Reply to Champion and Morris

B asically, Champion criticizes my article on three points: (1) that I "encourage others to squeeze every drop of information fkom their data regardless of certain consequences," (2) that I recommend a shift from ordinal to interval, even though the scale of the data is, in reality, ordinal (i.e., ordinal is ordinal), and (3) that I recommend the illegitimate use of certain statistics, because their assumptions are not met (and assumptions, according to Champion, cannot be violated in any manner or degree). Each of these criticisms is not only based on a misinterpretation of my article, but reflects a position that leads to a poor selection of statistical techniques. First, I am neither encouraging others to squeeze out all information nor to disregard the consequences. In my article I encourage researchers to select statistics partially on the basis of answering the relevant substantive problems in question. This may require a strong variance measure that simply does not exist for ordinal data. Because the researcher does not have interval data, should he disregard the statistical analysis of this apparently important problem? Or should he reasonably (on the basis of sound rationale) select relevant statistics and interpret them with caution? I offer rather clear justification for the researcher to select interval statistics with ordinal data, because of the small error resulting from assigning an interval (especially linear) scoring system to ordered categories. Assigning an interval scale (with small error) does not mean that the researcher should disregard the consequences. In fact, the researcher must know a great deal about the consequences before he can select the appropriate statistical techniques and provide a sound rationale for using them in the face of not having the appropriately scaled variables. This requires a great deal more in the way of reasoning and knowledge of statistics than merely selecting those statistical techniques for which the data precisely meet the scale operations. Champion's second criticism (the scale of one's data is real and cannot be changed) reflects an indefensible philosophical position. He indicates that certain variables are in fact ordinal and they somehow exist "out there" in the real world as ordinal variables. But ordinality is a construct imposed upon a variable by the researcher. Is a variable inherently ordinal (or interval or nominal for that matter), or is the scale of a variable the consequence of an attempt to impose order in the universe? How a variable is scaled "out there" is beyond scientific analysis. We attempt to measure phenomena in a particular way and then call the resulting scale nominal, ordinal, interval or ratio depending on the operations used in the measurement. It may well be that some ordinally measured variables are more predictive under some interval scales. It is my contention that we need to experiment with scoring systems and evaluate their relative predictive ability, instead of assuming by fiat that ordinal is ordinal. Finally, the third criticism concerns one major part of my article, namely, that the assumptions of statistical techniques are inviolate. However, the major question is not (as Champion implies) what can you do for assumptions, but what can assumptions do for you? The answer is that they provide a logically deduced interpretation for the statistical technique. But as I show in my article, certain assumptions can be violated with only minor disturbance on the deduced interpretation (i.e., small errors). To restate an example, under certain circumstances, when the normality assumption of analysis of variance is violated, differences apparently significant at the .01 level are actually significant at the .02. Consequently, this test can be used and interpreted with accuracy, even though an assumption has been violated. The test is robust. It is not illegitimate to use the test under these circumstances and we are not wrong when we do it. Morris claims tl-pat the assignment of numbers to ordered categories becomes increasingly subject to error ("strained") as the number of