# Controled Factorial Experiment Design: which name or resource?

I'm designing an experiment which has to factors (A,B) with respectively 4 and 5 levels.

Since this is quite a large amount, I figured I use a factorial design. However, it is unclear whether the treatment will work at all, at any level or factor.

So I designed the following experiment:

All participants perform a test that is a negative control (no additions/treatment) and then those same participants perform a test with a randomly assigned level of each factor.

This allows me to test if the treatment at any level has any effect (T-test) and then check which combination of factor/level specifically is effective (ANOVA).

I've been looking for a proper resource on this, I assume this is a factorial design, but the addition of the control over all participants before the random treatment makes it hard to find the proper title/resource on this design.

Can anyone point me in a proper direction?

## 1 Answer

It is a repeated-measures factorial design, albeit of a very simple sort. You have one "within-subject" factor (pre-test and post-test (after treatment) and two "between-subjects" factors (A and B).

But these data don't need any sort of repeated-measures analysis. Simply take the differences (I'd do it as $$y_{i,j, k} = w_{i, j, k} - x_{i,j,k},$$ where $y$ is the score to analyze, $w$ is the post-test score and $x$ is the pre-test score.

The $y_{i,j,k}$ can be analyzed as a two-way treatment structure in a completely randomized design structure.

• thanks. I gather that i is the ith participant and j and k the respective levels? – puredevotion Jul 11 '14 at 19:54
• You're welcome. It doesn't matter how you assign the indices as long as you do it consistently. – Dennis Jul 11 '14 at 20:12