Practice Problems: TWO-FACTOR ANOVA




A research study was conducted to examine the impact of eating a high protein breakfast on adolescents' performance during a physical education physical fitness test. Half of the subjects received a high protein breakfast and half were given a low protein breakfast. All of the adolescents, both male and female, were given a fitness test with high scores representing better performance. Test scores are recorded below.

Group High Protein Low Protein
Males10
7
9
6
8
5
4
7
4
5
Females5
4
6
3
2
3
4
5
1
2


  1. Complete the following ANOVA table.


    SourceSSdfMSF
    Protein Level201
    Gender451
    Protein Level x
    Gender    		51
    Within 36 16
    Total


  2. Graph your data.

  3. Are there any significant main effects or an interaction effect.

  4. Interpret your answer.



Answer


Researchers have sought to examine the effect of various types of music on agitation levels in patients who are in the early and middle stages of Alzheimer's disease. Patients were selected to participate in the study based on their stage of Alzheimer's disease. Three forms of music were tested: Easy listening, Mozart, and piano interludes. While listening to music, agitation levels were recorded for the patients with a high score indicating a higher level of agitation. Scores are recorded below.

Group Piano Interlude MozartEasy Listening
Early Stage Alzheimer's21
24
22
18
20
9
12
10
5
9
29
26
30
24
26
Middle Stage Alzheimer's22
20
25
18
20
14
18
11
9
13
15
18
20
13
19


  1. Complete the following ANOVA table.


    SourceSSdfMSF
    Type of Music7402
    Degree of Alzheimer's301
    Music x Alzheimer's2602
    Within 178 24
    Total


  2. Graph your data.

  3. Are there any significant main effects or an interaction effect.

  4. Interpret your answer.



Answer


A study examining differences in life satisfaction between young adult, middle adult, and older adult men and women was conducted. Each individual who participated in the study completed a life satisfaction questionnaire. A high score on the test indicates a higher level of life satisfaction. Test scores are recorded below.

Group Young Adult Middle AdultOlder Adult
Male4
2
3
4
2
7
5
7
5
6
10
7
9
8
11
Female7
4
3
6
5
8
10
7
7
8
10
9
12
11
13


  1. Complete the following ANOVA table.


    SourceSSdfMSF
    Age1802
    Gender301
    Age x Gender02
    Within 44 24
    Total


  2. Graph your data.

  3. Are there any significant main effects or an interaction effect.

  4. Interpret your answer.



Answer


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