In light of questions such as this: Interpretation of Shapiro-Wilk test and others. I was wondering if it is better to state that "data were (formally) tested for violation of normality (p < x) and equal variance assumptions (p < x)" instead of stating that "data were tested for normality and homogeneity of variance"? Or is this not what these tests do?
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I think it's fine to say "data were tested for normality and homogeneity of variance" if that's what you did; it will be understood.
While it's important that people understand that you cannot confirm that you have either normality or equality of variance, making sure they know this is not the purpose of what you're doing - you're not teaching people statistics and you're not responsible for making sure they understand that hypothesis tests can't confirm that the distributions that the data were drawn from are normal or have the same variance.
should not have included it in the question. I have been asked to include a test (such as Shapiro-Wilk) instead of using QQ-plots, but my sample size is relatively small.
In the same situation if I could not convince the editor of the pointlessness of the test, I would probably be inclined to do one and report it at face value but I would not be able to resist adding a sentence pointing out how pointless it is to do so with a small sample (or indeed, with a large one, for the converse reason).
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$\begingroup$ I would agree with this from Glen_b and would add (to the OP) that you've not made a case for using the word formally or even said what you mean by it. It sounds like a cop-out as in "I know this is a rigmarole, but I've gone through the motions". If you think a test is defensible, you need not be so evasive. If you think a test is superfluous or ridiculous, don't use it. Admittedly, these are counsels of perfection, as most of us face gatekeepers who insist on certain actions and wording that they prefer. $\endgroup$– Nick CoxMar 29, 2016 at 17:46
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$\begingroup$ @Nick Cox Yes this is exactly what 'formally' meant in this case. I am sorry, I should not have included it in the question. I have been asked to include a test (such as Shapiro-Wilk) instead of using QQ-plots, but my sample size is relatively small. $\endgroup$– MoritzMar 30, 2016 at 7:35
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$\begingroup$ @Moritz I've added a comment to my answer on that issue $\endgroup$– Glen_bMar 30, 2016 at 8:02