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 9.2,8.1 and 7.8 mm and standard deviations were 2.2, 3.3 and 3 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). μ = MSTreatments = 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 = i 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.

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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 9.2,8.1 and 7.8 mm and standard deviations were 2.2, 3.3 and 3 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).
μ =
MSTreatments =
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 =
i
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.
Transcribed Image Text: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 9.2,8.1 and 7.8 mm and standard deviations were 2.2, 3.3 and 3 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). μ = MSTreatments = 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 = i 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.
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
Treatments
Error
Total
DF
i
i
i
SS
{to two
decimal places)
i
i
i
MS
{to two
decimal places)
i
i
F
{to two
decimal places)
i
P
(to three
decimal places)
i
Transcribed Image Text: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 Treatments Error Total DF i i i SS {to two decimal places) i i i MS {to two decimal places) i i F {to two decimal places) i P (to three decimal places) i
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