Talk:Cronbach's alpha

Definition of symbols is confusing

In the definition of the systematic and conventional formulas, it is first stated that σ^2(X) denotes the variance of X, whereas in the following sentence it is defined as the sum of the entire covariance matrix of individual items. I'm not aware of this equivalence and it would seem more logical not to conflate these two.

Early comments

It is very difficult to find information on the appropriateness of Cronbach's alpha for continuous variables. Can someone please add a statement about using Cronbach's alpha for the reliability of discrete vs. continuous variables?

Do you mean here or in the article? I'm a specialist in Cronbach's alpha, and there is no problem whatsoever with continuous variables. JulesEllis 22:56, 14 January 2007 (UTC)

It would be nice to have a guide as to what are considered adequate values for Cronbach alpha, what the implications are for using a test with a Cronbach alpha of, say .5 Tim bates 11:08, 9 October 2006 (UTC)

Some people say that 0.70 is a professional standard for reliability. I'm not aware of where this comes from. I've also heard 0.60.

However. you cannot blindly apply a simple rule of thumb for three reasons. First, alpha assumes that the components are multually parallel (or, at least, multually tau-equivalent). This is rare, if it exists at all. In the typical situation the components are indvidual items which diffier in content and difficulty. In these cases, alpha is not an unbiased estimate of reliabiity, but instead is a lower bound on reliability. So, if you have a test with alpha = 0.50 but the test is composed of hertogeneous items, the reliability may well be much higher than 0.50.

Second, reliability is sample-specific. An alpha of 0.50 in a homogeneous subsample (with reduced true score variability) may be quite high.

And third, the reliability of a test (especially the internal consistency estimates of reliability) cannot be evaluated without respect to the purpose of an instrument. If a test is included in a screening battery, a reliability of 0.50 might be sufficient (because it will be combined with other scores). Or if the test is designed to be pass/fail, the overall reliability may be low (like 0.50) while the pass/fail consistency is quite a bit higher. Amead 01:07, 11 October 2006 (UTC)

The 'alpha' in this title is a really bad idea. Any way to change it (Move has just failed for me)?

Charles Matthews 13:59, 15 Feb 2004 (UTC)

How about a redirect, so this title would still be in the database (for those whose software is happy with it), and the content would be at Cronbach's alpha. Vicki Rosenzweig 14:23, 15 Feb 2004 (UTC)

OK, tried that with copy+paste and as you can see it goes to 'Cronbach's α'. So, I'm not up to speed with the coding for the alpha.

Charles Matthews 14:33, 15 Feb 2004 (UTC)

Cronbach's α or Cronbach's &_alpha; (without the underscore is contrary to the ASCII norm of the English Wikipedia headings, so this is now Cronbach's alpha --Henrygb 00:36, 10 Aug 2004 (UTC)

I realise it's what comes through from a template, but it seems to me misleading to say that the title "Cronbach's alpha" is "wrong". You'll see it written in that form in innumerable articles that use coefficient alpha - and Cronbach himself spelt it out in his original article title. Any objections to just deleting the template? seglea 5 July 2005 23:29 (UTC)

Condition under which alpha is the reliability

It was stated that alpha is equal to the reliability if the items are parallel, and smaller otherwise. This is incorrect. The necessary and sufficient condition for alpha to be equal to the reliability is that the items are essentially tau-equivalent (Lord & Novick, 1968). This allows the items to have different means and even different variances. I know that most text books deal only with the parallel case, but then the statement should be "if" and not "if and only if". So I corrected this.

JulesEllis 23:04, 14 January 2007 (UTC)

Other roles of alpha

The current article was only about the role of alpha in classical test theory. This is unfortunate, because Cronbach himself rejected much of that theory and developed the generalizability theory for this reason. I also added a little section about the intra-class correlation and factor analysis. I think I should write an article about that too, because it happens too often that people are not aware that they are actually the same in many two-facetted applications. JulesEllis 06:04, 15 January 2007 (UTC)

introduction

"$\sigma _{X}^{2}$ is the variance of the observed total test scores, and $\sigma _{Y_{i}}^{2}$ is the variance of component i for person y"

-Should this just read: ...is the variance of component i? y isn't a person ... we're talking about a distribution for one test item, not the score for one person 131.172.99.15 01:48, 31 July 2007 (UTC)snaxalotl

