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204 13 ANOVA - 13 ANOVA(Comparison of Three or more means...

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13 ANOVA (Comparison of Three or more means) Previously we looked at 2-sample Z and 2-sample T tests, which can be used to test if two samples came from populations with the same mean. In this chapter, we will learn a test to check if three or more samples are from populations with the same mean. As an example we will use the following data. Assume the treatments are three antiseptics and the observed values are bacterial counts. Treatment observed values mean s x SS = 2 ) ( - x x 1 20 32 27 25 26 4.9666 74 2 24 30 20 22 24 4.3205 56 3 35 22 28 27 28 5.3541 86 The ANOVA (AN alysis O f VA riance) test may seem a little surprising at first since the statistic does not explicitly contain any means, but rather it uses a comparison of two estimates of variation and thus has an F distributiom. This is the same distribution we used when testing if two samples came from populations with the same variance (the 2sample F test). The F statistic will be equivalent to the following: F = variances sample the pooling on based variance sample means sample
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