10 x 0"-3869 = 0"'8l25, 

 or the observation + 1"'01 must, by Chauvenet's criterion, be rejected. 



We have now thirteen observations left, and we find anew their mean and 

 standard deviation as +0"'0346 and 0"'3110, 



OK 



a k =, or \ (l+ fc ) = 0-9808. 



Thus ka- = 2-07 x 0"'3110 = 0"'6438. 



According to Chauvenet's criterion, since the next observation is 0"'63, we are 

 on the borderland of rejection, but should not reject. Chauvenet's criterion here, as 

 elsewhere, seems to reject too easily. 



(7) We now turn to Irwin's criterion. The difference arithmetically between the 

 first negative 1"'40 and the second //> 44 = 0"'96 arithmetically. Hence 



X = 0"-96/0"-5326 = 1-802. 

 Hence, from Table XIX, P A = "015. 



The occurrence therefore of such a difference between the first and second has 

 odds of about 66 to 1 against it, and we should feel strongly inclined to reject 

 1"'40 as an anomalous observation. 



On the positive side the difference is 1"'01 - 0"'63 = 0"'38, or in terms of 

 o- = 0"-3869 for the fourteen observations = 0"'38/0"-3869 = '9822. Our Table 

 XIX does not admit of very exact bivariate interpolation, but we see that for 

 this value of X, P\ for n= 14 is roughly of the order '145, or the odds are only 

 about 6 to 1 against such a value as 1"'01 occurring; we should hesitate therefore 

 to reject it. 



If rejecting 1"'40 we consider the difference between the negative first and 

 second observations, i.e. X =(0" '44 -0"'30)/0" "3869 ='3619, our Table XIX indicates 

 a probability of the order '5, and there is no suggestion of further rejection. For 

 the positive measures the difference between the second and third gives us 

 X = (0"'63 - 0"'48)/0"-3869 = '3877, 



o2 



