Stephen Black wrote: "The opinion I arrived at was that levels of measurement is one of those topics that we like to torture students with but has no real utility (another example is the negative/positive reinforcement distinction). Even though the t-test is supposed only to be used with data which satisfies a rather restrictive set of assumptions, it turns out to be "robust" when its assumptions are violated, so it can be happily (and justifiably) used in lots of other cases.
Most of the literature on this question is quite old. I ransacked my file, and came up with the following relatively recent paper supporting this point of view. Wilkinson is a noted statistician who invented the SYSTAT computer programme for analyzing data. Here's the abstract of his paper with Velleman: "The psychophysicist S.S. Stevens developed a measurement scale typology that has dominated social statistics methodology for almost 50 years. During this period, it has generated considerable controversy among statisticians. Recently, there has been a renaissance in the use of Steven's scale typology for guiding the design of statistical computer packages. The current use of Steven's terminology fails to deal with the classical criticisms at the time it was proposed and ignores important developments in data analysis over the last several decades." It would be interesting to hear how current textbooks of psychological statistics deal with this issue." 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. Theoretical statisticians manipulate numbers and distributions with little concern for how those numbers might relate to any real phenomenon. That is not a criticism -- that is what they do and they do it well. I doubt that we would have many of the very useful statistical techniques we have today if theoretical statisticians were not doing what they are doing. But that doesn't make them subject experts in how statistics are used in the social and behavioral sciences. Psychometric operationalization is the process of taking qualities and turning them into quantities, making calculations and then reinterpreting the quantities in ways that will say something meaningful about those qualities we want to understand. It is in this process that it becomes relevant and important for us to understand just what information is contained in a number. Nominal data in numerical form contains the minimum amount of information, a 1 is different from a 2, a red car is different from a blue car. With nominal data, the two is not twice as much as and one and the two is not even more than the one. It is just different. 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. 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. 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. 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. Rick Dr. Rick Froman Associate Professor of Psychology John Brown University [EMAIL PROTECTED] --- You are currently subscribed to tips as: [EMAIL PROTECTED] To unsubscribe send a blank email to [EMAIL PROTECTED]
