Research Statistics Central

Factorial treatment designs are popular, due to advantages of research on multiple treatment factors and how they interact.  But if the design includes a control treatment that is not part of the factorial, problems occur in estimation of least squares means.  A typical example is shown here, with 2 fertilizer and 3 irrigation treatments, giving 6 factorial treatment combinations, plus a control that is defined by a 3rd level of fertilizer, and a 4th level of irrigation: Fert1:Irrig2               Fert2:Irrig1             Fert1:Irrig1 Fert2:Irrig3               Fert1:Irrig3             Fert2:Irrig2           Control Other situations might have the control sharing a level of one of the factors, for example the control might be defined as Fert2:Irrig4.  But this still causes problems with estimation of least squares means due to the levels of one factor not occurring with all levels of the other factor. Let's jump into a SAS example, but using random numbers to allow easy creati