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I need to select a statistical test in order to answer the question of whether the TASR238 genotype is a good predictor of the ability to taste PTC (phenotype)

Here are the data I collected for my lab report:

    PTC taster      
Genoty   Strong  Weak   Non
T/T       10     4      2
T/t       30     26     12
t/t       5      4      18

(also found here)

I think I have to use $\chi^2$, but would it be an $\chi^2$ test for differences? How do I calculate expected phenotype based on genotype, would it just be the total number of genotype?

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Are you supposed to consider the genotypes as nominal categories (i.e. just genotype 1, 2, or 3)? In that case, the sounds like a classic $\chi^2$ test situation (I think this one is usually called the 'test of homogeneity' or 'test of independence'). – Macro Apr 28 '12 at 14:49

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Given that the tasting ability is ordinal, you could consider ordinal logistic regression, if you have learned that yet (since you tagged your question with homework). There are also tests of ordinal differences, such as Jonckheere-Terpstra, that are more similar to the spirit of $\chi^2$. But those don't mark one variable as dependent and the other as independent.

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Looking at your data, both your response and explanatory variable are ordinal and there are ways you can account for both in ordinal logistic regression. In R, the polr() function in Venables and Ripley's library(MASS) will let you do this. Hint - the answer is "yes there is a significant relationship" - and even a Chi square test will show this but a test that takes the ordinal nature of the data into account is superior in many respects. – Peter Ellis Apr 30 '12 at 11:04

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