Question

EXHIBIT 2 Vaccines and Risk Revisited Dr. Loring Dales of the Immunization Branch of the California Department of Health Service writes, where are the data we have on (a) percentages of California children who had received 4 doses of DTP by their 2nd birthday .. and (b) numbers of autism cases in California's Department of Developmental Services regional service center system ..... Questions 1. Fill out all the entries in the table that are missing. Your instructor may have you retype the table if you are not required to turn in this actual page. TABLE 3.5 California 1980-1994 Data for x and y DTP Number Year Coverage of Autism ху (%) Cases 1980 50.9 176 1981 55.4 201 1982 52.1 212 1983 47.7 229 1984 48.9 246 1985 54.3 293 1986 54.1 357 55.3 347 1987 1988 1989 60.9 2. Compute the correlation coefficient between DTP Coverage and Autism Prevalence 436 62.2 522 1990 663 65.9 67.3 69.8 1991 1992 1993 823 1,042 73.6 1,090 1994 75.7 1,182 Σχο Σy Σχy 2x Σy = 3. Has this exercise changed your perception of the data presented in Beyond the Numbers 3.2? Why or why not?

Answer 1

Solution; Number of X2 1980 11135.4 1982 1983 1984 Year DTP Coverage Autism coses (x) Y ху y? 50.9 176 8958.4 2590181 30976 1981 55.4 201 3069.16 40401 52.1 212 11045.2 2714.41 44944 47.7 229 10923.3 2275. 29 52441 48.9 246 12029.4 2391:21 60516 1985 54.3 293 15909.9 2948.49 85849 1986 54.1 357 19313.7 2926.81 127449 1987 55.3 347 19189.1 3058.09 1988 60.9 436 26552.4 3708.81 190096 1989 62.2 5:22 324684 272484 19901 65.9 663 43691-7 4342.81 439569 1991 67.3 823 55 387.91 4529.29 677329 1992 69.8 1042 72731.6 4872.04 1085764 1993 73.6 1090 80 224 5416096 1188100 1994|| 7507 1182 89477.4 5730.49 1397124 Ex=894.1 3y=7819 EXY=50937.8 =54443.51 SY=5813451 120409 3868.84 we get, Ex = 894.1 X = EX- n 894.1 15 = 59.607 Ey = 78 19 Y=EY n 7819 15 521. 267

Page No. Date * = 59.607 Y = 521.267 EXY = 509037.8 Ex2 = 54443.51 EY² 5813451 Correlation coefficient between X andy is given by formula de cov(x, y) ΣΧΥ – ху n Jasje Asy-7) Now, putting values in formula x 509037.8 59.607X 521.267 15 ha FC T 75 -X54443.5159.60717 2.x5813457–1521.267 33935.85 31071.162 YE 3629.567 – 3552.944)/387563.4 – 271719-285 8876323.624 X 2864-688 2864.688 76.623* 115844-115 2864.688 =1.962 2979.316 Correlation () = 0.962 This is strong positive correlation between X and Y.