Yes it should- I'm editing it now. 85.224.241.118 17:52, 5 September 2007 (UTC)

The formula is not visible. Is there any problem with the page or my browser.Can anyone confirm?? Qomarf (talk) 10:45, 3 October 2010 (UTC)qomarf

Constructs

Could somebody be so kind to look at the following sentence in the article:

"Coding two (or more) different variables with a high Cronbach's alpha into a construct for regression use is simple. Dividing the used variables by their means or averages results in a percentage value for the respective case. After all variables have been re-calculated in percentage terms, they can easily be summed to create the new construct. "

Why would you weigh a variable more if its average is lower? Consider the most absurd case: a scale from -3 to +3 with average 0 has to be combined with a scale from 0 to 6 with average 3, and similar variance in the data. According the above prescription the scale from -3 to +3 is infinitely more important.

It seems more logical to linearly transform the different intervals to a standard interval, if the variances/ranges of the data in the items is similar, and if not, you could use the z-values to add the scores in an independent way.

What is the correct procedure? —Preceding unsigned comment added by 217.121.96.59 (talk) 14:09, 28 June 2008 (UTC)

Problem with Definition

The Definition section contains a couple of problems, both apparently stemming from the use of undefined symbols that "everybody knows". (Yes, I use σ for std. dev. too -- but I define it when I expect anyone else to see it. I would edit the article if I could, but I came here to learn about α because I don't know much about it.) The problems:

(1) The 2nd expression purports to show the "standardized" statistic. Is this stat any different from the one in the first equation (but perhaps using "standardized" variables inside it)? In that case it is not a "standardized Cronbach's α", it is simply Cronbach's α. Or is the stat itself normalized in some way compared to the first one? If so, what is the standardization that was applied to the first stat, to produce the 2nd?

(2) The RHS of the 2nd definition is not dimensionally homogeneous. Or more likely, it depends on some standardization of the "average variance" [sic] that is not obvious. What standardization is that? (And what does "average" even mean, here? Arithmetic mean? Expected value? Max Likelihood estimate? something else? I can guess, but guessing is not usually the point of an encyclopedia article.) Jmacwiki (talk) 02:32, 30 June 2008 (UTC)

Perfectible introduction?

Hi, I visited this page in order to have a rough idea of what was this "alpha" indicator. The introduction gave me no clue about it. Rather than providing historical or technical details, I think it should briefly explain WHAT Cronbach's alpha is or measures... Regards. Eusebius en (talk) 08:21, 28 August 2008 (UTC)

I'd like to change some of the introduction. The implication is made, without reference, that the alpha coefficient is worthless as a measure of internal consistency. This is false, and I'm not sure where the writer gets this from. As an economics student, I am constantly exposed to the use of alpha in this regard both in my own department and in the applied math and stat departments. There is extensive literature both using alpha in this regard and proving its worth. It is true, however, that alpha has significant drawbacks (it increases as more items are added, for instance). This is addressed however, with references, in the article body. I'd like to change the intro to something that more accurately reflects the strengths and weaknesses of alpha, rather than just saying "this is a misbelief (sic)." Any objections? —Preceding unsigned comment added by 136.152.148.17 (talk) 21:29, 17 March 2009 (UTC)

I agree with both sets of points, but it would be good if someone went further by removing the jargon from the introdiction (or else giving enough explanation of specialist terms: "tests", "instruments"). In addition, more work is needed on the "definition" section to give meaning to the quantities involved. Melcombe (talk) 09:40, 18 March 2009 (UTC)

Completely agree that the intro is inappropriate. Anybody who knows anything about this, please feel free to edit! Jmacwiki (talk) 23:13, 21 March 2009 (UTC)

Absolutely agree. I've rewritten the intro based primarily on versions prior to the anonymous re-write by 219.153.62.104. The fact that alpha increases with the addition of items is definitely a drawback, but certainly not one that renders the measure useless - the intro as it stood was nowhere near NPOV and not a reasonable reflection of the status of consensus on the measure. I'd guess it was the work of an overzealous undergrad student. Rewrites to my version of the intro are encouraged, but need to be NPOV and reflect a reasonable consensus viewpoint. CowboyBear (talk) 05:55, 24 March 2009 (UTC)

