I developed the ez package for R as a means to help folks transition from stats packages like SPSS to R. This is (hopefully) achieved by simplifying the specification of various flavours of ANOVA, and providing SPSS-like output (including effect sizes and assumption tests), among other features. The
ezANOVA() function mostly serves as a wrapper to
car::Anova(), but the current version of
ezANOVA() implements only type-II sums of squares, whereas
car::Anova() permits specification of either type-II or -III sums of squares. As I possibly should have expected, several users have requested that I provide an argument in
ezANOVA() that lets the user request type-II or type-III. I have been reticent to do so and outline my reasoning below, but I would appreciate the community's input on my or any other reasoning that bears on the issue.
Reasons for not including a "SS_type" argument in
- The difference between type I, II, and III sum squares only crops up when data are unbalanced, in which case I'd say that more benefit is derived from ameliorating imbalance by further data collection than fiddling with the ANOVA computation.
- The difference between type II and III applies to lower-order effects that are qualified by higher-order effects, in which case I consider the lower-order effects scientifically uninteresting. (But see below for possible complication of the argument)
- For those rare circumstances when (1) and (2) don't apply (when further data collection is impossible and the researcher has a valid scientific interest in a qualified main effect that I can't currently imagine), one can relatively easily modify the
ezANOVA()source or employ
car::Anova()itself to achieve type III tests. In this way, I see the extra effort/understanding required to obtain type III tests as a means by which I can ensure that only those that really know what they're doing go that route.
Now, the most recent type-III requestor pointed out that argument (2) is undermined by consideration of circumstances where extant but "non-significant" higher-order effects can bias computation of sums of squares for lower-order effects. In such cases it's imaginable that a researcher would look to the higher-order effect, and seeing that it is "non-significant", turn to attempting interpretation of the lower-order effects that, unbeknownst to the researcher, have been compromised. My initial reaction is that this is not a problem with sums of squares, but with p-values and the tradition of null hypothesis testing. I suspect that a more explicit measure of evidence, such as the likelihood ratio, might be more likely to yield a less ambiguous picture of the models supported consistent with the data. However, I haven't done much thinking on the consequence of unbalanced data for the computation of likelihood ratios (which indeed involve sums of squares), so I'll have to give this some further thought.