Statistical Tests 



165 



Observed frequencies 



Expected frequencies 



d 



d^/expected frequencies 



RgA 



160 



151.06 

 8.94 

 0.53 



Rg a 



103 



108.94 



-5.94 



0.32 



rgA 



115 



108.94 

 6.06 

 0.34 



rga 



142 



151.06 

 9.06 

 0.54 



/2 _ 



1.75; n = 3 



When we compare our observed ratio with an expected ratio 

 on the basis of 41.9 per cent crossing over, x^ = 1-73. Since 

 there are four terms in the ratio we still have three degrees of 

 freedom, and on that basis x^ tells us that we could expect such 

 a ratio on the basis of chance alone in over 50 per cent of 

 similar famiUes. Obviously, the hypothesis of linkage with 

 41.9 per cent crossing over is highly probable. 



The standard error can also be used to determine whether a 

 given ratio deviates less from one based on independent assort- 

 ment or from one based on linkage. Let us illustrate this method 

 with some data from Wright's work on the guinea pig. An ani- 

 mal homozygous for black and for rough fur {BB RR) was 

 crossed with one with brown and smooth fur (bbrr). The Fi 

 was testcrossed to the recessive. If there is linkage, the BR and 

 br phenotypes are the parental types and the Br and bR animals 

 would represent crossovers. Let us combine the two parental 

 types and also the (wo possible crossover types. If there is no 

 linkage, the parental and nonparental types should be in the 

 ratio of 1 : 1, but if there is linkage, the ratio would not be 1 : 1 

 and would vary with the strength of the linkage. Therefore, the 

 observed combined ratio is tested against a 1 : 1 ratio. The 

 results are: 



BR hr Br bR 



88 96 98 93 



Observed 184 191 



Expected 187.5 187.5 



Deviation —3.5 3.5 



<r = ^ /184J91 ^ V93.72 = 9.68 

 \ 375 



d 3.5 



9.68 



= 0.36 



The deviation of the observed ratio from a 1 : 1 ratio is only 

 0.36 times the standard error. Therefore, this ratio agrees very 

 well with expectation based on independent assortment, and 

 there is no evidence to support the idea of linkage. 



