Homework SourseA sample of adults with hearing aids were randomly assigned
A sample of adults with hearing aids were randomly assigned to one of three conditions that focused on lists of practice words that are typically challenging for individuals with hearing loss to accurately perceive. Following 12 weeks of structured practice with a speech-language pathologist, they were assessed using a testing of speech perception to yield a “hearing score”. State the null and research hypotheses, assess the assumptions of ANOVA, and interpret the results (F-ratio, post hoc results when applicable), and describe the outcome of the study with respect to null hypothesis.
Between-Subjects Factors
N
ListID
List1
24
List2
24
List3
24
List4
24
Descriptive Statistics
Dependent Variable:HearingScore
ListID
Mean
Std. Deviation
N
List1
32.75
7.409
24
List2
29.67
8.058
24
List3
25.25
8.316
24
List4
25.58
7.779
24
Total
28.31
8.372
96
Tests of Between-Subjects Effects
Dependent Variable:HearingScore
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Corrected Model
920.458a
3
306.819
4.919
.003
Intercept
76953.375
1
76953.375
1233.793
.000
ListID
920.458
3
306.819
4.919
.003
Error
5738.167
92
62.371
Total
83612.000
96
Corrected Total
6658.625
95
a. R Squared = .138 (Adjusted R Squared = .110)
b. Computed using alpha = .05
1. Grand Mean
Dependent Variable:HearingScore
Mean
Std. Error
95% Confidence Interval
Lower Bound
Upper Bound
28.313
.806
26.712
29.913
2. ListID
Dependent Variable:HearingScore
ListID
Mean
Std. Error
95% Confidence Interval
Lower Bound
Upper Bound
List1
32.750
1.612
29.548
35.952
List2
29.667
1.612
26.465
32.868
List3
25.250
1.612
22.048
28.452
List4
25.583
1.612
22.382
28.785
Multiple Comparisons
HearingScore
Bonferroni
(I) ListID
(J) ListID
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
List1
List2
3.08
2.280
1.000
-3.06
9.23
List3
7.50*
2.280
.009
1.35
13.65
List4
7.17*
2.280
.013
1.02
13.31
List2
List1
-3.08
2.280
1.000
-9.23
3.06
List3
4.42
2.280
.335
-1.73
10.56
List4
4.08
2.280
.459
-2.06
10.23
List3
List1
-7.50*
2.280
.009
-13.65
-1.35
List2
-4.42
2.280
.335
-10.56
1.73
List4
-.33
2.280
1.000
-6.48
5.81
List4
List1
-7.17*
2.280
.013
-13.31
-1.02
List2
-4.08
2.280
.459
-10.23
2.06
List3
.33
2.280
1.000
-5.81
6.48
Based on observed means.
The error term is Mean Square(Error) = 62.371.
*. The mean difference is significant at the .05 level.
| Between-Subjects Factors | ||
|---|---|---|
| N | ||
| ListID | List1 | 24 |
| List2 | 24 | |
| List3 | 24 | |
| List4 | 24 |
Solution
Null hypothesis: The means of all testing conditions focused are equal
Alternative hypothesis: At least one of the means are not equal
Assuptions of Anova:
1.Each sample is drawn from normal population.
.2.The populaitons have common variance.
3.The samples are independent to each other.
4.The factor effects are additive in nature.
The F-value is 4.919, and P-value is 0.003
Since the P-value is less than 0.05 we reject the null hypothesis . hence conclude that at least two of the means are significant.
Post hoc results:
at 0.05,
the list 1 and list 3 are significantly different. Also list 1 and list 4 are significantly different.
finally we conclude that the means of the list of conditions are not equal
