Is my design nested or split plot? I have a design with four factors:


*

*Frame (positive negative neutral)

*Graphic ( graph no graph)

*Color (red grey) nested in graphic

*Position of color (nested in color, which is nested in graphic)


I am having difficulty understanding if this is an incomplete nested design or a split plot design.  
 A: Split-plot is a type of nested design. The phrase comes from Statistics' youth, spent at the agricultural testing station of Rothhamstead, UK, where so many different experimental designs were created. Split-plots really were portions of plots. You might put a particular type of fertilizer over an entire plot, and then plant different varieties of peas on that plot. A different plot would have different fertilizer - but the same varieties of pea. So you envisage 2 or more factors, but different levels of randomization. Fertilizers are randomly assigned to plots - then for each plot, variety is randomly assigned to the split portion. All nested designs have that feature: different levels of randomization, applied to different subjects.
Back to your question:
What I need to know is how these factors are distributed in your actual design. I also need to know what the response is: what are you measuring from all of these design features?
If you have "red" on one design, do you have "grey" somewhere else on the same design? Or is it omitted from that particular design? If Red and Grey appear on one design or the other (but not together) - it seems that they are not nested.
I can't say exactly from what you have said, but it looks like a single-plot, un-nested factorial design - only unbalanced. Frame is crossed with graphic - colour and position are probably crossed also - but in that subset of the experiment that contains graphs. You can then test for those effects using the contrasts. If everything is balanced within the "graph" section, you want to look at "mean with red" - "mean with grey"; also "Position 1"-"Position 2" - or whatever seems to be of interest.
If I have understood your question correctly, the design is neither nested nor split-plot - but it is incomplete - simply because some factor combinations do not apply.
This can be analysed by obtaining an estimate of the standard deviation and using that to test for particular contrasts - i.e. comparisons of the means - to test hypotheses of interest to you.
