It has been shown that the X chromosome is frequently enriched for female biased genes, and has a deficit of male biased genes. For example in this paper, and this one.
However, I'm struggling to find papers which test the general distribution sex-biased genes. I am trying to find out if the X is enriched for sex biased genes, e.g. if the X hosts 20% of all protein coding genes, it would be enriched if it carried 30% of all sex-biased genes.
Are there any such studies?
I think I found an answer tucked in the methods section at the back of the Allen paper where 15% of sex-biased genes were X-linked, I'd suggest this means that 15.55% ($100 \times (\frac{1075}{1075 + 4938 + 4323})$) of sex-biased genes are X-linked - other examples are still sought:
"Genes associated with chromosomes 2 (4,323 genes, 37%), 3 (4,938 genes, 43%), and X (1,705 genes, 15%) were used in the analysis; these chromosomes accounted for 10,967 (95%) of the genes... a further 547 (4.7%) of the genes ... were omitted"