Course Notes - Department of Mathematics and Statistics

Since 1 is excluded there is strong evidence that there is an increasedrisk of catching the river blindness. Fred is 95% confident that the oddsare increased by between 1.9 - 3.03 times. This is too much of a risk forFred, so he has instructed Carol to avoid the rainforest when planningtheir west african journey.Part IIINow Fred turned his attention to the whether or not married couplestended to be similar heights, since he had split the heights into threecategories he realised he could not deal with this problem using Oddsratio or Relative risk, instead he would have to use Chi-squared. Fredhated calculating Chi-squared by hand, not because it was difficult,more that it was time-consuming. He first calculated the expectedvalues and put them in the table in square brackets []. Recall theequation for expected values is:E ij = r i×c jnWife HeightsHeights of Husband Tall Medium Short TotalTall 20 [16.58] 30 [32.52] 16 [16.90] 66Medium 18 [23.36] 49 [45.83] 26 [23.81] 93Short 14 [12.06] 23 [23.65] 11 [12.29] 4852 102 53 207The next step is to calculate the chi-squared statistic, the formula forthis is:no.ofrows∑i=1no.ofcolumns∑j=1χ 2 = (O ij − E ij ) 2E ijThis generated a Chi-squared statistic of 3.064, this needed to be comparedagainst the critical value for a 3 × 3. This has a degree of freedomof 4, using R qchidist(0.95,4) we get the value of 9.487729 as the criticalvalue at 95%. Since our value of 3.064 < 9.488 there is no evidence ofassociation between the heights of the husbands and the heights of thewives. So those couples that Fred first observed must have just been aco-incidence, an not indicative of an overall pattern.165