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.