This continues the previous problem on chromosome and criminals 8.51 A study of
ID: 3310211 • Letter: T
Question
This continues the previous problem on chromosome and criminals 8.51 A study of chromosome abnormalities and criminality examined data on 4124 Danish males brn in Copenhagen. H. A. Witkin et al., "Criminality in XYY and XXY men, Science, 193 1976), pp. 547-555.) The study used the penal registers maintained in the offices of the local police chiefs and classified each man as having a criminal record or not. Each was also classified as having the normal male XY chromosome pair or one of the abnormalities XYY or XXY. Of the 4096 men with normal chromosomes, 381 had criminal records, while 8 of the 28 men with chromosome abnormalities had criminal records. Some experts believe that chromosome abnormalities are associated with increased criminality. Do these data lend support to this belief? Report your analysis and draw a conclusion. The calculation from the previous question used the normal approximation even though the suitability of this approximation was in question. There are other methods that do not require the normal approximation. In this case Fisher's exact test can be used and associated with this test are confidence intervals for the odds ratio. The data can be presented in the following 2 by 2 table criminal non-criminal abnormal normal 8 381 2 3715 0. This h sis can also be stated in terms of the odds, theta. The relationship between the odds and proportion is theta = p/(1-p). Which of the following 1. The null hypothesis stated in terms of proportions is Ho. (p1-p2) expresses Ho: (p1-p2) 0 in terms of the odds, Enter a or b b. Ho: theta 1/1heta2 = 0 The ratio theta1theta2 is called the odds ratio (OR). We discussed this in the notes for chapter 2. Note that the odds ratio can be defined by interchanging the roles of the two populations so that theta2 theta1 is also an odds ratio When considering OR 1 either definition for the odds ratio can be used. The choice for which odds is in the numerator will affect the choice of the alternative hypothesis 2. Using rfiddle (or other software) carry out Fisher's exact test. Note that the following commands in r-fiddle produce the table above (without the labels) c(828-838 1 4096-381 ) %296 matrix(ncol-2) Next we send this table (called a matrix in r-fiddle) to fisher.test Cl8.28-838 1.4096-381) %>96 matroincol-2) %> % fishertestarternative-greater) Using the output, report the p-value. Round to 3 digits (eg 0.123) 3. Is the difference significant at the alpha = 0.196 level (ie, is the pvalueExplanation / Answer
1. H0: theta1/theta2 = 1
2. Using an online Fisher Exact Test calculator, the Fisher exact test statistic value is 0.003332. The result is significant at p < .10. (http://www.socscistatistics.com/tests/fisher/Default2.aspx)
3. Yes