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Active Learning Lecture Slides For use with Classroom Response Systems Comparing Groups: Analysis of Variance Methods

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Copyright © 2013 Pearson Education, Inc. 14.1 Which of the following could be the null hypothesis for a One Factor ANOVA problem? a) b) c) d) The two variables are independent.

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Copyright © 2013 Pearson Education, Inc. 14.1 Which of the following could be the null hypothesis for a One Factor ANOVA problem? a) b) c) d) The two variables are independent.

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Copyright © 2013 Pearson Education, Inc. 14.2 Do energy drinks consumed before a race allow you to finish the race sooner? Sixteen different people were randomly selected in groups of four to consume PowerAde, Propel, Gatorade and water before a race. What would be the degrees of freedom of the F test statistic? a) b) c) d) e)

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Copyright © 2013 Pearson Education, Inc. 14.2 Do energy drinks consumed before a race allow you to finish the race sooner? Sixteen different people were randomly selected in groups of four to consume PowerAde, Propel, Gatorade and water before a race. What would be the degrees of freedom of the F test statistic? a) b) c) d) e)

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Copyright © 2013 Pearson Education, Inc. 14.3 Do energy drinks consumed before a race allow you to finish the race sooner? Sixteen different people were randomly selected in groups of four to consume PowerAde, Propel, Gatorade and water before a race. The sample means were 20.5, 20.25, 17.75 and 20.75, respectively. Is this evidence that Gatorade reduces the time to complete a 5K? a) Yes, 17.75 is significantly different from the others in the 20s. b) No, all of the means are essential the same. c) There is insufficient information. We need information about the variation in the samples.

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Copyright © 2013 Pearson Education, Inc. 14.3 Do energy drinks consumed before a race allow you to finish the race sooner? Sixteen different people were randomly selected in groups of four to consume PowerAde, Propel, Gatorade and water before a race. The sample means were 20.5, 20.25, 17.75 and 20.75, respectively. Is this evidence that Gatorade reduces the time to complete a 5K? a) Yes, 17.75 is significantly different from the others in the 20s. b) No, all of the means are essential the same. c) There is insufficient information. We need information about the variation in the samples.

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Copyright © 2013 Pearson Education, Inc. 14.4 Do energy drinks consumed before a race allow you to finish the race sooner? Sixteen different people were randomly selected in groups of four to consume PowerAde, Propel, Gatorade and water before a race. For what value of the F test statistic would we have a p-value of 0.05? a) 1.96 b) 3.01 c) 3.26 d) 3.49

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Copyright © 2013 Pearson Education, Inc. 14.4 Do energy drinks consumed before a race allow you to finish the race sooner? Sixteen different people were randomly selected in groups of four to consume PowerAde, Propel, Gatorade and water before a race. For what value of the F test statistic would we have a p-value of 0.05? a) 1.96 b) 3.01 c) 3.26 d) 3.49

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Copyright © 2013 Pearson Education, Inc. 14.5 Do energy drinks consumed before a race allow you to finish the race sooner? Sixteen different people were randomly selected in groups of four to consume PowerAde, Propel, Gatorade and water before a race. The test statistic for this test was 1.62 and the p-value was 0.237. What is the conclusion? a) We have statistically significant evidence to show that energy drinks helped decrease the average run time. b) We do not have statistically significant evidence that there was a difference in the average run time for the four drinks. c) We have statistically significant evidence that at least one of the drinks had a different run time than the others.

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Copyright © 2013 Pearson Education, Inc. 14.5 Do energy drinks consumed before a race allow you to finish the race sooner? Sixteen different people were randomly selected in groups of four to consume PowerAde, Propel, Gatorade and water before a race. The test statistic for this test was 1.62 and the p-value was 0.237. What is the conclusion? a) We have statistically significant evidence to show that energy drinks helped decrease the average run time. b) We do not have statistically significant evidence that there was a difference in the average run time for the four drinks. c) We have statistically significant evidence that at least one of the drinks had a different run time than the others.

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Copyright © 2013 Pearson Education, Inc. 14.6 According to the Bonferroni method, if you wanted to be at least 95% confident in ALL 10 confidence interval comparisons of two means, what confidence level would each individual confidence interval need to be? a) 95% b) 99% c) 99.5% d) Cannot be determined

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Copyright © 2013 Pearson Education, Inc. 14.6 According to the Bonferroni method, if you wanted to be at least 95% confident in ALL 10 confidence interval comparisons of two means, what confidence level would each individual confidence interval need to be? a) 95% b) 99% c) 99.5% d) Cannot be determined

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Copyright © 2013 Pearson Education, Inc. 14.7 Which of the following cases represent indicator variables for a regression model to compare three groups? a) b) c) d)

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Copyright © 2013 Pearson Education, Inc. 14.7 Which of the following cases represent indicator variables for a regression model to compare three groups? a) b) c) d)

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Copyright © 2013 Pearson Education, Inc. 14.8 A teacher randomly assigned her students to three different study methods. Five students used flashcards (s = 6.181), five students re-read their notes three times (s = 4.183) and five students listened to the lectures again on video tape (s = 10.368). The MSE equals 54.4 and the data does not exhibit any outliers or heavy skew. Which of the following assumptions of Fishers confidence intervals is NOT met? a) Randomization used in applying treatments. b) Data comes from a Normal distribution. c) Populations have identical standard deviations. d) A and B are not met. e) A and C are not met.

