I'm following the example in Andy Field's R book where he suggests that after failing the test for homogeneity of regression slopes, one might do a robust ANCOVA ala Wilcox 2005. I'm able to run the tests no problem, and interpreting them is also not an issue, but for output of the following nature (see below), does anyone know of a standard way to report this data?
I think a way to start at least will be to report the standard ANCOVA up to the point where the interaction is significant and then say robust procedures were followed, how to report these though are a bit beyond me.
ancova(covGrp1, dvGrp1, covGrp2, dvGrp2)
[1] "NOTE: Confidence intervals are adjusted to control the probability"
[1] "of at least one Type I error."
[1] "But p-values are not"
$output
X n1 n2 DIF TEST se ci.low ci.hi p.value crit.val
[1,] 10.30 20 12 -22.166667 2.7863062 7.955575 -47.42320 3.089867 0.0213100575 3.174696
[2,] 11.30 28 17 -19.184343 2.7536447 6.966891 -39.98396 1.615273 0.0167914292 2.985495
[3,] 12.45 32 23 -20.350000 3.9162704 5.196270 -35.02758 -5.672423 0.0008787346 2.824637
[4,] 14.00 27 34 -8.314171 1.4638404 5.679698 -23.71193 7.083583 0.1524122220 2.711016
[5,] 16.10 14 17 3.431818 0.3796813 9.038682 -22.28197 29.145604 0.7085490133 2.844860
ancboot(covGrp1, dvGrp1, covGrp2, dvGrp2,tr = .2, nboot=2000)
[1] "Note: confidence intervals are adjusted to control FWE"
[1] "But p-values are not adjusted to control FWE"
[1] "Taking bootstrap samples. Please wait."
$output
X n1 n2 DIF TEST ci.low ci.hi p.value
[1,] 10.30 20 12 -22.166667 -2.7863062 -47.00379 2.670459 0.0355
[2,] 11.30 28 17 -19.184343 -2.7536447 -40.93482 2.566135 0.0185
[3,] 12.45 32 23 -20.350000 -3.9162704 -36.57264 -4.127360 0.0015
[4,] 14.00 27 34 -8.314171 -1.4638404 -26.04606 9.417719 0.1525
[5,] 16.10 14 17 3.431818 0.3796813 -24.78674 31.650380 0.6980
I actually managed to get an answer from Andy Field about this...
I'm posting his message below in case anyone else runs into this issue.
Andy Field Hi John, the thing with the Robust stuff is that there simply isn't any real guidance because people don't use them much (yet). I guess for the ANCOVA methods in the R book, you could report the value of Dif and its CI and p for each of the design points. You'd probably need to explain a bit what the 'design points' actually mean as well. It's unchartered territory but my general principle is be clear about what you did, and you can;'t go wrong reporting confidence intervals:-)
Dear John,
If you are going to be fair (depends how you look at it) to other robust techniques, then I would say you report it as simply as a regular ANCOVA. You state which package and assumptions you used. You give the p values and associated CIs for each statistic of interest. Although the additional information provided by the procedure is potentially helpful, nobody asks for it when (often incorrectly) "standard" procedures are used.
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