Scales-Transform.txt ============================================================================== On the BITNET STAT-L list, April 1991: ALAN C. ACOCK opined: >> It seems to me that many tranformations done to make interval level distributions more nearly normal in their distributions do so at the expense of the requirements of interval or ratio measures. Given the normality assumptions are not as critical with large samples, it seems strange to use them as much as we do. ---------- I (KLW) reply ---> In my mind, whether a measuring system produces interval rather than ordinal data ultimately boils down to whether the function relating the measurements to the "true scores" (actual magnitudes of the attribute being measured) is linear (interval data) or just monotonic (ordinal data). That seems like a metaphysical question to me. The data of psychophysics show that our own sensory/cognitive mechanisms generally provide us with noninterval data (if we are willing to accept measurements of the physical magnitudes of stimuli as being more true than are our psychological sensations). Lacking any way to verify the nature of the relationship between our measurements and the truth, how can we ever know that data are interval? Consider this resolution of the problem: Transform the data as needed (with order-preserving nonlinear transformations). Since the population to which we wish to generalize is most often an abstraction (like the population of correlation coefficients of which you were thinking), just generalize your statistical conclusions to that population from which your transformed data could be construed to represent a random sample. That is, define the population on the sample, define the true variable in terms of the (transformed) data on hand. ======================================================================== Date: Sat, 13 Apr 1991 17:53 EST From: D_HOWELL@uvmvax.bitnet Subject: Re: metaphysics and scales of measurement To: PSWUENSC@ECUVM1.bitnet Karl, RIGHT ON! re: your comment on the metaphysical nature of scales of measurement. I am just finishing up the third edition of _Statistical Methods for Psychology_, and if I can sneak your comment into the copy-edited version I will do so. I like the way you made your point. Dave Howell David C. Howell Dept. of Psychology University of Vermont Burlington, VT 05405 D_Howell@uvmvax.uvm.edu ======================================================================== Date: Sun, 14 Apr 91 11:25:33 EDT From: "Karl L. Wuensch" Subject: Re: metaphysics and scales of measurement To: D_HOWELL@uvmvax Thanks for the comment on my note regarding metaphysics, psychophysics, and scales of measurement. Can we expect a barrage of contrary arguments from psychometricians? Essentially my argument reduces to this: the variable that I am analyzing is that variable which is a linear transformation of the (nonlinear transformed) data that I fed my statistical machine. That is, I define the "reality" with which I am dealing as being a linear transformation of the data at hand. While I am not very well versed in philosophy, this sounds somewhat transcendental to me, but falls short of solipsism. ======================================================================== Date: Mon, 27 Apr 1998 11:02:06 -0400 Reply-To: "Psychology department faculty, staff and student list" Sender: "Psychology department faculty, staff and student list" From: "Wuensch, Karl L." Subject: Re: To Transform, or Not to Transform Comments: To: Francesca Collins Comments: cc: STAT-L To: ECUPSY-L@ECUMAIL7.ECU.EDU Consider a little psychometrics: Our nervous system's perceptual apparatus (a product of "Mother Nature") already does nonlinear (generally order-preserving) transformations of most of the physical energies it can detect (Fechner's law, Stevens law, etc. - if you plot psychological sensation as a function of the physical intensities, you typically do not get a linear function, but rather something like a log function or a power function), presumably because the transformed data are more useful than the untransformed. From that perspective, what could be more "natural" than to transform data to make it more useful? Francesca asked: >Could someone please justify for me - in brief and global terms - the >transformation of non-normal data? Surely, data in the form that Mother >Nature intended it is preferable to the log of Mother Nature. I can't get >past the idea that transformed data = a more convenient version of the >actual data. ======================================================================== Date: Mon, 27 Apr 1998 11:14:59 -0400 Reply-To: "Psychology department faculty, staff and student list" Sender: "Psychology department faculty, staff and student list" From: "Wuensch, Karl L." Subject: FW: To Transform, or Not to Transform To: ECUPSY-L@ECUMAIL7.ECU.EDU Dave Howell's response to Francesca's query, cross-posted from STAT-L. ---------- From: David Howell [SMTP:David.Howell@UVM.EDU] Sent: Monday, April 27, 1998 10:50 AM To: Multiple recipients of list STAT-L Subject: Re: To Transform, or Not to Transform Francesca, My favorite example is a study that two of my colleagues did several years ago. They recorded activity levels in rats by placing them in a spring-mounted cage and using an electrical transducer to record the movement of the cage. Every time the rat moved, so did the cage. And every time the cage moved, the transducer recorded an event. Now, are the data (voltages) "in the form that Mother Nature intended" any more meaningful than the "log of Mother Nature?" I'm certain that the data were highly dependent on the strength and elasticity of the spring, and I doubt that you could construct a cage which would replicate their results even to a linear transformation. Similarly, suppose that they had recorded the time that it took a rat to cross the cage. Would "time" be a more meaningful measure than speed? And certainly speed and time are not linearly related. There may be some measures that are the measure that God intended for us to use, but I'm not sure what they are. You might suggest that they are the physical ones of time and distance, but, as I suggested above, why is time better than speed? David C. Howell Phone: (802) 656-2670 Dept of Psychology Fax: (802) 656-8783 University of Vermont email: David.Howell@uvm.edu Burlington, VT 05405 http://www.uvm.edu/~dhowell/StatPages/StatHomePage.html http://www.uvm.edu/~dhowell/Psych95/LiesHomePage.html