Following my short experience in statistics, it seems that the type of sums of squares (type I,II,III,IV…) used in getting ANOVA results could make a dramatic difference in test results (especially of models with interactions and missing data). However I have not seen a paper yet reporting it. Why is that so?
I would really appreciate if one could provide an example paper reporting it (not of statistics itself) in one way or another, or the reason why it is not common.
This is not an easy question to answer (at least for me) but my guess is that the great majority of people go with the default settings of the program that they are using (irrespective of whether this is the correct approach or not). And I am fairly confident, that those who know which type of sums of squares to use (and deviate from the default settings), will make sure to mention this in the methods.
I personally find it more concerning that many papers fail to mention carefully enough which program/package/functions were used to run the analyses. Knowing this may help narrowing down which settings were used.
I don’t have a paper at hand at the moment that would report the type of sums of squares that were used to run the analyses, but if I will come across one, I will add it to my answer.
Searching on Google Scholar using a key word of the field you are interested in with the addition of “sums of squares” will lead you to the papers you are asking for. For example in my case I searched xylem water sums of squares, which resulted in this paper http://onlinelibrary.wiley.com/doi/10.1046/j.1469-8137.2003.00816.x/full (see Table 1 and 2 footnotes).