Inference on One-Way Layout

When the effect of $ k$ different groups is of our interest, an experimental design of one-way layout (or one factor layout) can be considered. The groups are generally referred as ``treatments'' or ``factor levels.'' For example, a researcher wants to investigate the blood cholesterol of men in three different socioeconomic groups, say level 1, level 2 and level 3. In general the data set of the experiment can be presented in the following table.

Level Sample data Sample size
1 $ X_{11},\ldots,X_{1n_1}$ $ n_1$
$ \vdots$ $ \vdots$ $ \vdots$
k $ X_{k1},\ldots,X_{kn_k}$ $ n_k$

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