Necessary Assumptions

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Chapter: Biostatistics for the Health Sciences: One-Way Analysis of Variance

The assumptions for the one-way analysis of variances are:


The assumptions for the one-way analysis of variances are:

1. Xij = μj + εij, where i is the ith observation from the jth group, j = 1, 2, . . . , k; k is the group label for k 3 group; μj is the mean for group j; and εij is an independent error term.

2. The εij has a normal distribution with mean 0 and variance σ2 independent of j.

3. Under the null hypothesis, μj = μ for all j.

To express this in nonmathematical terms, all observations in the jth group are inde-pendent and normally distributed with the same mean and variance. However, two different groups can have different means but must have the same variance. Under the null hypothesis, all groups must also have the same mean.

The sensitivity of the analysis to violations of these assumptions has been well studied; see Miller (1986) for a discussion. When these assumptions are violated, we can use a nonparametric alternative called the Kruskal–Wallis test (refer to Sec-tion 14.6.)

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