MathBench > Statistical Tests

Goodness of Fit Tests

Example 1: Testing for a dihybrid ratio

Recall that in a dihybrid cross, you expect a 9:3:3:1 ratio of phenotypes -- if you don't recall this, you can review it in the module called "Counting Mice with Fangs". In that module, we considered two (hypothetical!) genes in mice. T and t coded for normal teeth or vampire fangs, respectively, and F and f coded for smooth or fuzzy fur, respectively.

A dihybrid mouse would have one copy of each of the 4 alleles and would look completely normal: normal mouse However, if two such mice mated, they would have offspring that showed the whole range of possible phenotypes: normal ( normal mouse), fanged (fanged mouse), fuzzy (fizzy mouse), and fuzzy and fanged (fuzzy fanged mouse). Furthermore, these phenotypes should appear in approximately the ratio 9:3:3:1, resulting in a nursery that looks something like this (if 16 babies were born):

normal mouse normal mouse normal mouse fuzzy mouse
normal mouse normal mouse normal mouse fuzzy mouse
normal mouse normal mouse normal mouse fuzzy mouse
fanged mouse fanged mouse fanged mouse fuzzy fanged mouse

But, as we discussed in that module, the process of generating new mice is random, so the ratio will not be exact. Now we have the tools to test whether an actual litter approximates the 9:3:3:1 ratio.

If Mr. and Mrs. Mouse are both heterozygous for both traits (TtFf), then their offspring should follow the 9:3:3:1 ratio. So if they had 30 babies, how of each type would you expect?

mouse deer

all normal



fuzzy and fanged

Mr. and Mrs. Mouse have 15 normal, 7 fanged, 6 fuzzy, and 2 fuzzy fanged babies. Does Mr. Mouse have any cause for jealousy?

observed ("o") expected ("e") (o-e) (o-e)2 (o-e)2/e
fuzzy fanged
Total 30 30