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 8.9, 7.4 and 7.8 mm and standard deviations were 1.5, 2.2 and 2.1 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). u= MS Treatments 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). MSError = 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 Error Total

Answer 1

Group Mean tun steridav od deviation Sample size X li ATAS - 8.91 Sets n=13 NAO *2=74 Sr. 2.2 12:19 *3=78. $3 = 2.1 ne MT. :18 Total observation No niining 13+19+18 50 Grand mean wont naif A2 Rat ng als 50 13x 8-9 + 19x7.4 +18X7-8 А. 27.934 50 396) 50 sspucat ment 2+1 na ² (Whion nix + 2 tr ting tz - N(M.)2 3 ial 1388.9 +1987:47 1887.8"_ 17.8722 50 x 7.9342

ni- 3-12 . df treatment economic olt, Ms treatment the Sštreatment to en freatment 17-8722 2 8.9361 2 b) s serrov: S. (n-1) SIE ( 1 ) 3 + (,-) S + (x-1) - =(3-1)65+ (1-4) 2-27 (15 –1) 2-4 189.09 SSς νYoν MS errore o 50-3 189.09 47 :: 4.0232 TO 7:5 Spreatorante +Servor,

17.8722 4 189.09 206.9622 F: Ms treatment Marron 9.936) 4.0232 2-2211 pidfireatment dtervar 47 (50-3) P value = 0.119154. ss DE ms. Source Fi Р Treatments 2 17-8722 8.9361 2.2211 0.119753 Errov. 40 4-0232 Total 49 20-68622