Talk:Level of measurement

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

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)

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)

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)

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)

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

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)

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)

I worked it into the text. Thanks. --Ancheta Wis (talk) 12:26, 25 April 2009 (UTC)

Some of the critiques of Stevens are pointing to dead links.

To all editors: a 'dead link' condition can be flagged with {{dead link}} if one follows the bad link and get a 404 error. It will help other readers, if we then return to the article and tag the bad link. --Ancheta Wis (talk) 14:00, 25 April 2009 (UTC)

Operationalism

I have never heard of 'Operationism', a term used in this article, but there is an article on Bridgman's Operationalism. It appears that this article ought to be reviewed for accuracy; if this is a typo, then it should be possible to backtrack to the edits which introduced this, using the article history. --Ancheta Wis (talk) 15:15, 25 April 2009 (UTC)

Interval data example actually ratio?

Isn't height data ratio data? A height is a length and the zero point is not arbitrary. It means "no height". Either I'm correct or something else is wrong with this article. I'm not sure which, so I didn't make an edit.

There's already a good example in the interval data section: temperature in Celsius. Just delete the height example?

 will (talk) 02:57, 5 January 2010 (UTC)

I agree - the height example is not appropriate. I've removed it. -- Avenue (talk) 08:28, 5 January 2010 (UTC)

Vicson?

I reverted a change that somebody made. They deleted the reference to the Stevens material, which is important to the history of this topic. They added a claim about Vicson, but didn't provide a reference or any description of his/her fifth type of scale. --Lou Sander (talk) 13:00, 7 June 2010 (UTC)

Intelligence Citations Bibliography for Articles Related to IQ Testing

This is a great article from which I have already learned a lot. I'd like to help it improve more and to help other articles improve more by sharing information. I have posted a bibliography of Intelligence Citations for the use of all Wikipedians who have occasion to edit articles on human intelligence and related issues. I happen to have circulating access to a huge academic research library at a university with an active research program in those issues (and to another library that is one of the ten largest public library systems in the United States) and have been researching these issues since 1989. You are welcome to use these citations for your own research and to suggest new sources to me by comments on that page. It would be particularly helpful to Wikipedia articles on IQ testing to bring in more levels of measurement perspective with citations to reliable sources. -- WeijiBaikeBianji (talk) 23:17, 2 July 2010 (UTC)

Likert scale as example of interval level?

I was surprised to see the Likert scale given unreservedly as an example of interval-level data. Surely this assertion is a bit controversial and should at least have a caveat.

Also, it should have a hyperlink to the Wikipedia entry for Likert scale, (where, incidentally, the issue of whether it is interval or ordinal is teased out a bit more).

Likert scales as interval?

I've been analyzing Likert scale data with Rasch models for years and have yet to see an instance in which those data were anything but ordinal. The spacing between the rating categories is interval in name only. Anyone can demonstrate this for themselves. Obtain ratings on a group of items that vary in the challenges, importance, frequency, or agreeability they pose from a group of people who vary across all the possible score groups. Divide the items into two groups by their total sum scores. Now sum the ratings for each respondent twice, once for the low-scoring group of items (the hard test) and again for the high scoring group (the easy test). Plot the pairs of summed ratings. This plot will always be a curve. If the scores were linear, equal-interval measures, the plot would be a line.

Scores summed from ratings or counts must be ordinal and plot in a curve. This is because the maximum and minimum possible scores are bounded by the concrete limits of the variation observed in the particular questions asked and the sample responding. Say we start with a twenty-item survey and 5-point Likert scale. The person who obtains a maximum score of 50 on the low scoring group of ten items (the hard test) is highly likely to obtain the maximum of 50 on the high scoring items (the easy test), too. Conversely, the person who obtains a minimum score of 10 on the high scoring group of ten items (the easy test) is highly likely to also obtain the minimum score on the low scoring group of items (the hard test).

