I am working through a designed experiments texbook and I would like to see if I got one exercise right.

The story is about measuring the effect of baking powder on the height of biscuits. The exoerimental factor is the amount of soda with, say, 3 levels - let us call it low amount, medium amount and high amount. 24 biscuits will be prepared, each new biscuit will be randomly assigned to a baking powder level and prepared accordingly. Once done, the height of each biscuit will be measured, so we end up with 3 columns of data, 8 rows with the measured heights . This is a completely randomised design and can be easily analysed with a one-way ANOVA.

The question is : suppose after you get the data set you are told that the dough for each column was only prepared once and then 8 biscuits were prepared from each dough and measured. How and what would change in the analysis?

I think that the model would look the same in bith cases:

Hij= mi + eij

Where Hij is the height of the jth biscuit in group i and eij is the random noise component

but the interpretation of the term m and e would be different. If I am analysing the completely randomised design then mi is the effect of the baking soda eij has all the random effects of measurement errors and also the effects of the individual dough .

If I am analysing the case where only one dough was prepared per baking soda amount then mi is the confounded effect of the dough and the soda amount and eij the random effect of is all the rest. So, basically I would not be able to confidently assume that the soda has an effect even if I would see in the analysis an mi that is significantly different from zero.

Would you agree with this interpretation? The book ahs no answers to the questions so I am left to my own devices here.

thanks a lot!