Question

Reserve Problems Chapter 13 Section 2 Problem 2 An article in the American Journal of Emergency Medicine compared the ability to detect acute traumatic aortic injury (ATAI) on cervical x-ray images. The data consisted of 13 cases of ATAI, 19 cases with negative aortography (NAO) and 18 cases with multiple trauma (MT) without aortography. Measurements of the cervical soft-tissue width at the third cervical vertebrae generated the following results. Averages were 9.9, 9.2 and 7.4 mm and standard deviations were 3.6, 2.4 and 1.5 mm for the ATAI, NAO, and MT groups, respectively. Consider an ANOVA for these data. a) Use the sample sizes and group averages to compute the grand mean width and the mean square for treatments. Round your answer to two decimal places (e.g. 9.87). MS Treatments =L b) Use the sample sizes and standard deviations in the groups to compute the mean square error. Round your answer to two decimal places (e.g. 9.87). MS Error = c) Use the results in the previous parts to conduct the ANOVA test and prove that the mean widths do not differ. Calculate the P-value for the test. Source DF SS (to two decimal places) MS (to two decimal places) F (to two decimal places) P (to three decimal places) Treatments 2 Error 47 Total 49

Answer 1

Answei ATAI NAO 19 18 count (n) Mean (x) 9. Str.dev (s:) 3.6 2.4 Grand Mean(t) knitti / en: 8.734 10101 square of deviation of sample Moan from 0.217 1.78 Grand Mean (x-Xg) 32.04 14.66 1.953 53.832 2n(x-x)" Lo 20-1) 155.52 103.68 38.25 294.45 S5w Number of treatments dt between K-1=2 N = En =50 dt within Nok = 47

26.916 55B/K-1 MS Between = 5.832 2 26.92 MS Within SS "/rk 397-450 = 6.329 = 6.33 a] Grand Mean (M) = 8.734 8.73 MS Treatments 26.92 b.] MS Error = 6.33 c] ANOVA Table DF 55 MS f Р Source 0.020 Treatments 4.25 2 53.83 26.92 EYO 47 297.45 6.33 Total 49 351.28