This data set represents 33 individuals responding to different types of drugs w
ID: 3309656 • Letter: T
Question
This data set represents 33 individuals responding to different types of drugs with the output is the level of pain.
Perform two-factor Full-Factorial ANOVA and answer the following questions
which of the following statements interpret the ANOVA output below?
Gender
Drug
Pain
male
C
12.4
female
A
7.69
male
C
14
female
A
9.69
male
C
11.6
female
A
8.89
female
A
6.94
female
A
2.13
female
A
7.26
female
A
5.87
male
B
12.9
female
C
12.2
female
A
7.2
male
C
13.9
male
A
8.18
male
B
16.6
female
C
9.41
male
C
11.2
female
B
8.35
male
A
7.24
female
A
6.81
male
B
9.81
female
A
6.67
female
A
6.98
female
A
7.07
female
C
2.4
male
B
7.84
female
B
3.84
male
B
9.42
male
A
7
male
A
7
female
A
5
male
A 8
The overall effects of drugs and gender are weak as evident by a large total sum of squares of 337.55420
The interaction between drugs and gender is significant as evident by high ratio between model mean square and error mean square
The overall effects of drugs and gender are insignificant as evident by a large error sum of squares of 157.39648
The overall effects of drugs and gender are significant as evident by a small model degree of freedom
The overall effects of drugs and gender are significant as evident by a small value of error mean square of 5.8295
The effect of drug is more significant than the effect of gender
The overall effects of drugs and gender are significant as evident by the high F-ratio associated with a probability area of less than 0.05
Gender
Drug
Pain
male
C
12.4
female
A
7.69
male
C
14
female
A
9.69
male
C
11.6
female
A
8.89
female
A
6.94
female
A
2.13
female
A
7.26
female
A
5.87
male
B
12.9
female
C
12.2
female
A
7.2
male
C
13.9
male
A
8.18
male
B
16.6
female
C
9.41
male
C
11.2
female
B
8.35
male
A
7.24
female
A
6.81
male
B
9.81
female
A
6.67
female
A
6.98
female
A
7.07
female
C
2.4
male
B
7.84
female
B
3.84
male
B
9.42
male
A
7
male
A
7
female
A
5
male
A 8
Explanation / Answer
We have following output for full factorial ANOVA:
Tests of Between-Subjects Effects
Dependent Variable: Pain
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Corrected Model
180.158a
5
36.032
6.181
.001
Intercept
1811.208
1
1811.208
310.697
.000
Gender
73.489
1
73.489
12.606
.001
Drug
50.902
2
25.451
4.366
.023
Gender * Drug
30.406
2
15.203
2.608
.092
Error
157.396
27
5.829
Total
2738.664
33
Corrected Total
337.554
32
a. R Squared = .534 (Adjusted R Squared = .447)
Using above output, we can check the validity of stataments made:
1. The overall effects of drugs and gender are weak as evident by a large total sum of squares of 337.55420
We can not conclude for total sum of square in this way, hence first statement is not valid.
2. The interaction between drugs and gender is significant as evident by high ratio between model mean square and error mean square
The interaction between drug and gender is not significant (at 5% level), because the p-value is reported as 0.092 < 0.05, but if we consider higher significance level i.e. 10%, we can conclude the interaction to be significant.
3. The overall effects of drugs and gender are insignificant as evident by a large error sum of squares of 157.39648
Incorrect.
4. The overall effects of drugs and gender are significant as evident by a small model degree of freedom
Incorrect
5. The overall effects of drugs and gender are significant as evident by a small value of error mean square of 5.8295
Incorect
6. The effect of drug is more significant than the effect of gender
We can not make this conclusion
7. The overall effects of drugs and gender are significant as evident by the high F-ratio associated with a probability area of less than 0.05
Correct.
Tests of Between-Subjects Effects
Dependent Variable: Pain
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Corrected Model
180.158a
5
36.032
6.181
.001
Intercept
1811.208
1
1811.208
310.697
.000
Gender
73.489
1
73.489
12.606
.001
Drug
50.902
2
25.451
4.366
.023
Gender * Drug
30.406
2
15.203
2.608
.092
Error
157.396
27
5.829
Total
2738.664
33
Corrected Total
337.554
32
a. R Squared = .534 (Adjusted R Squared = .447)
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