Hi I've responded here to Rick, but the same arguments would apply to Charlotte's recommendations against the use of means with ranks. I would also repeat Karl Wuensch's comment that non-parametric procedures can often be conceptualized as simply parametric tests carried out on ranks derived from the original scores. This would have to provide considerable support to the use of parametric tests on ordinal data.
On Wed, 10 Oct 2001, Rick Froman wrote: (I hope I have the attribution right this time!) > Current textbooks of psychological statistics (including the > grad level text I used over the summer), still discuss these > distinctions precisely because they are relevant to > psychometrics if not to mathematical statistics. I am not > surprised that a mathematical statistician/computer scientist > would not see the relevance. Going further back in history, it was psychologists who disagreed with Stevens, including such psychometric specialists as Lord. > Ordinal data contains nominal information but also contains > basic quantitative information in terms of order (A has more > of this thing than B does). You cannot make direct ratio > comparisons with data that is only ordinal. It would not make > sense to discuss the average ranking in a class because the > units are not at equal intervals. We wouldn't say that the > average high school class ranking in our freshman class is > 20th because the mean is a balance point of a distribution > and it assumes equal intervals between the units. I don't see the connection between ratio statements and the use of means. The question is more whether you want the distance from the "center" to be reflected in your statistic (e.g., should a rank of 1 pull the average more toward itself than a rank closer to the mean on the opposite side will pull the average in that direction). Does a class with students having HS ranks of 1, 4, 5, 6, 7, for example, have more intellectual power than one with students having ranks 3, 4, 5, 6, 7? Or does a class with ranks 1, 4, 4, 4, 7 have more variability in it than one with ranks 1, 1, 4, 7, 7? These are not questions that can be easily answered by simply saying the numbers are ranks and should never be used to compute a mean. > And, of course, since it is not ratio data, it would be > inappropriate to say that our college freshman are twice as > highly ranked as yours if your freshman average high school > ranking is 40th. So, it is not because the t-test is not > robust with regard to violation of its assumptions that it is > not appropriate for ordinal data. It is not appropriate > because the means, which are calculated in t-tests, are not > meaningful with ordinal data. The t-test is used to test differences between averages, not the ratios. So again the connection between the ratios and the t-test escapes me. > Anyone who is teaching the use of statistics in psychological > applications as a mathematical exercise and does not > repeatedly stress thinking about what information is > contained in the numbers when we try to interpret them should > not bother with teaching scales of measurement because, to > them, these concepts truly are meaningless and will only be > perceived by students as useless academic trivia. Well, I'm loathe to have myself classified as someone teaching anything as a "mathematical exercise" or not stressing "thinking about what information is contained in the numbers," but I would put scales of measurement pretty far down the list with respect to understanding and using statistics in a meaningful way. > I think back when we spent most of our time in stats teaching > and learning to hand calculate various procedures, the > mechanics was all we had time for. Now that we have > mechanical means of computation available, we should go into > more depth about what the numbers mean and how they should be > interpreted. I agree with taken proper advantage of the more powerful tools available today, but calculation and conceptualization are not divorced, and I think student thinking benefits from judicious use of calculation. Best wishes Jim ============================================================================ James M. Clark (204) 786-9757 Department of Psychology (204) 774-4134 Fax University of Winnipeg 4L05D Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED] CANADA http://www.uwinnipeg.ca/~clark ============================================================================ --- You are currently subscribed to tips as: [EMAIL PROTECTED] To unsubscribe send a blank email to [EMAIL PROTECTED]
