The coffee might contain "real" sugar, or it might contain "fake" sugar (i.e., artificial sweetener), or it might contain "none" at all, so the sugar variable is a three level factor. We also varied the kind of sugar involved. The amount of coffee / caffeine was held constant, and we varied whether or not milk was added: so milk is a binary factor with two levels, "yes" and "no". Suppose we took 18 people, and gave them some coffee to drink. Suppose we were interested in finding out whether or not the tendency of people to babble when they have too much coffee is purely an effect of the coffee itself, or whether there’s some effect of the milk and sugar that people add to the coffee. The coffee.Rdata file contains a hypothetical data set (the coffee data frame) that produces an unbalanced 3×2 ANOVA. So, if you want to avoid handing control of your data analysis to stupid software, read on…Īs usual, it will help us to work with some data. It’s actually a little terrifying, when you think about it. In fact, reading the psychological literature, I’m kind of amazed at the fact that most people who report the results of an unbalanced factorial ANOVA don’t actually give you enough details to reproduce the analysis: I secretly suspect that most people don’t even realise that their statistical software package is making a whole lot of substantive data analysis decisions on their behalf. The net result of this, I think, is that a lot of active researchers in the field don’t actually know that there’s several different “types” of unbalanced ANOVAs, and they produce quite different answers. A lot of stats textbooks tend to gloss over it too. It might be a consequence of this messiness, or it might be a shortage of time, but my experience has been that undergraduate research methods classes in psychology have a nasty tendency to ignore this issue completely. Unbalanced designs need to be treated with a lot more care than balanced designs, and the statistical theory that underpins them is a lot messier. Or, to put it another way, we have an unbalanced design. For one reason or another, it’s typical to end up with more observations in some cells than in others. However, there’s one huge difference between the ANOVAs that you’ll see in a lot of real scientific articles and the ANOVA that I’ve just described: in real life, we’re rarely lucky enough to have perfectly balanced designs. It’s been one of the standard tools used to analyse experimental data for many decades, and you’ll find that you can’t read more than two or three papers in psychology without running into an ANOVA in there somewhere. \)įactorial ANOVA is a very handy thing to know about.
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