Random block mixed ANOVA We tested proliferation of 4 types of cells (between-subject factor) during 3 consequent time points (within-subject factor). All test were done in 4 blocks with 1 plate of each type of cells in each block (so 4 independent experiments with n = 1 of each group in each block). Blocks were separated by each other by several weeks. Of course blocks differ between each other a little, but general differences between proliferation rate of different cell lines are evident. I use STATISTICA (Statsoft). How should I enter a program for correct analysis?
Without addition of blocks as a factor there is no differences between groups due to differences between blocks. I tried to add block as an independent factor add got it as a factorial design. I used interaction of block x group as the between-subject MS error term for MS group (between-subject factor) and interaction of block x group x time point as the within-subject MS error term for MS time and MS time x group (within-subject tests). Was I correct? (I'm confused by very high F-ratios in F time point x group due to very low MS block x group x time. Generally at each block differences are evident, but it is confusing...).
 A: I assume your scientific question concerns whether the rate of growth for each of the cell types is different. I furthermore assume you have used some appropriate method of titration so that the cell counts may be assumed to be equal at time $t=0$ for each of the $n=4$ cell types.
You have used overlapping notation to indicate the cell types and the blocks. Were all 4 cell types propogated on a single plate 4 different times (for a total of 16 cell cultures that were measured over time) or did each plate get 1 cell type (so that 4 cell cultures were measured over time). I will call the 16 cultures case a factorial design and the 4 cultures case a block design.
If you have the block design with 4 plates having one cell count measured over 3 time periods for a total of 12 observations, then the time x group x block model is overspecified. That would explain why you have such a large F value, since it's an approximation of $\infty$ obtained by the numerical solver in your statistics package. This is the wrong modeling choice. You should drop the effect due to block and only test the interaction between group and time.
If you have a factorial design, you can fit a factorial model and test for a group effect only if you use a GLM. This is because, techincally, there are no replicates in this study. A block x group x time model will have a total of 4 x 4 x 3 = 48 effects for which you only have 48 observations. Fitting a saturated model is okay if you make some probabilistic assumptions about the rate of growth for your cell counts, you would have to resolve to using a Poisson model which could be okay. This is also known as a loglinear modeling approach.
Otherwise, I would drop the block effect entirely. You have simply replicated your experiment 4 times. If this is the case, as before, testing the time x group effect will address the hypothesis of whether cell counts grow at different rates for the 4 cell types or groups.
Factors in this study are absolutely not nested.
