STAT/BIOSTAT 550, 2014: Homework 6a (Half-homework only): Due May 23.


In both these questions you may approximate 1.96 by 2 if you wish.

1. In a simple backcross experiment between two inbred lines, hybrid AB/ab individuals are crossed with ab/ab individuals, and the numbers of recombinant offspring are counted.
Among a total of 120 offspring in which the F1 hybrid individual was female, 53 were of the recombinant types.
Among 90 offspring in which the F1 hybrid individual was male, 37 were of the recombinant types.
(a) Is there evidence for linkage, using only the data on the offspring of hybrid males?
(b) Is there evidence for linkage, using only the data on the offspring of hybrid females?
(c) Assuming male and female recombinantion frequencies are the same, is there evidence for linkage?
(d) Is there evidence from this experiment that male and female recombination frequencies differ?

(Note; the answers to this question are only even slightly interesting if you use a standard test with type-1 error 0.025)

2. A scientist plans to test for linkage by collecting a sample families with two offspring, in which one parent is heterozygous for a dominant genetic disease allele, D, and has marker type ab. (The other parent is unaffected.) He decides he will test for linkage using the standard Normal approximation to the binomial distribution, and wants a type-1 error of no more than 0.025.
(i) He first plans the standard phase-unknown back-cross analysis, in which he can only determine the number of families in which one child is recombinant and the other is not (probability 2r(1-r)).
How many families does he need to collect to have power 0.975 if the true recombination rate is 0.2?
(ii) In the same situation, how many families does he need to collect to have power 0.975 if the true recombination rate is 0.32?
(iii) Suppose it were possible to phase each affected heterozygous parent.
How many 2-child families would the scientist then need to collect to have power 0.975 to detect linkage if the true value of r were 0.32?