Question

A dihybrid cross is performed in Drosophila - one parent is heterozygous for both genes (B/b ; F/f) and is test-crossed with a homozygous recessive type (b/b ; f/f). (where B = black body; b = brown body; F = forked bristles; f = unforked bristles.)

The results are:

black, forked 230

black, unforked 210

brown, forked 240

brown, unforked 250

How many degrees of freedom would you use in this case?

What would be the expected number for each phenotype?

Calculate the chi-square value for this cross.

Assuming p=0.05, what critical value would you use to compare the calculated chi-square value against?

Do you reject or not reject the expected ratio in this case

Answer 1

Chi-Square Test of independence
	Observed Frequencies
	0
0	forked	unforked					Total
black	230	210					440
brown	240	250					490
Total	470	460					930
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	forked	unforked					Total
black	470*440/930=222.366	460*440/930=217.634					440
brown	470*490/930=247.634	460*490/930=242.366					490
Total	470	460					930
	(fo-fe)^2/fe
black	0.262	0.268
brown	0.235	0.240

Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 2- 1 ) =   1

expected number-

	Expected Frequencies
	forked	unforked					Total
black	470*440/930=222.366	460*440/930=217.634					440
brown	470*490/930=247.634	460*490/930=242.366					490
Total	470	460					930

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   1.006

Critical Value =   3.841   [ Excel function: =CHISQ.INV.RT(α,DF) ]  
Decision: test statistic,X² < critical value , So, Do not reject the null hypothesis