1. One-Way Analysis of Variance: Comparing Several Means
BPS 7e Chapter 27
© 2015 W. H. Freeman and Company

2. Goal of Analysis of Variance
The purpose of analysis of variance is to compare the:
variances of several populations.
proportions of successes in several populations.
means of several populations.

3. Goal of Analysis of Variance (answer)
The purpose of analysis of variance is to compare the:
variances of several populations.
proportions of successes in several populations.
means of several populations.

4. Comparing Several Means
The more populations, the larger the expected difference between the largest and smallest observed means, even if the population means are equal. This is known as the problem of:
regression.
t tests.
multiple comparisons.
hypothesis testing.

5. Comparing Several Means (answer)
The more populations, the larger the expected difference between the largest and smallest observed means, even if the population means are equal. This is known as the problem of:
regression.
t tests.
multiple comparisons.
hypothesis testing.

6. Comparing Several Means
Step 1 of dealing with the problem of multiple comparisons of means is to carry out:
several two-sample t tests.
a single two-sample t test of the most likely difference.
an informal test based on boxplots.
an overall test.

7. Comparing Several Means (answer)
Step 1 of dealing with the problem of multiple comparisons of means is to carry out:
several two-sample t tests.
a single two-sample t test of the most likely difference.
an informal test based on boxplots.
an overall test.

8. Analysis of Variance F Test
How do we calculate the analysis of variance F statistic for testing the equality of several means?
F = variation among individuals in the same sample / variation among the sample means
F = variation among the sample means / variation among individuals in the same sample
F = variation among individuals in the same sample / standard deviation the same sample
None of the above

9. Analysis of Variance F Test (answer)
How do we calculate the analysis of variance F statistic for testing the equality of several means?
F = variation among individuals in the same sample / variation among the sample means
F = variation among the sample means / variation among individuals in the same sample
F = variation among individuals in the same sample / standard deviation the same sample
None of the above

10. Analysis of Variance F Test
The conditions for ANOVA state that we have __________ from each population, that each population has ___________, and that all populations have ____________.
an independent SRS; the same standard deviation; Normal distribution
an independent SRS; Normal distribution; the same standard deviation
the same standard deviation; an independent SRS; Normal distribution
an independent SRS; Normal distribution; different standard deviation

11. Analysis of Variance F Test (answer)
The conditions for ANOVA state that we have __________ from each population, that each population has ___________, and that all populations have ____________.
an independent SRS; the same standard deviation; Normal distribution
an independent SRS; Normal distribution; the same standard deviation
the same standard deviation; an independent SRS; Normal distribution
an independent SRS; Normal distribution; different standard deviation

12. Analysis of Variance F Test
True or False: If the ANOVA F test is significant, then we conclude that exactly one comparison of means is non-zero. We just don’t know which one.
True
False

13. Analysis of Variance F Test (answer)
True or False: If the ANOVA F test is significant, then we conclude that exactly one comparison of means is non-zero. We just don’t know which one.
True
False

14. Analysis of Variance F Test
True or False: The alternative hypothesis in ANOVA is
True
False

15. Analysis of Variance F Test (answer)
True or False: The alternative hypothesis in ANOVA is
True
False

16. Analysis of Variance F Test
True or False: If the null hypothesis in ANOVA is false, the observed variability in the sample means will be greater than the variability you would expect if the means are equal.
True
False

17. Analysis of Variance F Test (answer)
True or False: If the null hypothesis in ANOVA is false, the observed variability in the sample means will be greater than the variability you would expect if the means are equal.
True
False

18. Analysis of Variance F Test
True or False: The P-value for ANOVA will be small when the F test statistic is large.
True
False

19. Analysis of Variance F Test (answer)
True or False: The P-value for ANOVA will be small when the F test statistic is large.
True
False

20. Analysis of Variance F Test
Eighty-three patients undergoing elective knee arthroscopy were randomly divided into three treatment groups. Group 1 was given an NSAID drug before and after surgery. Group 2 was given a placebo before surgery and the NSAID after. Group 3 was given the placebo before and after surgery. Using ANOVA, researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery.
What was the null hypothesis?

21. Analysis of Variance F Test (answer)
Eighty-three patients undergoing elective knee arthroscopy were randomly divided into three treatment groups. Group 1 was given an NSAID drug before and after surgery. Group 2 was given a placebo before surgery and the NSAID after. Group 3 was given the placebo before and after surgery. Using ANOVA, researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery.
What was the null hypothesis?

22. Analysis of Variance F Test
Eighty-three patients undergoing elective knee arthroscopy were randomly divided into three treatment groups. Group 1 was given an NSAID drug before and after surgery. Group 2 was given a placebo before surgery and the NSAID after. Group 3 was given the placebo before and after surgery. Using ANOVA, researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery.
What was the alternative hypothesis?

23. Analysis of Variance F Test (answer)
Eighty-three patients undergoing elective knee arthroscopy were randomly divided into three treatment groups. Group 1 was given an NSAID drug before and after surgery. Group 2 was given a placebo before surgery and the NSAID after. Group 3 was given the placebo before and after surgery. Using ANOVA, researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery.
What was the alternative hypothesis for this study?

24. Using Technology
Eighty-three patients undergoing elective knee arthroscopy were randomly divided into three treatment groups. Using ANOVA, researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery.
Using the output below, what was the F statistic for comparing the means?
0.012
4.79
2553
23.10

25. Using Technology (answer)
Eighty-three patients undergoing elective knee arthroscopy were randomly divided into three treatment groups. Using ANOVA, researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery.
Using the output below, what was the F-statistic for comparing the means?
0.012
4.79
2553
23.10

26. Using Technology
Eighty-three patients undergoing elective knee arthroscopy were randomly divided into three treatment groups. Using ANOVA, researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery.
Using the output below, what was the P-value for comparing the means?
0.012
4.79
0.024
0.006

27. Using Technology (answer)
Eighty-three patients undergoing elective knee arthroscopy were randomly divided into three treatment groups. Using ANOVA, researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery.
Using the output below, what was the P-value for comparing the means?
0.012
4.79
0.024
0.006

28. Using Technology
Using the output below, which of the following conclusions is correct regarding the mean pain score one day after surgery? Use  = 0.05.
It does not differ significantly among the three treatment groups.
It differs significantly among all three treatment groups.
It is significantly lower for Group 1 compared with Group 3.
It is significantly lower for Group 1 compared with Group 2.

29. Using Technology (answer)
Using the output below, which of the following conclusions is correct regarding the mean pain score one day after surgery? Use  = 0.05.
It does not differ significantly among the three treatment groups.
It differs significantly among all three treatment groups.
It is significantly lower for Group 1 compared with Group 3.
It is significantly lower for Group 1 compared with Group 2.

30. Conditions for ANOVA
Which of the following is NOT a condition for ANOVA to produce valid results?
There must be an SRS from each of the populations.
Each population follows the Normal distribution.
All SRSs are the same size.
All populations have the same standard deviation.

31. Conditions for ANOVA (answer)
Which of the following is NOT a condition for ANOVA to produce valid results?
There must be an SRS from each of the populations.
Each population follows the Normal distribution.
All SRSs are the same size.
All populations have the same standard deviation.