This post was mentioned on Friendfeed by pgh: Main Effects and Interaction Plots (illustrates the effects between variables which are not independent) – http://peltiertech.com/WordPress/main-effects-and-interaction-plots/ ……

Re the date with a Judge, if anyone’s confused, Jon is talking about his related post at http://peltiertech.com/WordPress/dating-site-photo-effectiveness/#comment-27604

Jon, unlike a date, at least the judge would let me finish my sentance. A date would probably bail. (Now, that’s a bad pun)

Pity I didn’t manage to work “Cleavage drinking” into it.

I think flirty and smiley in this analysis are distinct expressions, so the factor has three levels, rather than being two factors of two levels.

The combination of categories you invented may be more likely to get you a date with a judge than with a possible mate.

I’d think it would be fairly robust to compare the ‘Smile’ and ‘Not Smile’ groups , as this is a simple binary variable…you do it or you don’t.

But I’m not so sure about comparing ‘flirty face’ against them. Are there interaction effects between flirting and smiling? What if you’ve got a flirty face but you’re not smiling? Assuming that is possible, of course.

You might want to do a future post demonstrating how to work up the same data set using first ANOVA and then multiple regression with dummy variables for the nominal factors. Could serve as a great introduction to GLM for which Excel lacks direct support but in simpler cases can be done with multiple regression and dummy variables. If you do this, be sure also to emphasize the importance of scrutinizing residuals, and of using means-of-means instead of overall means because those give LS estimators.

Jon, despite your disclaimer note, you’ve set up your main effects plot in a sophisticated way, compensating for the imbalanced distribution of your factors in the available data.

This is a tricky point, but where strong interactions exist, the average effect of a factor level becomes highly dependent on (or biased by) the distribution of the other factors in the study. You could have shown simple sample average responses at each factor level, but a Main Effects plot is borrowed Design of Experiments terminology that often implies something more, conveying average values for a balanced design (which this clearly wasn’t).

Interaction plots are often very enlightening even for random imbalanced datasets. Under such conditions, showing a Main Effects plot is tricky because of the potential confusion between raw equal weighting of every sample point and balanced weighting across all other factors as you have used here. While there is value in first plotting raw averages for each factor level, calling it a Main Effects plot may offer more confusion than utility, no?