Chest deceleration measurements were made on dummies in car crash tests involvin
ID: 3252962 • Letter: C
Question
Chest deceleration measurements were made on dummies in car crash tests involving small, medium and large cars to investigate whether the size of the car was related to crash trauma. Smaller measurements correspond to less trauma to the crash test dummies. The data are given in the following table. a) State the null and alternative hypotheses for the ANOVA test. b) Use SPSS to carry out the ANOVA, and report the test statistic and p-value. c) Write a brief conclusion of the ANOVA analysis. d) Carry out the Bonferroni's multiple comparisons and summarize the results, if appropriate.Explanation / Answer
Solution
a)
The null and alternative hypotheses for the ANOVA test are given below.
Null hypothesis: Average crash trauma measurements for three car sizes is equal.
Alternative hypothesis: At least one car size have significantly different average crash trauma measurement.
b)
SPSS output for ANOVA test is given below.
Oneway
ANOVA
Crash trauma measurements
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
162.867
2
81.433
4.094
.028
Within Groups
537.000
27
19.889
Total
699.867
29
ANOVA output indicates that,
F Test statistic = 4.094
P value = .028
c)
ANOVA table indicates that F statistic is 4.094 and P-value is .028. Since P-value is less than level of significance .05, there is strong evidence to reject the null hypothesis.
Hence we can conclude that average crash trauma measurements for three car sizes are significantly different. In other words, at least one car size have significantly different average crash trauma measurement from remaining two car sizes.
d)
Output for Bonferroni’s multiple comparison test is given below.
Post Hoc Tests
Multiple Comparisons
Crash trauma measurements
Bonferroni
(I) Size of car
(J) Size of car
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
Small
Medium
2.600
1.994
.610
-2.49
7.69
Large
5.700*
1.994
.024
.61
10.79
Medium
Small
-2.600
1.994
.610
-7.69
2.49
Large
3.100
1.994
.395
-1.99
8.19
Large
Small
-5.700*
1.994
.024
-10.79
-.61
Medium
-3.100
1.994
.395
-8.19
1.99
*. The mean difference is significant at the 0.05 level.
Conclusions:
i) Bonferroni’s test indicates that there is no difference between average crash trauma measurements for small and medium sized cars, p > .05.
ii) Bonferroni’s test indicates that there is significant difference between average crash trauma measurements for small and large sized cars, p < .05.
iii) Bonferroni’s test indicates that there is no difference between average crash trauma measurements for medium and large sized cars, p > .05.
Hence only average crash trauma measurements for small and large sized cars differs from each other. Remaining two pairs do not have significantly different average.
ANOVA
Crash trauma measurements
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
162.867
2
81.433
4.094
.028
Within Groups
537.000
27
19.889
Total
699.867
29
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.