X Short Formula

Suppose the ratio is X:X, then the proportions are:
   X    and    X   
 X+X        X+X

Also, the expected numbers for each class would be
(n)   X    and (n)   X   
     X+X            X+X

Back to our example, we have the ambiguous segregation ratio 1.9640:1 which can be converted to proportions:

 1.9640  and    (1)   
 2.9640        2.9640

Then the expected number of each class are:

 (n)1.9640  and    n(1)   
   2.9640           2.9640

The short formula for a X of a 3:1 ratio is:
X = [a - a(3)] = 3.841
            3n

Now we know a is the expected number of the dominant class and a₂ is the expected number of the recessive class. Then substituting the ambiguous expected numbers for each class gives:

Now we solve for n to find the critical F family size such that more than r recessives indicates a 9:7 ratio and less than r recessives indicates a 3:1 ratio.

3.84 =        n²        x   (1.96-3) x   1  
            (2.9640)            1         3n

3.84 =   (1.04)   x  n 
          (2.9640)     3

n = 94.31

We must grow 95 plants to distinguish a 3:1 ratio from a 9:7 ratio.

Let n=94, we use the ambigous ratio to derive the observed class and test with a X to try to distinguish the two ratios.

The dominant class will have the observed number

(95)  1.964  = 62.9~63.
(95)  2.964

The observed number for the recessive class
(95)      1    = 32.
        2.964