13.4: Factorial Design – an Insight to other ANOVA Procedures

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A different way of looking at this model is considering a single population with one numerical and one categorical variable being sampled.

The numeric variable is called the response and the categorical variable is the factor.

The possible responses to the factor are called the levels.

The numbers of observations per level are called the replicates.

If the replicates are equal, the design is balanced.

The Hypotheses can then be stated in context using the format:

\(H_o\): There is no difference in mean response due to factor.

\(H_a\): There is a difference in mean response due to factor.

By thinking of the model in this way, it is easy to extend the concept to the multi‐factor ANOVA models that are prevalent in the research you will encounter in future studies.