Analysis of Variance (ANOVA). ANOVA can be used to test for the equality of three or more population means We want to use the sample results to test the following hypotheses. H 0 : 1 = 2 = 3 = . . . = k H a : Not all population means are equal
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H0: 1=2=3=. . . = k
Ha: Not all population means are equal
Two values could come from different populations, or distributions, which could have different means.
Two values could come from the same distribution.
Note: the book calls this nT
Source of Sum of Degrees of Mean
Variation Squares Freedom Squares F
Between SSTR k - 1 MSTR MSTR/MSE
Within SSE nT - k MSE
Total SST nT - 1
ObservationType 1Type 2Type 3
1 48 73 51
2 54 63 63
3 57 66 61
4 54 64 54
5 62 74 56
Sample Mean 55 68 57
Sample Variance 26.0 26.5 24.5
F = MSTR/MSE = 245/25.667 = 9.55
The mean number of hours worked at Plant 1 is not equal to the mean number worked at Plant 2.