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How to perform it

The basic assumptions which have to be fulfilled  are

If these assumptions are not met, the analysis of variance can still be performed, but using different test procedures which are beyond the scope of this text.

Assuming that the data follows a normal distribution, we first have to test for equal variances. Depending on the samples several tests are available:
Hartley's test Requirement: the samples have to be of equal size. The test statistic is defined as the ratio of the largest and the smallest variance of all samples.
Cochran's test Cochran's test should be used when the variance of one sample is considerably larger than all others. The test statistic is calculated as the ratio of the largest variance to the sum of all variances.
Bartlett's test Requirement: this test is sensitive to non-normal distributions. Bartlett's test is a combination of a test for normality with a test for equal variances.

In the next step the analysis of variances is performed (remember the goal is to compare means, not variances). The null hypothesis for the ANOVA is that all sample means are the same.  In order to achieve the ANOVA we have to calculate the mean of squares within each sample MSw and the mean of squares among the samples MSb. The mean of squares (MS) is defined as the sum of squares divided by the degree of freedom. The test statistic F, which is defined by the ratio of MSb to MSw, is distributed according to an F distribution. A value higher than the critical value Fk-1;n-k indicates that the null hypothesis has to be rejected.

Last Update: 2006-Jšn-17