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# Factorial Design Analysis

Here is the
regression model statement for a simple 2 x 2 Factorial Design.
In this design, we have one factor for time in instruction (1 hour/week versus 4
hours/week) and one factor for setting (in-class or pull-out). The model uses a dummy variable (represented by a Z) for each factor. In two-way
factorial designs like this, we have two main effects and one interaction. In this model,
the main effects are the statistics associated with the beta values that are adjacent to
the Z-variables. The interaction effect is the statistic associated with **b**_{3} (i.e., the t-value for this coefficient) because
it is adjacent in the formula to the multiplication of (i.e., interaction of) the
dummy-coded Z variables for the two factors. Because there are two dummy-coded variables,
each having two values, you can write out 2 x 2 = 4 separate equations from this one
general model. You might want to see if you can write out the equations for the four
cells. Then, look at some of the differences between the groups. You can also write out
two equations for each Z variable. These equations represent the main effect equations. To
see the difference between levels of a factor, subtract the equations from each other. If
you're confused about how to manipulate these equations, check the section on how dummy variables work.

Copyright ©2006, William M.K. Trochim, All Rights Reserved

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Last Revised: 10/20/2006