# Chi-square in biology: Testing for a dihybrid ratio

You may have noticed we haven't talked about using chi-square in biology yet. We're going to do that now.

In biology you can use a chi-square test when you expect to see a certain pattern or ratio of results. For example:

• you expect to see animals using different kinds of habitats equally
• you expect to see a certain ratio of predator to prey
• you expect to see a certain ratio of phenotypes from mating

We'll focus on the last one. If that's what you're also doing in class, what a coincidence!

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: However, if two such mice mated, they would have offspring that showed the whole range of possible phenotypes: normal ( ), fanged (), fuzzy (), and fuzzy and fanged () . 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):

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 160 babies, how many of each type would you expect?

 all normal fanged fuzzy fuzzy and fanged

Mr. and Mrs. Mouse have 80 normal, 33 fanged, 33 fuzzy, and 14 fuzzy fanged babies. Does this data support the double hybrid model of the data?

 observed ("o") expected ("e") (o-e) (o-e)2 (o-e)2/e normal fanged fuzzy fuzzy fanged Total 160 160 Check