Split plot design with psudo replicates I am working on a project and need to analyze data that I know is an example of a split plot design but I am having trouble setting the model up correctly.
Here's the situation:
A bakery is testing cookies.  They are interested in how sugar levels and freshness impact taste ratings (on a scale of 1 -10).  They bake cookies at three sugar levels (1/2 of what the recipe calls for, the regular amount, and double what the recipe calls for) and hand out 5 cookies to 5 random customers on each of 3 days (the day the cookies are baked - day 1, the following day - day 2, and the following day - day 3).  The bakery bakes 9 batches of cookies and each batch is randomly assigned to one of the 3 sugar levels.  So we have information on 135 cookie ratings.
I know that the 5 cookies per batch are psudoreplicates so I averaged those to come up with 3 average taste ratings per batch - one for each freshness level (day 1, day 2, and day 3).
I am trying to analyze this using a mixed model with average taste rating as a response variable, sugar level and freshness as random factors and batch(sugar level) as a covariate.  But my model isn't coming out correctly.  Thus far I am working in Minitab but I could also use SAS.
 A: You should model the raw data as is, not replace by averages. And, this are not really pseudoreplicates, the five cookies are given to five different persons, yes? And, as the response is the ratings, not some measured characteristics of the cookies, the variation in the ratings is what is relevant. 
Before going into the split-plot model. some comments on the design. 
Design of experiments for food sensory research is a very specialized field, some links. By only asking some persons about giving the product some rating, how do you know they interpret/use the scale the same way? Maybe it would have been better to ask some more specific questions and even better a design where the same experimental persons where asked of comparing/evaluating different variants of the cookies ... 
So you have a data file with 135*5=675 observations, in a format something like:
rating    batch   level    day
  .         1       1       1
  .         1       1       1
  .
  .
  .
  .         1       1       2 
  .

where rating is a numerical variable, the others are factors. Batch with 9 levels, level with 3 (sugar) levels, day with 3 levels.
There is a nesting structure batch/day and we model level (the focus variable) as a fixed effect. Maybe we are also interested in day as a fixed effect. I do not know about SAS but in R with package lme4 we could say: 
library(lme4)
mod  <-  lmer(rating ~ level + day + (1 | batch/day), data=your_data_frame)

The notation | batch/day can be read within batch, and then for each batch, within day, and the 1 before it stands for a constant. So gives a set of random constants with that structure.    
There are some similar questions, so look at split-split plot design with unbalanced repeated measures in lme4 or nlme (SAS translation),   Split plot in time mixed-effect model in R,    Cheat Sheet ANOVA Alphabet Soup & Regression Equivalents
EDIT

Trying to answer the question in the comment by @MichiganWater. It seems to me that pseudoreplication here maybe depends on the goal of the analysis. If the goal is to ascertain some objective property of the cookies, then the five people trying cookies from the same batch is pseudoreplication. But the OP speaks about taste ratings without further explication, and taste is not an objective property of the cookies, it is an interaction between cookie and the person eating it. As an example, I, as part of my Asberger, have sense hypersensitivity, and for me food tastes the same if cooked without salt as with (unless really to much). That would make me an outlier in a sense experiment, probably. I don't know how large the variation in subjective taste is, but it is there. So if subjective felt taste is the objective, then variation between persons should be relevant. 
But, using the mixed model analysis I proposed, maybe this does not make a large difference. The mixed model analysis estimates the variance at each level (block(level)/day/person), and that information could be interesting itself. But in testing the effect of level, only the variance from the level below would be used. I quote from Casella "Statistical Design" (page 5)

This is an example of a nested design, where Tanks are nested in Diets
  and Fish are nested in Tanks. In such designs the testing is
  straightforward – the nested factor provides the error mean square for
  the factor in which it is nested. (See Section 1.5.) Of course, we can
  test the significance of tanks using MS(Tank)/MS(Fish), but this is
  wasted effort. There is typically no interest in assessing the
  significance of tanks; they are merely there to hold the fish! 

So in using the modern mixed model formulation, maybe the question about pseudoreplication is taken care of automatically? I would like to look at this with a simulated example, but that will have to wait. Will think more about this. But anyhow, the original data should be used, and not the reduction to summaries, since they are more informative.
