Chapter 7
The 2-way Classification
Dejen Tesfaw (PhD)
Email:
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Tel: 0935316506
Addis Ababa University
College of Natural Sciences
Department of Statistics
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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’t
have
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 one
category 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
.
”
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The 2-way Classification
2

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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.

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