8.7 Analysis of Variance (ANOVA)

So far we have compared one sample to a standard (the one-sample t-test) and two samples to each other (the two-sample and paired t-tests). Sometimes we want to find out if there is a difference between several samples. A technique that is useful in such cases is the so-called Analysis of Variance, or ANOVA for short. It is based on breaking the variation in the data down into several parts.

It may seem confusing at first that ANOVA, which is a technique for comparing three or more sample means, is based on the variation in the data. The best way to understand how this works is probably to work through an example. We will compare three different surface treatment methods for steel. An experiment is performed where steel parts are surface treated and subjected to abrasive wear tests. After the tests the weight loss is measured. We are interested in finding out if the surface treatments affect the amount of wear. The measurement data are given in Table 8.5, where the columns represent the treatments (A, B and C) and the rows correspond to five different metal parts exposed to each treatment. In total, 15 parts are used in this experiment. Below the table, the mean weight loss is given for each treatment and for the experiment as a whole (grand mean). Also, the differences between the grand mean and the treatment means are given. It is important to point out that the metal parts are allocated randomly to the treatments and tested in random order, to ...

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