I'm studying Biomedical Computer science and I have to research a paper about genotype-phenotype association.
In this paper the authors use a correlation analysis by first calculating the Pearson correlation and then calculating the hypergeometric distribution to filter out insignificant associations.
Under Methods/Associating genes to phenotypes
While the correlation measures the strength of association between an organism's genomic content and its phenotype, we also applied another method, exploiting the hypergeometric distribution function, to determine the significance of these
associations [...] where a result smaller or equal to 20% response is considered negative. So for a given gene found in M species, the hypergeometric function provides the probability by random chance that the gene is found in m species which contain the COG and are also positive in the laboratory test.
The following criteria were applied to the correlated data set. The intersection between a specific COG and a phenotype had to contain at least 3 organisms, and for any intersection, 30% of the microbes had to share the COG. The scores were adjusted using the standard Bonferroni error correction for multiple testing.
Since the Bonferroni correction is one of the most conservative, it is likely that some biologically relevant associations were unnecessarily discarded. In this case $\alpha$ was set as less than equal to 0.01, therefore, any hypergeometric distribution score less than or equal to 0.0001 was deemed significant. Using these criteria, we set a 0.8 and a 0.9 correlation threshold to assess the significance of the COG-phenotype associations.
My question is: Is this a valid scientific correlation analysis or not? Are there any reservations?
Also, can you give me an idea for a good statistics book for science?