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Exam 10: Comparing More Than Two Means

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Exam 1: Preliminaries: Introduction to Statistical Investigations46 Questionsadd course
Exam 2: Significance: How Strong Is the Evidence75 Questionsadd course
Exam 3: Generalization: How Broadly Do the Results Apply64 Questionsadd course
Exam 4: Estimation: How Large Is the Effect61 Questionsadd course
Exam 5: Causation: Can We Say What Caused the Effect30 Questionsadd course
Exam 6: Comparing Two Proportions46 Questionsadd course
Exam 7: Comparing Two Means46 Questionsadd course
Exam 8: Paired Data: One Quantitative Variable48 Questionsadd course
Exam 9: Comparing More Than Two Proportions46 Questionsadd course
Exam 10: Comparing More Than Two Means28 Questionsadd course
Exam 11: Two Quantitative Variables73 Questionsadd course
Exam 12: Modeling Randomness129 Questionsadd course
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College students tested to see if how well you know a person affects your ability to detect a lie from that person. To do this, they came up with 10 statements about a person in their group. Five of these statements were true and five were False. The group tried to make up statements that no-body (not even close friends) would know if they were true or False. The students then presented these statements to people that fit in three groups: close friends, acquaintances, and complete strangers and counted how many statements each person correctly identified as true or False. A summary of the results are as follows. College students tested to see if how well you know a person affects your ability to detect a lie from that person. To do this, they came up with 10 statements about a person in their group. Five of these statements were true and five were False. The group tried to make up statements that no-body (not even close friends) would know if they were true or False. The students then presented these statements to people that fit in three groups: close friends, acquaintances, and complete strangers and counted how many statements each person correctly identified as true or False. A summary of the results are as follows. -The two graphs, A and B, show dotplots from two different data sets. Suppose I want to com-pare the means in A and do another comparison of means in B. For each case I compute an F-statistic. Which of the following will be true about these statistics? -The two graphs, A and B, show dotplots from two different data sets. Suppose I want to com-pare the means in A and do another comparison of means in B. For each case I compute an F-statistic. Which of the following will be true about these statistics? College students tested to see if how well you know a person affects your ability to detect a lie from that person. To do this, they came up with 10 statements about a person in their group. Five of these statements were true and five were False. The group tried to make up statements that no-body (not even close friends) would know if they were true or False. The students then presented these statements to people that fit in three groups: close friends, acquaintances, and complete strangers and counted how many statements each person correctly identified as true or False. A summary of the results are as follows. -The two graphs, A and B, show dotplots from two different data sets. Suppose I want to com-pare the means in A and do another comparison of means in B. For each case I compute an F-statistic. Which of the following will be true about these statistics?

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Question 1
Correct Answer:
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C

If changing the third treatment group from blue to purple increases the difference in the purple group's average score from the other two groups, all else remaining the same, what will be the impact on the strength of evidence for finding a difference in the average scores on the three exams?

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Question 2
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A

In a neurological study of the effect of environment on mental development, rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), Standard (cage with other rats), Enriched (cage with other rats and toys), and Super Enriched (cage with other rats and toys changed on a periodic basis). After two months, the rats were tested on a variety of learning measures, one of them being the number of attempts needed to learn to navigate a maze. The data for the maze task are below, along with means and standard deviation for each group. In a neurological study of the effect of environment on mental development, rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), Standard (cage with other rats), Enriched (cage with other rats and toys), and Super Enriched (cage with other rats and toys changed on a periodic basis). After two months, the rats were tested on a variety of learning measures, one of them being the number of attempts needed to learn to navigate a maze. The data for the maze task are below, along with means and standard deviation for each group. -Which of the following plots would be appropriate to investigate the relationship between test condition and number of attempts needed to learn to navigate a maze? Select all that apply. -Which of the following plots would be appropriate to investigate the relationship between test condition and number of attempts needed to learn to navigate a maze? Select all that apply.

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Question 3
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C, D

In a neurological study of the effect of environment on mental development, rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), Standard (cage with other rats), Enriched (cage with other rats and toys), and Super Enriched (cage with other rats and toys changed on a periodic basis). After two months, the rats were tested on a variety of learning measures, one of them being the number of attempts needed to learn to navigate a maze. The data for the maze task are below, along with means and standard deviation for each group. In a neurological study of the effect of environment on mental development, rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), Standard (cage with other rats), Enriched (cage with other rats and toys), and Super Enriched (cage with other rats and toys changed on a periodic basis). After two months, the rats were tested on a variety of learning measures, one of them being the number of attempts needed to learn to navigate a maze. The data for the maze task are below, along with means and standard deviation for each group. -Does the analysis using the Mean Group Diff statistic allow you to determine which test conditions differ significantly from which others? -Does the analysis using the Mean Group Diff statistic allow you to determine which test conditions differ significantly from which others?

