4.3. One-Way Classification

In the previous section, we considered an interlaboratory study where four bivariate observations corresponding to two different methods were made in three different laboratories. The purpose of the study was to compare the three laboratories and decide if these laboratories provide, on the average, the same bivariate measurements. The three groups or classes of interest were three laboratories, which define a categorical variable (or factor) with three levels represented by these laboratories. In general, a one-way classification model can be defined for a variable with A levels or groups. If we denote by yij, the p by 1 vector of responses on the jth unit of the ith group, then we can write

where ij is the

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