Thus, the maximums and minimums from both sets of items will plot on the identity line. But what happens in between? By definition, with one set of items easier, or more important, frequent, or agreeable, than the other, the paired values must move away from the identity line. Someone who obtains a score of 45 on the low scoring items will have a higher score on the other group of items, but there are only five available higher score groups, so the range of possible variation is restricted by the arbitrary ceiling of 50. But someone who scores 25 on the low scoring items might score 35 or 40 on the other, high scoring, group (I tried to create a figure to illustrate the point, but I couldn't get it to display properly so I deleted it).

So, though Likert scales are widely referred to as providing interval measures, it is mathematically impossible for them to do so. The ordinal unit of measurement provided by Likert scales must change size as the score moves away from the middle of the scale to either extreme. One way to obtain interval measures that vary from negative infinity to positive infinity, and so do not suffer from the range restriction, is to employ the two-stretch transformation effected by a log-odds unit, as in Rasch model applications. WPFisherJr (talk) 20:56, 26 December 2010 (UTC)WPFisherJr

I am working with the Likert as well, and I wonder if Likert should not be the type of scale.--John Bessa (talk) 16:24, 31 May 2011 (UTC)

Table in theory section

This needs a column for examples.--John Bessa (talk) 16:26, 31 May 2011 (UTC)

Ordinal scales

I have made several carefully explained edits to the section. They were reverted without explanation. Please explain.Miradre (talk) 00:38, 8 July 2011 (UTC)

Carefully explained vandalism is still vandalism. See WP:Vandalism. aprock (talk) 00:43, 8 July 2011 (UTC)

I corrected and removed factual errors and incorrect arguments. That is not vandalism.Miradre (talk) 00:46, 8 July 2011 (UTC)

Here is the edits I made, each one explained in edit comments:

• [2] Note that year of the study. He is talking about old ratio IQs, not the modern development deviation IQs
• [3] OR synthesis and unsourced conclusion which is incorrect. Yes, psychologists do construct the tests so that one SD is constant number of points but that does not mean one SD is linearly related to IQ.
• [4] Minor edit.

Please explain what is incorrect with the above.Miradre (talk) 05:03, 9 July 2011 (UTC)

You can dress up your vandalism however you like, that does not excuse it. aprock (talk) 06:41, 9 July 2011 (UTC)

Your continued incivility is noted. Wikipedia:Vandalism does not include content disputes.

What is wrong with my comments and reason for removing this incorrect material? Miradre (talk) 06:47, 9 July 2011 (UTC)

Level or Scale?

The original citation for this idea [Stevens, 1946] referred to them as scales of measurement. The Handbook of Parametric and Nonparametric Statistical Procedures [Sheshkin, 2007] refers to it as scales of measurement. Almost all of the citations referenced use "scale" rather than "level": of the 35 references+notes, 6 contain "scale" in its title, while only 1 contains "level". All the references that are from Psychology and Statistics, including review papers and textbooks cited used the term "scale."

Searching for the phrase "scales of measurement" on Google returns about 3x more results than "levels of measurement," providing additional, albeit weak evidence regarding the preference by frequency.

I believe both are correct terms, and we should recognize that. However, "scales of measurement" is a more widely accepted scholarly term, as well, as a more accessible term for the student learning about this, and we should rename the article to reflect this.

[1] Stevens, S.S (June 7, 1946). "On the Theory of Scales of Measurement". Science 103 (2684): 677–680. doi:10.1126/science.103.2684.677.

[2] Sheskin, David J. (2007). Handbook of Parametric and Nonparametric Statistical Procedures (Fourth ed.)

-- Embryonix (talk) 09:42, 8 December 2011 (UTC)

Nominal Data is Categorical, Ordinal Data not?

According to Hastie, Tibshirani, and Friedman: The Elements of Statistical Learning the concept Categorical Data is used in two ways. Either unordered (a.k.a. Nominal or Qualitative Data) and ordered (a.k.a. Ordinal and a more special concept Rank Data). While this article appears to be a bit more restrictive on this at the moment, I would opt for adjusting to this. Any other opinions? 134.102.219.52 (talk) 09:42, 10 January 2012 (UTC)