Imagine a world in which people are taught that there’s two kinds of counting: there’s potato-counting, and there’s counting other stuff (beans, points, cards, etc.) Potatoes are special, so that potato-counting gets its own courses, under the name “Kartoffelanalysis”. When you take a *Kartoffelanalysis 101* course, nobody mentions that you could use the same techniques to count other objects. Potatoes are special and unique. More advanced students learn that there are special techniques for counting a mix of potatoes and other things, and these sophisticated techniques are called Mixed Kartoffelanalysis. Only a select few ever learn that counting potatoes works pretty much the same way as counting other stuff.

Does this sound not quite right in the head? How about we start telling people that 99.9% of the time, an ANOVA is just a linear model? Than an ANCOVA is also just a linear model with a mix of categorical and continuous covariates? These things don’t need any fancy words or their own SPSS menu, anymore than we need special bicycles for people with blond hair. Also, please stop putting ANOVA tables in papers, nobody cares. Show us the data, for God’s sake.

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Well, I have to confess something: I’ve never learned ANOVA. Where I work (ENSAE) we teach the linear model directly, and I was trained in that way. So I find the ANOVA terminology very confusing. I vote with both hands in favour of ditching ANOVA!

Up to a point.

Yes, ANOVA is a linear model or a linear mixed model, and tables of mean squares shouldn’t be inflicted on readers, and there’s no excuse for oneway fixed-effects ANOVA or ANCOVA

On the other hand, if you have a reasonably complicated but small set of experiments to design, it is useful to think about contrasts and about which ones are orthogonal, and about how to get the contrasts you care about having a variance estimate with as many degrees of freedom as possible. Tables of expected mean squares are a useful tool in this process, though they should be worked out by computers, not by humans.

I never studied ANOVA, and for small, complex designed experiments the people who studied design of experiments seriously can do things I can’t. For example, if you have four seawater CO2/acidity concentrations when growing sea urchins, and you’re then studying gene expression using paired expression arrays, what’s the best design for allocating samples to arrays, given assay error, variation between technical replicates, variation between biological replicates from the same experimental replicate, and variation between experimental replicates?

You’re right, ANOVA is slightly more general than simply the set of linear models with dummy variables. It’s nice to know that these advanced versions exist but as far as I can see teaching ANOVA in basic stats is a disaster. Students learn ANOVA as a set of procedures that one must follow, and no one tells them about the interpretation of ANOVA as a statistical model. Once you think of these analyses as fitting models to data, it’s much easier to see what sort of models could make sense and which are completely bogus. If you don’t know that then you end up following a flowchart in a textbook that tells you which button to click in SPSS depending on your type of data. A lot of people don’t even plot the data.

I agree. It’s similar how you’re supposed to write a paper the way it should be written, not what you did chronologically. ANOVA may have come first, but that’s not the point. Maybe it’s tradition, the fact Fisher proposed it, or the unfounded idea that people understand partitioning variability before they would understand a linear model. Also – I never remember the “Types”

Indeed it would be a very happy world one where you only need to learn to count once, whether they are kartoffeln, gummi bären or gene counts you are counting. Having to map from one framework to another seems like a lot of effort for not much gain, and possibly increasing the confusion in people’s head.

You know, Geoff Koeppel and Shelly Zedeck wrote a whole book about this.

No, I didn’t know that. I haven’t found the book on Google Scholar, though, do you mean Zedeck’s APA handbook?

Data analysis for research designs : analysis of variance and multiple regression/correlation approaches (1989); W.H. Freeman