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

**NECESSARY ASSUMPTIONS**

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

*1. X _{ij} *=

2. The ε* _{ij}* has a normal distribution with mean 0 and variance σ

3. Under the null hypothesis, *μ** _{j}* =

To express this in nonmathematical terms, all
observations in the *j*th 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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