Talk:Level of measurement

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[edit] Direct links to terms

I modified the source so you can link to a measurement type using a HTML label.

Just put in Nominal Measurement

Thanks User:dmccreary

[edit] Source

I seem to recall that some physicist classified these "levels of measurement" in some paper published in the early 20th century, and perhaps proved mathematically that under specified assumptions, no other levels than these four are possible. Are there scholarly references that can be added to the article, that are not just textbook explanations of the same information that's already here? Michael Hardy 22:58, 28 Aug 2004 (UTC)

Perhaps someone tried to prove that these were the only four levels, but Stevens in the 1959 article cited in the article presents a fifth "level" that he called "logarithmic-interval". This handled scales such as Richter's scale of earthquake intensity that had a fixed zero but non-linear units. In later work, a number of researchers presented a higher scale of measurement called "absolute" that could not be rescaled by a multiplier. This includes probability. A more complete axoimatization of measurement is in the three volumes: Krantz, David H., Luce, R. Duncan, Suppes, Patrick and Tversky, Amos 1971. Foundations of Measurement: Volume 1: Additive and Polynomial Representations. New York: Academic Press. Suppes, Patrick, Krantz, David H., Luce, R. Duncan and Tversky, Amos 1989. Foundations of Measurement: Geometrical, Threshold, and Probabilistic Representations. San Diego: Academic Press. Luce, R. Duncan, Krantz, David H., Suppes, Patrick and Tversky, Amos 1990. Foundations of Measurement: Representation, Axiomatization, and Invariance. San Diego: Academic Press. This is very dense material, and not cited in normal textbook versions. Still, I think it would be important to say that the four common levels are not the end of the story.

NChrisman 18:44, 4 September 2006 (UTC)

I added a reference to Stevens's article which is often quoted as the origin of this subject. I have also seen references to Guttman's "A Basis for Scaling Qualitative Data" which was published 7 years earlier (American Sociological Review, 1944, 9:139-150) but I didn't include that since I haven't read or even seen the article myself. Perhaps someone else has read this source and can add or comment? :Jlefeaux 14:29, 19 Nov 2004 (UTC)

Guttman scales are was to generate an interval measurement from ordinal scales. It is not a work on this level of measurement debate. Although Stevens had limited citations in Science, his work derives more from the operationalism debate (Campbell and others).

NChrisman 18:44, 4 September 2006 (UTC)

Those levels are described in Earl Babbies 'The practice of social research', a popular textbook for students in social sciences. --Piotr Konieczny aka Prokonsul Piotrus Talk 19:24, 16 October 2005 (UTC)

I published an article about limitations in Stevens' taxonomy for the field of cartography: Chrisman, N. R. (1998) Rethinking levels of measurement in cartography. Cartography and GIS, 25, 231-242.

NChrisman 18:44, 4 September 2006 (UTC)

[edit] IQ

Article states: Most measurement in psychology and other social sciences is at the ordinal level; for example attitudes and IQ are only measured at the ordinal level.. But Babbie's specifically states that 'about the only interval measures commonly used in social scientifc research are constructed measures such as standarized intelligence tests' (IQ). --Piotr Konieczny aka Prokonsul Piotrus Talk 19:24, 16 October 2005 (UTC)

Raw scores, and standardized scores derived from raw scores, for IQ tests do not have an underlying unit of a scale and so, in Stevens' schema, don't constitute interval level measurements. Having said that, when analysed with Rasch models many such tests meet the criteria for interval level measurement to a reasonable extent. The transformation of raw scores is non-linear when these models are applied, but all the same, the transformation is close to linear in a substantial range of the raw scores, for most tests. So it depends how strict your criteria are. There's an argument both ways, depending on this. Certainly, though, person estimates produced by IQ test are no more or less 'interval-level' than those produced by many attainment tests, or various other tests for that matter. Stephenhumphry 10:57, 17 October 2005 (UTC)

