Better approach than a 5x5 ANOVA?

[Bamboozled]

I have two continuous variables, A and B, each with 5 levels. I have a factorial, repeated-measures, test design with data for each of the 5x5 cells.

It might help if I give a simple analogy for the problem:

Let's say, for example, I want to measure the effect of amount of salt (A) and sugar (B) in a cake recipe on peoples' ratings of taste.

I have 0-4 units of salt, and 0-4 units of sugar, and ratings for taste (0-100) for every permutation of these combinations (e.g. 25 cells per participant).

I want to examine the influence of A and B on my collected scores, and their interaction. However, I have never used a repeated-measures ANOVA for anything over 2x2 before and am unsure how best to proceed - a 5x5 ANOVA seems like a fairly inelegant solution!

All suggestions gratefully received, thanks in advance.

[noetsi]

I am not sure why this is a repeated measures design. Normally that looks at change in a unit given a series of interventions over time. You are doing a simple factorial ANOVA as far as I can tell. If you want to reduce the number of levels the only way you can do that is collapse levels together. Well you can also do I believe what is called a fractional design such as Latin Squares, but I don't work with that so you might check with others on it.

[Bamboozled]

Hi Noetsi,

Thanks for the reply. It's repeated measures as each participant is providing data for each cell of the ANOVA. To revisit the cake analogy, each participant is tasting each of the 25 possible recipe permutations and providing a rating score for each.

I wanted to avoid collapsing all the levels as it's important that I can still find where/when changes occurred (if indeed there is anything significant in the data), as opposed to a global finding of e.g. 'changing the amount of salt had a significant effect on ratings of taste'.

[noetsi]

You should look at latin squares or more generally fractional methods.

[Jake]

Instead of analyzing the full factorial design, it may be sufficient to include only the linear and quadratic effects of your two predictors (and also possibly their interactions). This would simplify things greatly, but you will have to decide for yourself if this simplified model does justice to your data. If you decide to go this route, you essentially have a multilevel model.

[Bamboozled]

Thanks to both of you. Will look into the suggestions a bit more, but I think the simplification route sounds like a good way to go. Appreciated.