Exploratory Design with Orthogonality



Brand does have an effect (tell Marketing if
ours is best).
Car has an effect so it was a good thing your
Statistician told you to Block on Car so that
variation would not go into error and hide the
significance of your results (no layoff).
Position did not have an effect after 5,000 miles
(but your mechanic will tell you to rotate your
tires every so often anyway).



Since a Latin Square is an orthogonal design,
main effects are not confounded.
In orthogonal designs, Type I and Type III
Sums of Squares agree.
In designs where not all combinations of
factors are considered, the usual EMS
algorithm does not apply.