using excel>data> data analysis> Two way ANOVA
we have
| Anova: Two-Factor Without Replication |
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| SUMMARY |
Count |
Sum |
Average |
Variance |
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| A |
2 |
77 |
38.5 |
144.5 |
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| B |
2 |
60 |
30 |
2 |
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| C |
2 |
83 |
41.5 |
60.5 |
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| 1 |
3 |
125 |
41.66667 |
85.33333 |
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| 2 |
3 |
95 |
31.66667 |
14.33333 |
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| ANOVA |
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| Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
| treatment |
142.3333 |
2 |
71.16667 |
2.497076 |
0.285953 |
19 |
| Block |
150 |
1 |
150 |
5.263158 |
0.148743 |
18.51282 |
| Error |
57 |
2 |
28.5 |
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| Total |
349.3333 |
5 |
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the decision rule for treatment: we will reject HO if F
>19.0
the null and alternate hypotheses for blocks is
Ho:all the means of block are same.
Ha : at least two mean differs significantly
the decision rule for blocks : reject Ho if F> 18.5
SST = 142.333, SSB =150 , SS total =349.33, and SSE = 57
an ANOVA table.
| ANOVA |
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| Source of Variation |
SS |
df |
MS |
F |
P-value |
| treatment |
142.333 |
2 |
71.167 |
2.50 |
0.285953 |
| Block |
150 |
1 |
150 |
5.26 |
0.148743 |
| Error |
57 |
2 |
28.5 |
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| Total |
349.333 |
5 |
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since p-value for treatment and blocks are greater than so we
conclude that means are same for block and treatments
