In a recent question the original poster was faced with deciding which ratios to use in a Chi-squared analysis. They were supposed to decide on, "logically", what test-ratio to use.
A supplied sample contains four types of seeds and the total number is 64. The types of seeds are large red 42, large white 8, small red 10 and small white 4. Calculate goodness of fit.
My initial assumption was that in order to solve the problem, you would need to think about the genotype of each parent.
Lets say: L = large seeds; s = small seeds; R = red seeds; w = white seeds
If both parents were LsRw, the phenotype-distribution of the offspring would follow a 9:3:3:1 ratio.
If one parent was LsRw, and one parent was ssww, you would have a 1:1:1:1 ratio.
And if one parent was LsRw, and the other parent was Lsww or ssRw, you would have a 2:2:1:1 ratio.
Obviously, out of all of these ratios, the example question follows most closely with the 9:3:3:1 ratio.
So, to solve this question statistically, would you make the null hypothesis There is no difference between the observed and expected ratios?
While the alternative hypothesis would be There is a different between the observation and the expected ratios?
And would a statistically significant result indicate that the null hypothesis must be rejected in favour of the alternative hypothesis, thus the parents are unlikely to be heterozygotic for both traits?