Necessary Assumptions
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The assumptions for the one-way analysis of variances are:
NECESSARY ASSUMPTIONS
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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