Crash Day 193 Before After 1. The numbers in the Figure above indicate the weather (overcast or not) of 434 location- matched triplets of days, one day on which a trafc accident took place, and two control days without an accident (the day before the accident and the day after the accident). This dataset could be analyzed as a 1:2matched case-control. The Venn diagram presentation of the data is rather unconventional. In matched casecontrol studies the data could alternatively be presented in 2 X 2-tables exposed unexposed case a,- I), control c,- d, for each matched set i = 1,. . . ,434. We denote H, = a, + b, + 0,: + (ii. (a) [10 Marks] We note that there are six types of location-specic 2 X 2-tables with the same exposure-case conguration. List these tables (i.e. different combinations of the numbers 0.1:, 6,, c; and di) and their counts. (b) [6 Marks] The null hypothesis assumes that there is no relationship between being a case and being exposed. Under the null hypothesis the distribution of the cell count a,- conditional on the row and column marginals is hypergeornetric. Find E(cg I as + q) and Var(o,- | a, + (1,) under the null. (c) [6 Marks] Test the null hypothesis of no association between weather and accidents using the CochraneMantelHaenszel (CMH) test statistic, given by 2 (23:: m 23:41 Emile.- + cs) 331mm | ...- + a.) 3 which is asymptotically distributed as X2 with one degree of freedom. Note: 3.5395(1) = 3.84