11 Imagine that you have conducted a study to evaluate how l

11) Imagine that you have conducted a study to evaluate how listening to different types of music and taking a test at different times of day impacts performance of college students on a mathematics exam. While one set of students took the exam in the early morning, a second set of students took the exam late in the afternoon. For the first half of both exams, students answered questions while listening to rock music, while for the second half of both exams, students answered questions while listening to classical music. Thus even though time of day was different across the two groups of students, both groups of students experienced the two types of music. When conducting the ANOVA you find the following values when evaluating the interaction between music and time of day: F = 6.84, effect degrees of freedom = 1, error degrees of freedom = 24, p-value = .003. When evaluating the main effect of time of day, you find the following values: F = .86, effect degrees of freedom = 1, error degrees of freedom = 24, p-value = .67. When evaluating the main effect of type of music, you find the following values: F = 4.23, effect degrees of freedom = 1, error degrees of freedom = 24, p-value = .04.

Using the information above, please answer the following questions:

A) What is the between-subjects variable in this study? (3 points)

B) What is the within-subjects variable in this study? (3 points)

C) Using the values that you have been given, report the results of the F-tests for each main effect and interaction as you would in a research paper and discuss the significance of each test. (6 points)

Solution

A)

Time of the day of exam is the between subjects variable in this study because there is different set of subjects used for studying these variable. What I mean is any subject who is giving exam in early in the morning will not be giving exam late in the afternoon.

B).

Type of music is the within subjects variable in this study because the same subject who is listening rock music in first half of the exam is listening classical music in second half.

C).

Since P-value for time of day is large , the effect of time of day is not signficant. But the effect of music seems significant since the P-value is pretty small. What this means is that change in the time of day will not have any significant impact on student\'s performance but change in listening music will have significant impact on the student\'s performance.

Since the P-value for interaction is very small, the interaction between the variables time of day and type of music is significant.