Chapter 7 The 2-way Classification Dejen Tesfaw (PhD) Email: [email protected]Tel: 0935316506 Addis Ababa University College of Natural Sciences Department of Statistics [email protected]1
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As a reminder, a factor is just any categorical independent variable. When there is only one factor in a design, you don’thave to worry about crossing and nesting. But when there are at least two factors, you need to understand whether they are fixed or random, because it will affect the analyses you can and should conduct. A factor is nested within another factor when each category of the first factor co-occurs with only onecategory of the other. In other words, an observation has to be within one category of Factor 2 in order to have a specific category of Factor 1. All combinations of categories are not represented. The expression “nested classification”refers to data sets in which factors are nested, or sometimes called “hierarchical.”[email protected]The 2-way Classification 2
[email protected]3 Two factors are crossed when every category of one factor co-occurs in the design with every category of the other factor. In other words, there is at least one observation in every combination of categories for the two factors. Crossed classification means that every level of every factor could be used in combination with every level of every other factor: in this way the factors “cross’’each other; their intersections are the subclasses or cells of the situation, where in the data arise. Absence of data from a cell does not imply non-existence of that cell, only that it has no data. If two factors are crossed, you can calculate an interaction. If they are nested, you cannot because you do not have every combination of one factor along with every combination of the other.