Two-Way ANOVA
1. Elementary Science 6 Achievement Test Score of 27 Pupils Classified According to Prior Elementary Science Achievement and Performance on a Test of Rigidity
1. Elementary Science 6 Achievement Test Score of 27 Pupils Classified According to Prior Elementary Science Achievement and Performance on a Test of Rigidity
Rigidity Tendency
Prior Elementary Science Achievement
Low Achievers
Average Achievers
High Achievers
High Rigidity 40 53 61
42
45
51
37 50 58
Average Rigidity 46 52 58
45 53 60
47
52
57
Low Rigidity
52 54 64
53
56 64
50
59 67
Alpha = 0.01
2. Scores of 80
individuals of both sexes on an attitude scale after the administration of four
different films
Males FILM
1 2 3 4
10 14 13 16
8 12 12 12
6 8 10 10
4 4 9 9
4 4 9 9
4 4 7 7
2 3 4 7
2 2 4 6
2 2 4 5
1 1 2 5
Females 14 14 10 18
12 13 10 16
12 12 10 15
10 11 9 14
8 10 9 13
6 9 7 10
4 7 7 10
2 6 6 10
2 3 5 10
1 2 4 9
Alpha = 0.05
3. Below are the scores of a group of fraternity and
nonfraternity men broken down by class on a attitude scale. Analyze these data following the factorial
design and make the appropriate F tests.
Set alpha 0.01.
Fraternity
Men
Freshmen Sophomores Juniors Seniors
12 22 26 30
8 18 20 26
10 12 18 20
6 20 16 22
8 8 10 18
Nonfraternity
Men
18 20 22 24
16 18 21 22
8 12 19 16
12 18 17 18
14 16 18 24
4. Apply the two-way
ANOVA to the following data. Use 5
percent level of significance.
English Low
Achievers Average
Achievers High Achievers
33 43 41
40 35 31
36 40 38
Filipino 36 42 48
35 43 49
37 42 37
Median Test and the Mann-Whitney Test
The median test is a non-parametric test that determines the
significance of the difference between the medians of two independent
groups.
1.
A
researcher wished to compare the effect of a treatment upon the number of
correct responses on an achievement test.
The experimental group received the treatment while the control group
did not. The data are indicated in the
table below:
Experimental Group Control
Group
46 24 48 16
45 24 46 15
43 23 42 15
41 21 40 14
31 19 38 13
31 17 28 12
27 16 19 10
26 13 18 10
26 12 18 9
25 9 17 8
2. Below are the scores of a group of students who used a
new teaching methodology and a group of students who were taught in traditional
way. Test the hypothesis of no
difference using the median test at 5% level of significance.
New
Method Traditional
Method
6 8 7 5
14 13 12 13
16 6 8 6
9 7 4 5
10 14 5 12
10 14
3.In the data below are two sample of scores
obtained on the standardized achievement test.
Apply the median test to test the hypothesis of no difference. Use 5% level of significance.
Group
A Group
B
47 40 30 48
35 37 32 40
30 43 33 42
40 32 35 34
25 29 46 28
Friedman Two-Way Analysis of Variance by
Ranks
When the data from K matched samples are in
at least an ordinal scale, the Friedman two-way of variance by ranks is used to
test the null hypothesis that the K samples have been drawn from
the same population. The matched samples may be the same group of
individuals who have been exposed to several conditions, or they be sets of
individuals who have been matched on relevant variables and are randomly
assigned to different conditions.
1.
How
significant is the difference in the impressions of school special services
personnel, classroom teacher, and department heads on the management practices
of their school administrator?
|
ITEM
|
Personnel Weighted Ave
|
Teachers weighted AVE
|
Heads Weighted Ave
|
|
1.
Interviews are conducted in recruiting
personnel
|
3.984
|
3.872
|
3.867
|
|
2.
Examinations play an important role in
recruitment
|
4.442
|
4.392
|
4.111
|
|
3.
Interviews are conducted before an applicant
takes the exam.
|
4.823
|
4.783
|
4.799
|
|
4.
The applicant is oriented towards the
practices of the organization.
|
4.217
|
4.314
|
4.333
|
|
5.
The applicant is likewise made aware of the
disciplinary measures of erring personnel.
|
4.632
|
4.698
|
3.983
|
2.
A company’s trainees are randomly assigned to
groups that are oriented on certain industrial inspection procedure by three
different methods and at the end of the orientation period they are tested for
inspection performance quality. The
following are their scores.
|
Method 1
|
84
|
71
|
81
|
64
|
76
|
87
|
|
|
Method 2
|
75
|
72
|
69
|
74
|
51
|
62
|
70
|
|
Method 3
|
79
|
57
|
62
|
66
|
79
|
|
|
3.
Below are the scores of three matched groups
under four conditions. Test the null
hypothesis using the Friedman two-way ANOVA.
Alpha = 0.01
Conditions
Groups I II III IV
A 9 4 1 7
B 6 5 2 8
C 9 1 2 6
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