Measurement theory: Frequently asked questions Version 3, Sep 14, 1997 Warren S. Sarle SAS Institute Inc. SAS Campus Drive Cary, NC 27513, USA saswss@unx.sas.com URL: ftp://ftp.sas.com/pub/neural/measurement.html Version 1 originally published in the Disseminations of the International Statistical Applications Institute, volume 1, edition 4, 1995, Wichita: ACG Press, pp. 61-66. Copyright 1995, 1996, 1997 by Warren S. Sarle, Cary, NC, USA. Permission is granted to reproduce this article for non-profit educational purposes only, retaining the author's name and copyright notice. Contents ” What is measurement theory? ” What is measurement? ” Why should I care about measurement theory? ” What are permissible transformations? ” What are levels of measurement? ” What about binary (0/1) variables? ” Is measurement level a fixed, immutable property of the data? ” Isn't an ordinal scale just an interval scale with error? ” What does measurement level have to do with discrete vs. continuous? ” Don't the theorems in a statistics textbook prove the validity of statistical methods without reference to measurement theory? ” Does measurement level detemine what statistics are valid? ” But measurement level has been shown empirically to be irrelevant to statistical results, hasn't it? ” What are some more examples of how measurement level relates to statistical methodology? ” Are there other theories of measurement? ” What's the bottom line? ” References What is measurement theory? Measurement theory is a branch of applied mathematics that is useful in measurement and data analysis. The fundamental idea of measurement theory is that measurements are not the same as the attribute being measured. Hence, if you want to draw conclusions about the attribute, you must take into account the nature of the correspondence between the attribute and the measurements. The mathematical theory of measurement is elaborated in: Page 1 of 14 Measurement theory: Frequently asked questions 05/31/2009 ftp://ftp.sas.com/pub/neural/measurement.html