A scientist wanted to study whether some gene frequencies (q) varies from one country to another. For this testing for the homogeneity of the q, he obtained the following data set:   (i) Treating this...

A scientist wanted to study whether some gene frequencies (q) varies from one country to another. For this testing for the homogeneity of the q, he obtained the following data set:

(i) Treating this as a 4 × k contingency table, construct a completely nonparametric test for homogeneity of the k samples.

(ii) Use the Hardy–Weinberg equilibrium for each country, and in that parametric setup, use the Wald test statistic to test for the homogeneity of the gene frequencies.

(iii) Use the likelihood ratio test under the setup in (ii).

(iv) Comment on the associated degrees of freedom for all the three tests, and also compare them in terms of (a) consistency, (b) power properties and (c) computational ease.