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Copyright © 2013 Pearson Education, Inc. 14.8 A teacher randomly assigned her students to three different study methods. Five students used flashcards (s = 6.181), five students re-read their notes three times (s = 4.183) and five students listened to the lectures again on video tape (s = 10.368). The MSE equals 54.4 and the data does not exhibit any outliers or heavy skew. Which of the following assumptions of Fishers confidence intervals is NOT met? a) Randomization used in applying treatments. b) Data comes from a Normal distribution. c) Populations have identical standard deviations. d) A and B are not met. e) A and C are not met.

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Copyright © 2013 Pearson Education, Inc. 14.9 Suppose that a scientist had 8 groups and he wanted to compare each of the groups to each other using a 95% confidence interval. How many comparisons would that be and how many – on average – would likely not contain the true population mean difference? a) 8 confidence intervals and none would not contain the true value. b) 16 confidence intervals and none would not contain the true value. c) 28 confidence intervals and 1.4 would not contain the true value. d) 32 confidence intervals and 1.6 would not contain the true value. e) None of the above.

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Copyright © 2013 Pearson Education, Inc. 14.9 Suppose that a scientist had 8 groups and he wanted to compare each of the groups to each other using a 95% confidence interval. How many comparisons would that be and how many – on average – would likely not contain the true population mean difference? a) 8 confidence intervals and none would not contain the true value. b) 16 confidence intervals and none would not contain the true value. c) 28 confidence intervals and 1.4 would not contain the true value. d) 32 confidence intervals and 1.6 would not contain the true value. e) None of the above.

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Copyright © 2013 Pearson Education, Inc. 14.10 An education researcher was researching which methods worked best to prepare students for the SAT. She randomly selected 5 students to take a class (C), 5 students to complete a workbook (W) and 5 students to complete a computer software program (SP). The results of Tukeys multiple comparisons are below. Between which groups was there a significant difference in the population mean SAT scores? a) C, W b) C, SP c) SP, W d) All of the above e) None of the above Groups Confidence Interval SP, W(-83.46, 192.66) C, W(18.54, 294.66) C, SP(-36.06, 240.06)

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Copyright © 2013 Pearson Education, Inc. 14.10 An education researcher was researching which methods worked best to prepare students for the SAT. She randomly selected 5 students to take a class (C), 5 students to complete a workbook (W) and 5 students to complete a computer software program (SP). The results of Tukeys multiple comparisons are below. Between which groups was there a significant difference in the population mean SAT scores? a) C, W b) C, SP c) SP, W d) All of the above e) None of the above Groups Confidence Interval SP, W(-83.46, 192.66) C, W(18.54, 294.66) C, SP(-36.06, 240.06)

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Copyright © 2013 Pearson Education, Inc. 14.11 An educational researcher is interested in determining what method works best for improving SAT scores. She randomly assigns 20 students to 4 groups: studying with a group using a workbook, studying in solitude with a workbook, studying with a group using a computer program and studying in solitude using a computer. To determine if the computer program had significantly different results than the workbook, what would be the null hypothesis for a Two Way ANOVA test? a) : mean SAT score is the same for each of the four groups. b) : mean SAT scores is the same for the computer program and workbook, for each fixed level of size of study group. c) : mean SAT score is the same for those that studied in solitude and those that studied in groups, for each fixed level of study method.

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Copyright © 2013 Pearson Education, Inc. 14.11 An educational researcher is interested in determining what method works best for improving SAT scores. She randomly assigns 20 students to 4 groups: studying with a group using a workbook, studying in solitude with a workbook, studying with a group using a computer program and studying in solitude using a computer. To determine if the computer program had significantly different results than the workbook, what would be the null hypothesis for a Two Way ANOVA test? a) : mean SAT score is the same for each of the four groups. b) : mean SAT scores is the same for the computer program and workbook, for each fixed level of size of study group. c) : mean SAT score is the same for those that studied in solitude and those that studied in groups, for each fixed level of study method.

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Copyright © 2013 Pearson Education, Inc. 14.12 In Two Way ANOVA, what does the term interaction mean? a) The effect on the response variable of changing from one level to another for the same factor is the same at each level of the other factor. b) The effect on the response variable of changing from one level to another for the same factor is NOT the same at each level of the other factor. c) This is when the levels of one factor are crossed with the levels of the other factor to form an experimental design. d) An experiment where both factors have a significant impact on the response variable.

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Copyright © 2013 Pearson Education, Inc. 14.12 In Two Way ANOVA, what does the term interaction mean? a) The effect on the response variable of changing from one level to another for the same factor is the same at each level of the other factor. b) The effect on the response variable of changing from one level to another for the same factor is NOT the same at each level of the other factor. c) This is when the levels of one factor are crossed with the levels of the other factor to form an experimental design. d) An experiment where both factors have a significant impact on the response variable.

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Copyright © 2013 Pearson Education, Inc. 14.13 What is the proper order to conduct a Two Way ANOVA problem? a) Test for interaction first, if not present proceed to test for main effects. b) Test for interaction first, if present proceed to test for main effects. c) Test for main effects first, if not present proceed to test for interaction. d) Test for main effects first, if present proceed to test for interaction.

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Copyright © 2013 Pearson Education, Inc. 14.13 What is the proper order to conduct a Two Way ANOVA problem? a) Test for interaction first, if not present proceed to test for main effects. b) Test for interaction first, if present proceed to test for main effects. c) Test for main effects first, if not present proceed to test for interaction. d) Test for main effects first, if present proceed to test for interaction.

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