Self Assessment Answer # 1
for Lesson 11

by Dr Jamie Love Creative Commons Licence 2002 - 2005

I hope you quickly understood that the expected phenotype ratio for a monohybrid cross is 3 : 1, but I have them ordered backwards!
That means the ratio to compare to 3 : 1 is 428 green pods : 152 yellow pods and not the other way around. You should recognize that the "3" in the 3 : 1 must be the organisms with the dominant phenotype and that must be the green phenotype because all the F1s were green. Besides, the dominant phenotype is always the most common phenotype among the F2s.
Never assume you are given the ratio in the expected pattern. Instead, learn to identify it from the data.
I also hope you realized that there is only one degree of freedom. We are working with only one degree of freedom because there are two categories (yellow and green) and the degree of freedom is one less than the number of categories.
Now let's do the chi-square!

The total number of pods is 580 (428 green pods + 152 yellow pods).
We'd expect ¼ of them, 145 pods, to be yellow (580 / 4 = 145) and the rest, 435, to be green. (That's 580 - 145 = 435 or 580 x ¾ = 435.)
We now have the numbers of expected and observed so we can use the 2 equation. 2 = [(O - E)2/E]

I'll do the yellow pods first. We observed 152 but expected 145 and that is a difference of 7. We square that to get 49 and divide it by the number of yellow pods expected to get 0.338. (That's 49/145 = 0.338 to three decimal places.)
Among the green pods we observed 428 but expected 435 and that is a difference of 7 (again) which when squared gives us 49 (again). We divide that number by the number of green pods (NOT the yellow pods) expected (435) to give us 0.113 (to three decimal places).
We sum (remember "") those together to give us a 2 = 0.451.

Degrees of Freedom 5 % Significance Levels
1
3.84
2
5.99
3
7.81
4
9.49

The table showed you the 2 for four different Degrees of Freedom but you should understand in this experiment there is only one Degree of Freedom so we are testing our 2 to see if it is less than 3.84.
You found that the chi-square for this experiment equals 0.451 and that is very much smaller than 3.84 so it is within an acceptable range (significant to 5%) for a 3 : 1 ratio.

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