Cornell’s Alternative Statistics, part deux

30/35 = .86

29/35=.83

As mentioned in my addendum below, and as Matt Williams points out in the comments, apparently using an ANOVA for a binary variable is not as silly as I make it seem. It is not hard to find people who agree with me, but it is also not hard to find literature supporting the use of an ANOVA under certain conditions. I think most people would agree that logistic regression or Chi-square would be better, but using an ANOVA test is not completely ridiculous, and may be common in certain fields.

It is interesting to point out that this group decided to use a Chi-squared test in “How descriptive food names bias sensory perceptions in restaurants”, so it is unclear what their stance is on ANOVAs with binary variables — sometimes they use it, sometimes they do nothing, and sometimes they do a Chi-squared test. My feeling is that I just spent more time thinking about the appropriate test to use on a binary variable than the authors ever did, and that they just accidentally calculated an ANOVA here, which happens to be an okay approximation of better statistical methods, and might be acceptable in certain fields.

This post was not meant to contain statistical advice — as I said, I’m not a statistician — but I guess if you decide to use an ANOVA on a binary variable you might want to be aware that it might raise some eyebrows for people in fields where this is not common, and might cause the reader to take a closer look at your statistics, and find other more serious problems such as the impossible percent of men reported in this paper.

ANOVAs have several assumptions about the underlying data, and a categorical variable clearly violates these assumptions. In the specific case where you have a binary outcome, such as gender, my colleague points out that there has been some research on when it is okay to use an ANOVA instead of a more appropriate test such as the Chi-squared test. Perhaps the Cornell Food and Brand Lab is aware of this work, and decided an ANOVA was appropriate for their data. However, if that is the case, then it is unclear why they decided to not report an ANOVA value in “Lower Buffet Prices Lead to Less Taste Satisfaction” for the exact same measure (gender percent) when they had a larger sample size and more normal-like distribution of values.

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