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Question 4

A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Compute the F-statistic using the summary statistics listed. A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Compute the F-statistic using the summary statistics listed. -Compute the F-statistic using the summary statistics listed.

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Question 5

A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Follow-up 95% confidence intervals are presented below. • • • The mean amount spent when classical music is playing is significantly higher than the mean amount spent when no music is playing. A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Follow-up 95% confidence intervals are presented below. • • • The mean amount spent when classical music is playing is significantly higher than the mean amount spent when no music is playing. -Follow-up 95% confidence intervals are presented below. • A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Follow-up 95% confidence intervals are presented below. • • • The mean amount spent when classical music is playing is significantly higher than the mean amount spent when no music is playing. • A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Follow-up 95% confidence intervals are presented below. • • • The mean amount spent when classical music is playing is significantly higher than the mean amount spent when no music is playing. • A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Follow-up 95% confidence intervals are presented below. • • • The mean amount spent when classical music is playing is significantly higher than the mean amount spent when no music is playing. The mean amount spent when classical music is playing is significantly higher than the mean amount spent when no music is playing.

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Question 6

What is the null hypothesis? Select all that apply.

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Question 7

The F statistic can be negative.

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Question 8

College students tested to see if how well you know a person affects your ability to detect a lie from that person. To do this, they came up with 10 statements about a person in their group. Five of these statements were true and five were False. The group tried to make up statements that no-body (not even close friends) would know if they were true or False. The students then presented these statements to people that fit in three groups: close friends, acquaintances, and complete strangers and counted how many statements each person correctly identified as true or False. A summary of the results are as follows. College students tested to see if how well you know a person affects your ability to detect a lie from that person. To do this, they came up with 10 statements about a person in their group. Five of these statements were true and five were False. The group tried to make up statements that no-body (not even close friends) would know if they were true or False. The students then presented these statements to people that fit in three groups: close friends, acquaintances, and complete strangers and counted how many statements each person correctly identified as true or False. A summary of the results are as follows. -Using the simulated null distribution of Mean Group Diff statistics in question 13, what is the strength of evidence against the null hypothesis? -Using the simulated null distribution of Mean Group Diff statistics in question 13, what is the strength of evidence against the null hypothesis?

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Question 9

As the size of the sample in each group increases, all else remaining the same, what will be the impact on the strength of evidence for finding a difference in the average scores on the three exams?

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Question 10

A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Follow-up 95% confidence intervals are presented below. • • • The mean amount spent when pop music is playing is significantly higher than the mean amount spent when no music is playing. A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Follow-up 95% confidence intervals are presented below. • • • The mean amount spent when pop music is playing is significantly higher than the mean amount spent when no music is playing. -Follow-up 95% confidence intervals are presented below. • A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Follow-up 95% confidence intervals are presented below. • • • The mean amount spent when pop music is playing is significantly higher than the mean amount spent when no music is playing. • A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Follow-up 95% confidence intervals are presented below. • • • The mean amount spent when pop music is playing is significantly higher than the mean amount spent when no music is playing. • A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -Follow-up 95% confidence intervals are presented below. • • • The mean amount spent when pop music is playing is significantly higher than the mean amount spent when no music is playing. The mean amount spent when pop music is playing is significantly higher than the mean amount spent when no music is playing.

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Question 11

A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -The p-value for the ANOVA F-test is less than 0.001. How would you interpret this value? A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals. The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days. Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below. -The p-value for the ANOVA F-test is less than 0.001. How would you interpret this value? -The p-value for the ANOVA F-test is less than 0.001. How would you interpret this value?

