RECOMBINATION IN SEXUAL ORGANISMS 63 



TABLE 3.1 



A Statistical Test by the Method of Chi Square (X^) of the 



Significance of the Differences between the Numbers of 



Randomly Sampled Gametes Containing Recombinations of Genes and the 



Numbers Expected on the Hypothesis of Random Assortment 



, , _ _ Parental-Type Recombination 



Parental Genotypes: y mt x y mt r^ ,. r- ,. 



J ^ "^ ^ Gametes Gametes 



Observed number 87 96 



Expected number 91.5 91.5 



Difference 4.5 4.5 



Difference corrected 4 4 



(Difference corrected)^ 16 16 

 ( Difference corrected )^ 



Sum 



Expected number 



(difference corrected)^ 



0.18 0.18 



expected number 

 n = 1, F = 0.55 



Many textbooks of statistics contain tables relating x^ to P for any n. The 

 number of degrees of freedom, n, is here one less than the number of classes ob- 

 served (two). Once we know the total number of members (183) in the two classes 

 and the number in any one class, then the number in the other class cannot vary — 

 it must give the total when added to the first. P is the probability of obtaining aX^ 

 as large or larger than a given value when the statistical hypothesis being tested is 

 true and the deviations are due to random sampling error. About 55 per cent of 

 samples, drawn from a population where old and new combinations were actually 

 present in a 50:50 ratio, deviate as much from expected as this sample did. It is 

 likely, therefore, that the discrepancy is due to sampling. It is concluded that the 

 data are consistent with the hypothesis of random assortment and that the genes 

 segregate independently. 



A F of 0.05 is usually considered critical; if random sampling alone so infre- 

 quently yielded such deviations, the hypothesis would be susp>ect. It should be 

 noted that numbers, not frequencies, were used for the calculations; this is because 

 the sensitivity of the X^ test depends upon the absolute size of the numbers em- 

 ployed. The Yates correction made of the differences consists in bringing them 

 one half unit closer to zero. It is imperative to use this correction when the 

 numbers being tested are small. The example given above is a simple application 

 of the X test; it may be adapted to the test of more complicated comparisons but 

 not without the understanding of the X^ method that can be obtained from a text- 

 book of statistics-. 



The system being tested must also be understood. For example, the numbers of 

 new and old combinations among the gametes produced in the same meioses cannot 

 be employed as above in aX^ test. Once a crossover event has occurred in meiosis, 

 the genotypes of all the progeny spores are fixed. Thus, the genotype of one 

 gamete was not obtained independently of its three sisters. Special methods must 

 be used for such tetrad analysis. 



