Chi Square 119 



Substituting, we have 



2 (25-21)2 (17-21)2 (4)2 (_4)2 ^g jg 



X = = = 



21 21 21 21 21 21 



= 0.762 + 0.762 



The value of x^ for this particular problem is 1.524, but what 

 does that mean? How do we know whether this ratio is a true 

 example of a 1 : 1 ratio merely by knowing that x^ = 1.524? 

 Without going any more deeply into the mathematics behind all 

 this, we may say that it is fairly generally agreed that whenever, 

 in a problem such as the one above, x^ is 3.841 or larger, the 

 observed ratio is probably not an illustration of the ratio for 

 which it was tested. To restate that, if x^ is 3.841 or larger it is 

 considered to be significaiitly great or merely significant. In a 

 ratio involving only two terms, such as 1 : 1 or 3 : 1, when x^ is 

 greater than 3.841 the chance of getting this ratio as the result 

 of chance alone is one out of 20. In other words, if we cross 

 a heterozygote with a recessive we should expect that our family 

 would segregate into an observed ratio having a x^ greater 

 than a 3.841 in only 5 per cent of the cases. In our problem, 

 X^ = 1.524. It has been calculated that a family with such a 

 X^ value would occur in 20 to 30 per cent of the families tested. 

 Since the probability of getting a 25 : 17 ratio when we expect 

 21 : 21 are between 20 and 30 per cent, it is highly probable that 

 our ratio is a true example of a 1 : 1 ratio. If, on the other hand, 

 our ratio had been 28 : 14, would it be considered a 1 : 1 ratio? 

 Now the value of x^ is: 



2 _ (28 - 21)2 (14 - 21)2 ^ q^ (-7)2 _ 49 49 

 ^ ~ 21 "^ 21 ~ 21 "^ 21 ~ 21 21 



= 2.333 + 2.333 = 4.666 



Since this value of x^ lies beyond the 5 per cent point, we should 

 say that it is significant and that a 28 : 14 ratio is probably not 

 a true example of a 1 : 1 ratio. 



The x^ method is equally applicable for testing a 3 : 1 ratio, 

 in which, of course, the expected frequency is different for each 

 term. Let us designate the observed frequency of any term by 

 X and the expected frequency by m, and let us use as an illustra- 



