Question
In: Statistics and Probability
Answer the one-way ANOVA questions using the data below. Use α = 0.01. 1 2 3...
Answer the one-way ANOVA questions using the data below. Use α =
0.01.
| 1 | 2 | 3 | 4 |
| 53 49 47 42 48 34 44 |
44 39 36 34 24 30 12 |
46 42 39 43 36 34 47 |
25 35 30 27 33 28 22 |
a) Compute the preliminary statistics below.
SSBG = ; dfBG =
SSWG = ; dfWG =
SST = ; dfT =
b) Compute the appropriate test statistic(s) to
make a decision about H0.
critical value = ____________ ; test statistic = ____________
Decision: Reject H0 or Fail to reject H0
c) Compute the corresponding effect size(s) and
indicate magnitude(s).
η2 = ____________ ; ---Select--- na trivial
effect small effect medium effect large effect
e) Regardless of the H0
decision in b), conduct Tukey's post hoc test for
the following comparisons:
3 vs. 4: difference = ;
significant: ---Select--- Yes No
1 vs. 2: difference = ;
significant: ---Select--- Yes No
Solutions
Expert Solution
a)
| count, ni = | 7 | 7 | 7 | 7 | ||
| mean , x̅ i = | 45.286 | 31.29 | 41.00 | 28.57 | ||
| std. dev., si = | 6.102 | 10.626 | 4.899 | 4.50 | ||
| sample variances, si^2 = | 37.238 | 112.905 | 24.000 | 20.286 | ||
| total sum | 317 | 219 | 287 | 200 | 1023 | (grand sum) |
| grand mean , x̅̅ = | Σni*x̅i/Σni = | 36.54 |
| square of deviation of sample mean from grand mean,( x̅ - x̅̅)² | 76.563 | 27.563 | 19.930 | 63.430 | |
| TOTAL | |||||
| SS(between)= SSB = Σn( x̅ - x̅̅)² = | 535.938 | 192.938 | 139.509 | 444.009 | 1312.393 |
| SS(within ) = SSW = Σ(n-1)s² = | 223.429 | 677.429 | 144.000 | 121.714 | 1166.5714 |
no. of treatment , k = 4
df between = k-1 = 3
N = Σn = 28
df within = N-k = 24
SSBG =1312.39 ; dfBG =3
SSWG = 1166.57 ; dfWG =24
SST = 2478.96 ; dfT =27
b)
| SS | df | MS | F | p-value | F-critical | |
| Between: | 1312.39 | 3 | 437.46 | 9.00 | 0.0004 | 4.72 |
| Within: | 1166.57 | 24 | 48.61 | |||
| Total: | 2478.96 | 27 |
critical value = ______4.72______ ; test statistic =
___9.00_________
Decision: Reject H0
c)
η2 = SSB/ SST
1312.39 / 2478.96
= 0.5294
D)
| population mean difference | critical value | lower limit | upper limit | result | |
| 1 vs 2 | 14.00 | 12.93 | 1.07 | 26.93 | Significant(means are different) |
| 3 vs 4 | 12.43 | 12.93 | -0.50 | 25.36 | Not Significant (means are not different |
Thanks in advance!
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orchestra answered 1 year agoRelated Solutions
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Answer the one-way ANOVA questions using the data below. Use α =
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a) Compute the preliminary statistics below.
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b) Compute the appropriate test statistic(s) to
make a decision about H0.
critical value = ; test statistic...
Answer the one-way ANOVA questions using the data below. Use α = 0.01. 1 2 3...
Answer the one-way ANOVA questions using the data below. Use α =
0.01.
1
2
3
4
53
49
47
42
48
34
44
44
39
36
34
24
30
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46
42
39
43
36
34
47
25
35
30
27
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b) Compute the appropriate test statistic(s) to
make a decision about H0.
critical value = ___________ ; test statistic = _____________
Decision: ---Select--- Reject H0 Fail to reject
H0
e) Regardless of the H0
decision in...
Answer the one-way ANOVA questions using the data below. Use α = 0.01. 1 2 3...
Answer the one-way ANOVA questions using the data below. Use α =
0.01.
1
2
3
4
53
49
46
42
51
34
44
44
39
36
34
23
30
12
46
42
39
37
43
34
47
25
32
30
27
33
28
31
a) Compute the preliminary statistics below.
