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AP Biology Name _________________________________
Provost/Walmsley Activity: Solving Chi2 Problems
On page 2 of your “Chi-square” packet you will see information on performing a Chi square on
various types of genetics crosses. Read this and take a look at the example below showing how a Chi
square analysis was performed on a 2-trait genetics cross.
Example for how to calculate a Chi square for a 2 trait cross.
In Guinea pigs, Black fur color (B) is dominant to albino (b), and Rough coat (R) is dominant to
Smooth coat (r).
A group of heterozygous black, smooth males (Bbrr) are mated with heterozygous black, heterozygous
rough females (BbRr). A total of 150 offspring are produced:
Observed offspring: 63 black, rough
51 black, smooth The expected ratio of offspring for the cross
12 albino, rough Bbrr x BbRr can be calculated from
24 albino, smooth a Punnett square (or the multiplication method) as:
Expected offspring:: 3/8 black, rough
3/8 black, smooth
1/8 albino, rough
1/8 albino, smooth
The number of expected offspring can now be calculated from this total of 150:
3/8 x 150 = 56 black, rough
3/8 x 150 = 56 black, smooth
1/8 x 150 = 19 albino, rough
1/8 x 150 = 19 albino, smooth
The calculations of the chi-square equation are again summarized in table form:
The calculated chi-square value = 0.875 + 0.446 + 2.57 + 1.32 = 5.22
There are 4 classes, so the degrees of freedom = (4 – 1) = 3 degrees of freedom.
In the chi–square table, the value in the significant deviation level = 7.8.
The null hypothesis would not be rejected.
Since the calculated value (5.22) is less than the table value (7.8), the differences seen here between
observed and expected offspring are not significantly different from that expected by chance alone.
The P value means that about 15 % of the time a cross like this is performed, there would be a
deviation similar to the one observed in this particular cross. 15% is higher than the .05 critical value
that is used to determine that the difference between observed and expected is statistically significant.
Class
Observed(o)
Expected (e)
(o-e)
(o-e)2
(o-e)2/e
black,rough
63
56
7
49
49/56 = 0.875
black, smooth
51
56
-5
25
25/56 = 0.446
albino, rough
12
19
-7
49
49/19 = 2.57
albino,
smooth
24
19
5
25
25/19 = 1.32
