Latin and Graeco-Latin Squares What we give up to do Exploratory Designs
It’s an orthogonal design so… The Type III tests on top match the Type I tests below. Main Effects Are not confounded with each other.
We are primarily interested in Brand, but what about interactions? If we put in even one interaction, then there are no df for error and this Interaction is completely confounded with Brand.
Notice • One cannot estimate and test Interaction terms since we do not have enough d.f. • Interaction terms are confounded with error and other terms. • As we shall see later with Fractional Factorials, they are likely confounded with each other too.
Since this is a screening design….. • Which variables might we investigate further? • How might we collect more data? • What about diagnostics on the model we fit?
What happened with our Diagnostics? • With Diagnostics we use Residuals as surrogates for Experimental Error in our Model • The Diagnostics are based on the assumption that our Residuals are independently distributed • This assumption was never true in an absolute sense • However, if the df for Error is “large” relative to the Model df, it is close enough to “true” so that our Diagnostics make sense • Remember, these designs are meant to screen factors for further study