[edit] On measurement and numbers

I have reverted the most recent edits. First, placing "ordinal numbers are ..." directly after the term Ordinal measurement seems to me to imply ordinal measurement is definable simply in terms of a number system. This runs the risk of going down a troubling path, and there is enough confusion about the meaning of measurement and scale as it is. Stevens (1946, p. 677) said: "The isomorphism between ... properties of the numeral series and certain empirical operations which we perform with objects permits the use of the series as a model to represent aspects of the empirical world" - which clearly implies that he had more than just a formal system in mind when proposing his measurement scales. Sophisticated works such as the Foundations of Measurement by Luce, Krantz, Suppes, & Tversky have been devoted to establishing formal foundations for measurement in which the assignment of numbers to objects in terms is justified in terms of structural correspondences between numbers and empirical qualitative relations. Secondly, I find the usefulness of the term nominal number dubious, and quickly find that I'm not alone [1]. Lastly, to refer to alphabetical sorting as a type of measurement reminds me of Lord's (1953) article On the statistical treatment of football numbers (i.e. it just starts getting silly). smhhms 07:02, 3 December 2005 (UTC)

[edit] Levels and their implications for formula; & intensive, extensive

In the past for my own amusement I did work out the permisable mathematical relationships or transformations of different levels. I was interested in this as it could help specifiy an unknown formula in the same way that dimensional analysis does. The piece of paper I wrote my results on has become lost long ago. I would like to read more about this.

I've also heard something about intensive and extensive measurements. I would like to read more about these. --62.253.52.46 10:15, 16 July 2006 (UTC)

See intensive quantity and extensive quantity and also the quantity article itself. Holon 02:37, 17 July 2006 (UTC)

Stevens thought that the distinctions between intensive and extensive were not needed. He argued that the only issue of importance was invariance under transformation. I, like many others, disagree since "ratio" scales behave differently when aggregated or disaggregated. The extensive measure "population" must be partitioned among sub units, while density (a derived intensive measure) behaves differently. NChrisman 18:45, 4 September 2006 (UTC)

[edit] Most information

I removed 'the mean gives the most information'; I think that this will just confuse people. Alternative measures of central tendency are under-utilized, and saying that the mean gives the most information may just exacerbate that. Plf515 02:15, 24 November 2006 (UTC)plf515

[edit] The mean gives the most information - why?

I notice that a lot of time has elapsed since Plf515 deleted the above comment, and the delete appears to have been reverted with no explanation. I also believe it should be removed, as it is wrong as it stands. E.g. if you actually want to know the mode, knowing the mean is unhelpful and gives no information! OK, one could argue that the arithmetic mean is based on information from all the points whereas the mode is not, but the geometric mean depends on all the points as well. Surely it depends what kind of information you are trying to distil from the data. In summary, I don't think the phrase adds anything to the article. A point which is perhaps worth making is that the the classification levels are successively more informative and can undergo successively more different meaningful operations (equality, comparison, arithmetic mean, geometric mean). Comments anyone? Kiwi137 (talk) 17:06, 15 January 2008 (UTC)

On my first quick reading of the page, this phrase also struck me as odd. But perhaps it depends on whether you think that more information is necessarily a good thing. Using the mode rather than the median may be most appropriate in context, as with choosing an appropriate level of approximation for numbers. Itsmejudith (talk) —Preceding comment was added at 09:57, 21 January 2008 (UTC)
I agree with the above that saying "the mean gives more information" is incorrect: the mean gives different information than the median or mode (likewise for the standard deviation compared to the MAD or maximum deviation), but it does not give strictly more information, nor is it in general preferable. I've thus removed the statements saying that "the mean gives more information."
Nbarth (email) (talk) 18:47, 2 March 2008 (UTC)

[edit] Related article?

Can someone look at the oprhaned article Nominal category and see if it is correct, if it should be linked to from here or merged, or whatever. Melcombe (talk) 09:11, 22 May 2008 (UTC)