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Statistical Hypothesis Testing and Pic
Analysis of Variance (ANOVA)

One Way Classification

Random samples of size n are selected from each of k populations. It will be assumed that the k populations are independent and normally distributed with means [pic][pic] and common variance [pic]. We wish to derive appropriate methods for testing the hypothesis: [pic] [pic] [pic] at least two of the means are not equal.
Table 1
K random samples
| |Population | |
| |1 |2 |……… |i |……… |k | |
| |[pic] |[pic] |……… |[pic] |……… |[pic] | |
| |[pic] |[pic] |……… |[pic] |……… |[pic] | |
| |. |. | |. | |. | |
| |. |. | |. | |. | |
| |. |. | |. | |. | |
| |. |. | |. | |. | |
| |[pic] |[pic] |……… |[pic] |……… |[pic] | |
|Total |[pic] |[pic] |……… |[pic] |……… |[pic] |[pic] |
|Mean |[pic] |[pic] |……… |[pic] |……… |[pic] |[pic] |

One way Sum of Squares Identity

[pic]
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