SSBG = ; dfBG
=
SSWG = ; dfWG
=
SST = ; dfT =
b) Compute the appropriate test statistic(s) to
make a decision about H0.
critical value = ; test statistic...
Answer the one-way ANOVA questions using the data below. Use α = 0.01. 1 2 3...
Answer the one-way ANOVA questions using the data below. Use α =
0.01.
1
2
3
4
53
49
47
44
51
34
44
44
39
36
36
39
30
12
46
42
39
37
36
34
30
25
35
30
40
33
28
31
Compute the corresponding effect size(s) and indicate
magnitude(s).
η2 = ; ---Select--- na
trivial effect small effect medium effect large effect
Conduct Tukey's Post Hoc Test for the following
comparisons:
3 vs. 4: difference = ;
significant: ---Select--- Yes...
Answer the one-way ANOVA questions using the data below. Use α = 0.05. 1 2 3...
Answer the one-way ANOVA questions using the data below. Use α =
0.05.
1
2
3
4
53
49
47
42
30
34
44
44
44
36
34
39
30
12
46
42
39
37
36
31
47
25
35
45
27
33
28
31
a) Compute the preliminary statistics below.
SSBG = ; dfBG
=
SSWG = ; dfWG
=
SST = ; dfT
=
b) Compute the appropriate test statistic(s) to
make a decision about H0.
critical value = ; test statistic...
Answer the within-subjects ANOVA questions using the data below. Use α = 0.01. 1 2 3...
Answer the within-subjects ANOVA questions using the data below.
Use α = 0.01.
1
2
3
4
53
49
47
42
51
39
44
44
39
36
34
39
30
29
46
42
39
37
36
34
26
44
35
30
27
33
28
31
Compute the corresponding effect size(s) and indicate
magnitude(s).
η2 = ; ---Select--- na
trivial effect small effect medium effect large effect
Conduct Scheffe's Post Hoc Test for the following
comparisons:
1 vs. 4: test statistic = ;
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Answer the within-subjects ANOVA questions using the data below. Use α = 0.01. 1 2 3...
Answer the within-subjects ANOVA questions using the data below.
Use α = 0.01.
1
2
3
4
53
49
47
42
51
39
44
44
39
36
34
39
30
29
46
42
39
37
36
34
26
44
35
30
27
33
28
31
Make an interpretation based on the results.
At least one week differs on the GRE verbal score.No week is
different on GRE verbal score.
e) Conduct Tukey's Post Hoc Test for the following
comparisons:
1...
Answer the within-subjects ANOVA questions using the data below. Use α = 0.05. 1 2 3...
Answer the within-subjects ANOVA questions using the data below.
Use α = 0.05.
1
2
3
4
53
26
47
42
51
34
44
44
39
35
34
39
30
12
42
42
39
37
36
34
47
25
35
30
27
24
28
31
a) Compute the preliminary statistics below.
SSBG = ; dfBG =
SSBS = ; dfBS =
SSE = ; dfE =
SST = ; dfT =
b) Compute the appropriate test statistic(s) to
make a decision about H0.
critical...
Answer the within-subjects ANOVA questions using the data below. Use α = 0.05. 1 2 3...
Answer the within-subjects ANOVA questions using the data below.
Use α = 0.05.
1
2
3
4
53
49
47
37
51
34
44
44
39
36
34
39
30
34
23
42
39
37
36
34
47
25
35
34
27
33
28
31
a) Compute the corresponding effect size(s) and
indicate magnitude(s).
η2 = ; ---Select--- na trivial
effect small effect medium effect large effect
b) Make an interpretation based on the
results.
At least one week differs on the...
Answer the within-subjects ANOVA questions using the data below. Use α = 0.05. 1 2 3...
Answer the within-subjects ANOVA questions using the data below.
Use α = 0.05.
1
2
3
4
53
49
21
42
51
34
44
44
31
36
34
39
30
12
46
42
46
37
36
34
47
25
31
30
27
33
28
31
a) Compute the preliminary statistics
below.
SSBG = _________ ; dfBG = __________
SSBS = _________ ; dfBS = ___________
SSE = __________ ; dfE = ___________
SST = __________ ; dfT = ___________
b)...
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