Introduction

See - Liu, B.H. 1998. Statistical Genomics: Linkage, Mapping, and QTL Analysis. pgs 145-146.

See Hanson, W.D. 1959. Agron. J.51:711-715. To distinguish between two segregation ratios which are x:1 and y:1 and observed frequencies of the two classes are a and b. Use the formula:

To distinguish a 3:1 ratio from a 9:7 ratio with a = 0.05,
then X²_{0.05, 1} = 3.84 and x:1 = 3/1, y:1 = 9/7:1.

(3/4)/(1/4) = x/1 1/4(x) = 3/4 x = 3/1

also

(9/16)/(7/16) = y/1 (7/16)y = (9/16)y = 9/7

Now

 n = 94.3

Also

Let a = # of dominant phenotypes
Let b = # of recessive phenotypes

To distinguish between two segregation ratios.

  a + b = 62.5 + 31.8 = 94.3 = n

About 95 individuals are needed to distinguish between a 3:1 versus 9:7 ratio. If the observed number of recessives phenotypes is greater than 32, the data will support the 9:7 ratio. If b < 32, then the data will support a 3:1 ratio.

9:7 hypothesis			3:1 hypothesis
class	dominant	recessive	total	dominant	recessive
observed	62	33	95	64	31
expected	53.44	41.56	95	71.25	23.75
X2 = 1.37 + 1.76 X = 3.13 X accept 9:7			X2 = 0.738 + 2.21 X = 2.95 X accept3:1

9:7 hypothesis			3:1 hypothesis
class	dominant	recessive	total	dominant	recessive
observed	64	31	95	62	33
expected	53.44	41.56	95	71.25	23.75
X2 = 2.087 + 2.683 X = 4.77 X reject 9:7			X2 = 1.201 + 3.603 X = 4.80 X reject 3:1

These results confirm that we would accept 9:7 ratio when we have more than 32 recessives and reject 9:7 ratio when we have fewer than 32 recessives and n = 95.