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

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.

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.

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.

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.

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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?

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?

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?

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?

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

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

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

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

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.

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.

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.

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.