Assuming that we have the following SNP and phenotype data, is the SNP significantly associated with the phenotype?

Question

So if I attempt this question using their method I put the data of genotype and phenotype into a data frame in R then use lm() to do linear regression and summary() to get an F statistic with p value 0.54. I'm not connecting what the F statistic means in this case to the answer.

Question 2: Assuming that we have the following SNP and phenotype data, is the SNP significantly associated with the phenotype? Here, we represent each SNP site as the number of minor alleles on that locus, so 0 and 2 are for major and minor homozygous sites, respectively, and 1 is for the heterozygous sites. We also assume that minor alleles contribute to the phenotype and the effect is additive. In other words, the effect from a minor homozygous site should be twice as large as that from a heterozygous site. You may use any test methods introduced in the chapter. How about permutation tests?

GENOTYPE: 1, 2, 2, 1, 1, 0, 2, 0, 1, 0

PHENOTYPE: 0.53, 0.78, 0.81, -0.23, -0.73, 0.81, 0.27, 2.59, 1.84, 0.03

Answer: Take the linear regression with F-test as an example, the p-value without the permutation test is 0.54 and is 0.55 after 1000 permutation (this number could be different with your answer because of the randomness of the permutation test).

Link to where I'm getting this: http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002828#pcbi.1002828-Balding1

Answer 1

Your approach is correct - it's not the only one permitted under their conditions, but it would be the standard way given only that information.

F-test compares a "full model" (predicting the phenotype using genotype and an intercept) versus a "reduced model" (predicting the phenotype using only the intercept, i.e. the mean value of phenotype). The p-value tells whether the full model predicts better, i.e. whether adding the genotype variable significantly improves the prediction. In this single-variable case, it should be approximately equal to the p-value for the beta coefficient of the genotype, if that's more familiar.

Anyway, this isn't specific to genetics, so you can check out other online sources - e.g. https://onlinecourses.science.psu.edu/stat501/node/295 for a longer, but accessible explanation of the F-test, and https://stats.stackexchange.com/ for many answers to similar questions.