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Question 12

In a neurological study of the effect of environment on mental development, rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), Standard (cage with other rats), Enriched (cage with other rats and toys), and Super Enriched (cage with other rats and toys changed on a periodic basis). After two months, the rats were tested on a variety of learning measures, one of them being the number of attempts needed to learn to navigate a maze. The data for the maze task are below, along with means and standard deviation for each group. In a neurological study of the effect of environment on mental development, rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), Standard (cage with other rats), Enriched (cage with other rats and toys), and Super Enriched (cage with other rats and toys changed on a periodic basis). After two months, the rats were tested on a variety of learning measures, one of them being the number of attempts needed to learn to navigate a maze. The data for the maze task are below, along with means and standard deviation for each group. -A simulated null distribution of 1,000 Mean Group Diff statistics follows. Describe how to use this distribution to calculate the p-value. -A simulated null distribution of 1,000 Mean Group Diff statistics follows. In a neurological study of the effect of environment on mental development, rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), Standard (cage with other rats), Enriched (cage with other rats and toys), and Super Enriched (cage with other rats and toys changed on a periodic basis). After two months, the rats were tested on a variety of learning measures, one of them being the number of attempts needed to learn to navigate a maze. The data for the maze task are below, along with means and standard deviation for each group. -A simulated null distribution of 1,000 Mean Group Diff statistics follows. Describe how to use this distribution to calculate the p-value. Describe how to use this distribution to calculate the p-value.

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Question 13

College students tested to see if how well you know a person affects your ability to detect a lie from that person. To do this, they came up with 10 statements about a person in their group. Five of these statements were true and five were False. The group tried to make up statements that no-body (not even close friends) would know if they were true or False. The students then presented these statements to people that fit in three groups: close friends, acquaintances, and complete strangers and counted how many statements each person correctly identified as true or False. A summary of the results are as follows. College students tested to see if how well you know a person affects your ability to detect a lie from that person. To do this, they came up with 10 statements about a person in their group. Five of these statements were true and five were False. The group tried to make up statements that no-body (not even close friends) would know if they were true or False. The students then presented these statements to people that fit in three groups: close friends, acquaintances, and complete strangers and counted how many statements each person correctly identified as true or False. A summary of the results are as follows. -A null distribution was generated for this example and is shown. What is the shape of this distribution? -A null distribution was generated for this example and is shown. What is the shape of this distribution?

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Question 14

Why do you do overall tests when comparing multiple means and not just do the follow-up confidence intervals?

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Question 15

The two graphs, A and B, show dotplots from two different data sets. Suppose I want to com-pare the means in A and do another comparison of means in B. For each case I compute a MAD statistic. Which of the following will be true about these statistics? The two graphs, A and B, show dotplots from two different data sets. Suppose I want to com-pare the means in A and do another comparison of means in B. For each case I compute a MAD statistic. Which of the following will be true about these statistics?

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Question 16

As the F statistic increases, the p-value decreases.

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Question 17

In a neurological study of the effect of environment on mental development, rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), Standard (cage with other rats), Enriched (cage with other rats and toys), and Super Enriched (cage with other rats and toys changed on a periodic basis). After two months, the rats were tested on a variety of learning measures, one of them being the number of attempts needed to learn to navigate a maze. The data for the maze task are below, along with means and standard deviation for each group. In a neurological study of the effect of environment on mental development, rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), Standard (cage with other rats), Enriched (cage with other rats and toys), and Super Enriched (cage with other rats and toys changed on a periodic basis). After two months, the rats were tested on a variety of learning measures, one of them being the number of attempts needed to learn to navigate a maze. The data for the maze task are below, along with means and standard deviation for each group. -What is the value of the Mean Group Diff statistic? -What is the value of the Mean Group Diff statistic?

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Question 18

The Mean Group Diff statistic cannot be negative.

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Question 19

College students tested to see if how well you know a person affects your ability to detect a lie from that person. To do this, they came up with 10 statements about a person in their group. Five of these statements were true and five were False. The group tried to make up statements that no-body (not even close friends) would know if they were true or False. The students then presented these statements to people that fit in three groups: close friends, acquaintances, and complete strangers and counted how many statements each person correctly identified as true or False. A summary of the results are as follows. College students tested to see if how well you know a person affects your ability to detect a lie from that person. To do this, they came up with 10 statements about a person in their group. Five of these statements were true and five were False. The group tried to make up statements that no-body (not even close friends) would know if they were true or False. The students then presented these statements to people that fit in three groups: close friends, acquaintances, and complete strangers and counted how many statements each person correctly identified as true or False. A summary of the results are as follows. -If the Mean Group Diff statistic had been smaller than the observed Mean Group Diff statistic calculated in question 12, how would the strength of evidence change? -If the Mean Group Diff statistic had been smaller than the observed Mean Group Diff statistic calculated in question 12, how would the strength of evidence change?

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