Chi-square equation can be used to estimate if the color is inherited with a Mendelian fashion:
X2 = [(Oblack - Eblack)2 / Eblack]+ [(Owhite - Ewhite)2 / Ewhite]
where O - number of observed phenotypes, E - number of expected phenotypes.
For the calculation, the number of offspring with specific phenotypes must be evaluated.
Assuming that B is a black allele and W is a white allele, the genotypes of parental dogs used for true breeding are BB (black) and WW(white).
The possible offspring are:
parents: BB (black) × WW (white)
offspring: BB (black), 2BW (black) and WW (white).
The expected phenotypic ratio of the offspring is:
3 black : 1 white.
As the total number of the offspring is 1204, the expected phenotypic ratio is:
903 black : 301 white
In the example, the observed phenotypic ratio of the offspring:
922 black : 282 white
Using chi-square equation, X2 is calculated:
X2 = [(922 - 903)2 / 903] + [(282 - 301)2 / 301] = 0.4 + 1.2 = 1.6
The number of degrees of freedom (df) equals 2 -1 = 1, due to the presence of two phenotypic classes.
From the X2 table, p-value = 0.2.
As 0.2 > 0.05, there is no difference between the expected and observed numbers of dogs. As a result, the coat color is inherited in a Mendelian fashion.