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Information About

Design Matrix




It can contain indicator variables (ones and zeros) that indicates group membership in an ANOVA and it represents the independent variables.
The advantage with a design matrix is that it is able to represent a number of different experimental designs and statistical models, e.g., ANOVA , ANCOVA , and Linear Regression .


EXAMPLE



One-way ANOVA


Example with a one-way analysis of variance ( ANOVA ) with 3 groups and 7 observations.
The first column in the design matrix models the grand mean of the ys, while the 3 remaining columns indicate the group membership of each observation. Here the first group consists of the 3 first observations and the next two groups each consist of two observations.

\begin{bmatrix}y_1 \ y_2 \ y_3 \ y_4 \ y_5 \ y_6 \ y_7 \end{bmatrix} =
\begin{bmatrix}1 & 1 &0 &0 \1 &1 &0 &0 \ 1 & 1 & 0 & 0 \ 1 & 0 & 1 & 0 \ 1 & 0 & 1 & 0 \ 1 & 0 & 0 & 1 \ 1 & 0 & 0 & 1\end{bmatrix}
\begin{bmatrix}\mu \ au_1 \ au_2 \ au_3 \end{bmatrix}
+
\begin{bmatrix}u_1 \ u_2 \ u_3 \ u_4 \ u_5 \ u_6 \ u_7 \end{bmatrix}