Standard and Probable Error 



115 



must not be mixed. Using the actual numbers in Wright's guinea 

 pig experiment, we may apply the method as follows: 



A 



48 



a 

 63 



Observed numbers 



Expected (1:1) numbers 55.5 55.5 



Observed deviation 7.5 7.5 



P • q 



n 



55.5 X 55.5 



111 



= 5.27 



7.5 

 5.27 



= 1.4 



The standard deviation or standard error is 5.27 and the ob- 

 served deviation is 7.5. The actual deviation is only 1.4 times 

 the standard error. If it were more than twice the standard 

 error, we should consider that the observed ratio probably is not a 

 true example of a 1 : 1 ratio and we should then proceed to search 

 for an explanation. In the guinea pig experiment, the deviation 

 is only 1.4 times the standard error so that we are safe in assum- 

 ing that a ratio of 48 : 63 is a 1 : 1 ratio within the limits of 

 probability and we do not need to try to explain the excess of 

 recessives. The same method may be used by converting the 

 numbers into percentage and finding the standard error in per- 

 centage; p and q are then also expressed in percentages. 



Observed numbers 

 Per cent of each class 

 Expected per cent 

 Deviation in per cent 



A 



48 



43.2 



50 



6.8 



a 



63 



56.8 

 50 

 6.8 



p • q 



n 



0.50 X 0.50 



111 



= 4.8 per cent 



6.8 per cent 

 4.8 per cent 



= 1.4 



The deviation expressed in per cent is 6.8 and the standard error 

 is 4.8 per cent. Again the deviation is 1.4 times the standard 

 error. With either method the result is the same, but the student 

 must remember that if the standard error is expressed in per cent, 

 the deviation must also be expressed in per cent. 



While the equation a = 



P ' q 

 n 



is the equation for the standard 



error of any ratio, the student will frequently find that his calcu- 

 lations will be simplified for figuring the standard error of a 1 : 1 



