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# Analysis of Variance and Comparing with Repeated Measures Design

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We considered Mary's interest in doing a study to see if learning of 6th graders on a math lesson is affected by background noise level. There, she was planning to use 2 noise conditions and then analyze her outcomes using a t-test for independent groups. Describe the study Mary might plan where she would use a one-way analysis of variance (ANOVA) for independent groups instead of a t-test to study differences between noise levels. What is her independent variable here? Describe the conditions she could create for this study. What is her dependent variable? Describe a way to measure the DV so that each participant would have one score at the end that would be on a continuous scale of measurement. Support your responses.

Consider Mary's study of whether the learning of 6th graders on a math lesson is affected by background noise level. Describe the pros and cons of Mary using a repeated measures design for this study. What would you probably choose to do? Support your responses.

https://brainmass.com/statistics/multivariate-anova/analysis-variance-comparing-with-repeated-measures-design-589185

#### Solution Preview

What is her independent variable here? Describe the conditions she could create for this study.
Answer: here, the independent variable is the background noise level.
We know that one-way ANOVA requires only one independent variable which has at least 3 levels.
Since Mary wants to use a one-way analysis of variance (ANOVA), she must consider at least 3 levels of background noise level. For example, she may ...

#### Solution Summary

The solution gives detailed discussion on applying one-way analysis of variance using a real example and comparing it with repeated measures design. 286 words.

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## Multiple choice questions on design of experiments

For an independent-measures experiment comparing two treatment conditions with a sample of n = 10 in each treatment, the F-ratio would have df equal to __________.

18

19

1, 18

1, 19

A researcher reports an F-ratio with df = 3, 36 for an independent-measures experiment. How many treatment conditions were compared in this experiment?

3

4

36

39

A research report concludes that there are significant differences among treatments, with "F(2,27) = 8.62, p < .01." How many treatment conditions were compared in this study?

2

3

29

30

A research study compares three treatments with n = 5 in each treatment. If the SS values for the three treatments are 25, 20, and 15, then the analysis of variance would produce SS within equal to __________.

12

20

60

cannot be determined from the information given

In the F-ratio for a repeated-measures ANOVA, variability due to individual differences __________.

is automatically eliminated from the numerator but must be computed and subtracted out of the denominator

is automatically eliminated from the denominator but must be computed and subtracted out of the numerator

is automatically eliminated from both the numerator and the denominator

must be computed and subtracted out of the numerator and the denominator

A repeated-measures study uses a sample of n = 8 participants to evaluate the mean differences among three treatment conditions. In the analysis of variance for this study, what is the value for df total?

2

7

21

23

A repeated-measures analysis of variance with a sample of n = 8 participants, produces df within treatments = 14. What is the value for df error for this analysis?

6

7

21

Which of the following are sources of variability that contribute to SS between treatments in a repeated ANOVA?

treatment effect and chance/error

treatment effect and individual differences

treatment effect, individual differences, and chance/error

individual differences and chance/error

The results of a repeated-measures ANOVA are reported as follows, F(3, 27) = 1.12, p > .05. How many subjects participated in the study?

40

36

10

9

A two-factor study with two levels of factor A and three levels of factor B uses a separate sample of n = 5 participants in each treatment condition. How many participants are needed for the entire study?

5

10

25

30

The results of a two-factor analysis of variance produce df = 2, 24 for the F-ratio for fac-tor A. Based on this information, how many levels of factor A were compared in the study?

2

3

24

25

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