The following data are the morning and evening temperatures for three Michigan c
ID: 3181303 • Letter: T
Question
The following data are the morning and evening temperatures for three Michigan cities for four consecutive days in October. Enter the table "as is" into Excel, and use the Analysis Tool Pack to run a Two-Way Analysis of Variance (with Replication). Use the entire table, including row and column titles as the data block. Print and analyze (written comment) the results. Are there significant differences between the cities? Are there significant differences from morning to evening? Are there significant interactions between locations and time of day? Overall, what can we conclude? We are running this analysis to select a site for planting an apple orchard. Suggest a few other variables that might be of interest.Explanation / Answer
Answer:
Anova: Two-Factor With Replication
SUMMARY
Lansing
Ann Arbor
Grand Rapids
Total
Morning
Count
4
4
4
12
Sum
175
178
169
522
Average
43.75
44.5
42.25
43.5
Variance
30.25
17.66666667
29.58333333
22.09091
Evening
Count
4
4
4
12
Sum
229
238
235
702
Average
57.25
59.5
58.75
58.5
Variance
32.25
57.66666667
62.25
42.45455
Total
Count
8
8
8
Sum
404
416
404
Average
50.5
52
50.5
Variance
78.85714286
96.57142857
117.1428571
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Sample
1350
1
1350
35.26851
1.28E-05
4.413873
Columns
12
2
6
0.156749
0.856073
3.554557
Interaction
9
2
4.5
0.117562
0.889763
3.554557
Within
689
18
38.27777778
Total
2060
23
To test main effect cities,
Calculated F=0.1567, P=0.856 which is > 0.05 level. Ho is not Rejected.
We conclude that there is no mean difference between cities.
To test main effect Time,
Calculated F=0.35.268, P=0.000 which is < 0.05 level. Ho is Rejected.
We conclude that there is mean difference between morning and evening.
To test interaction effect,
Calculated F=0.1175, P=0.889 which is > 0.05 level. Ho is not Rejected.
We conclude that interaction effect is not significant.
Anova: Two-Factor With Replication
SUMMARY
Lansing
Ann Arbor
Grand Rapids
Total
Morning
Count
4
4
4
12
Sum
175
178
169
522
Average
43.75
44.5
42.25
43.5
Variance
30.25
17.66666667
29.58333333
22.09091
Evening
Count
4
4
4
12
Sum
229
238
235
702
Average
57.25
59.5
58.75
58.5
Variance
32.25
57.66666667
62.25
42.45455
Total
Count
8
8
8
Sum
404
416
404
Average
50.5
52
50.5
Variance
78.85714286
96.57142857
117.1428571
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Sample
1350
1
1350
35.26851
1.28E-05
4.413873
Columns
12
2
6
0.156749
0.856073
3.554557
Interaction
9
2
4.5
0.117562
0.889763
3.554557
Within
689
18
38.27777778
Total
2060
23
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