Solved – How to analyze a 2×3 design in which one level doesn’t differ on one of the factors

anovastatistical-power

I have a 2×3 factorial design for my experiment: 3 levels of information given to participants (None, Moderate, Extreme), and 2 levels of time that the information focuses on (2050 or 2100), for those who received information.

I'm curious about how to deal with the fact that my control group, receiving no information, basically does not differ on the Time factor. I'm a little worried that it reduces the power of my design to detect differences in the groups who did receive different (2050 or 2100) information.

What's the best way to approach this? Should I instead do a 2 (Moderate, Extreme) x 2 (2050, 2100) design, essentially excluding the control group? If so, what test should I do to then compare the control group to those who received different levels of information?

Best Answer

One strategy would be to see your design as containing 5 groups, which we could label:

C, M2050, M2100, E2050, E2100

You could then set up various planned contrasts that examine questions of interest.

Here are some example contrast weights for testing various research questions:

C    M2050   M2100  E2050  E2100  Comparison
+4   -1      -1     -1     -1     Control versus other
0    +1      +1     -1     -1     Moderate versus extreme
0    +1      -1     +1     -1     2050 versus 2100

You could achieve something similar, by first testing whether control is different to the average of the other four groups and then performing the $2\times2$ ANOVA omitting the control group. The default tests in the $2\times2$ are likely to correspond to many of the planned comparisons you would do anyway (i.e., M versus E, 2050 versus 2010, and the interaction between amount and duration). However, the contrast approach might be slightly more powerful because your error variance may be smaller (its based on deviations from the four non-control group means rather than one overall non-control mean).

In previous questions, you've asked about SPSS, so here's an example of testing a contrast using GLM in SPSS. And here's a lecture on how to do it using R.

Related Question