From the intro one may get the impression that alpha tests unidimensionality. Alpha assumes unidimensionality, doesn't test it. —Preceding unsigned comment added by 83.150.114.36 (talk) 13:56, 7 September 2009 (UTC)

I agree. The introduction contains too many technical details. It should start with presenting alpha as a measure of the internal consistency of a statistical variable. Agnerf (talk) 10:02, 18 February 2019 (UTC)

Types of items suitable for Cronbach's alpha

Could someone clarify on this page what sorts of items (continuous, ordinal, binary) are suitable for Cronbach alpha, and provide a reference? There is a comment at the top that the alpha's are fine for continuous variables, but no reference and I'm not sure about other sorts of item. Thanks! —Preceding unsigned comment added by Pizza37anna (talk • contribs) 13:32, 21 March 2009 (UTC)

Naming (Dec 2009)

Technically the correct name for this is Coefficient alpha. Shouldn't the content be under Coefficient alpha and Cronbach's alpha redirect? tryggvi_bt —Preceding undated comment added 00:49, 3 December 2009 (UTC).

Do you have any (preferably many) citations that use the term "Coefficient alpha" other than Cronbach's early paper? If "Cronbach's alpha" is the term generally used then that seems the most appropriate one to use here. Melcombe (talk) 10:11, 3 December 2009 (UTC)

There's no shortage of literature that uses the term "coefficient alpha" and really detailing it would be overkill. Below are a couple of articles that discuss the coefficient alpha within a broader consideration of methodology that use the term. But, most importantly, is Cronbach's last article where he states, "It is an embarrassment to me that the formula became conventionally known as Cronbach’s α." (Cronbach & Shavelson, 2004, p. 397).

Cortina, J. M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78(1), 98-104.

Cronbach, L. J. & Shavelson, R. J. (2004). My current thoughts on coefficient alpha and successor procedures. Educational and Psychological Measurement, 64(3), 391-418.

Osburn, H. G. (2000). Coefficient alpha and related internal consistency reliability coefficients. Psychological Methods, 5(3), 343-355.

tryggvi_bt —Preceding undated comment added 16:04, 7 December 2009 (UTC).

Wikipedia covention is, more or less, to use the name that is usually used, not necessarily to follow what whoever invented a thing uses or says should be used. Your quote iteself says that "the formula became conventionally known as Cronbach’s α." Your refs are from "psychology" and "Coefficient alpha" may be a common term there, but it seems that in more general statistics the term "Cronbach’s α" is used ... I write that on the basis that I have access to 3 different dictionaries of statistics each of which has something for "Cronbach’s α", but nothing for "Coefficient alpha" (or any mention of the term). My suggestion is just to add a note about the alternative name "Coefficient alpha" (with some of the above citations) to the present article. Melcombe (talk) 16:55, 7 December 2009 (UTC)

As of today, Google found 193,000 matches for "coefficient alpha", and 441,000 matches for "Cronbach's alpha". But, as i read through this article, I still don't understand how to calculate it. I suspect this may be cognitive dissonance over expressions like $\sigma _{X}^{2}$, which although it seems to be defined concisely, every important word there is jargon (variance, observed, total, test, score, sample, and component), and it isn't explained why there's a squared and a subscript, nor whether the sigma is the thing that i think it is. It's almost, but not quite, consistent with the set of symbols used on the page variance, but over there I see mention of covariance, and a whole bunch of other formulae. It leaves me so confounded that i start imagining the entire field of statistics is meant to confuse rather than to clarify. -- 99.233.186.4 (talk) 19:45, 16 February 2010 (UTC)

Missing Reference

I was just looking through and there is a citation to (McDonald, 1999) which does not appear in the references listed at the bottom. I skimmed and checked most of the others through the page and they seem to be there. Could someone either add the reference - or remove the citation? Dwmc (talk) 03:10, 21 April 2010 (UTC)

"Inflated" Alpha and the Number of Items

In the section on "Internal Consistency", the article states, "...however it should be noted that a greater number of items in the test can artificially inflate the value of alpha" (emphasis mine). If by "artificially inflate" is meant "mislead without sharing the number of items on which alpha is based," this is a fair statement. It is a fact that as the number of measurement units (e.g., items) increases, alpha will increase, ceteris paribus. However, the wording implies that shorter tests do not artificially limit the estimate of alpha, which can easily happen. The number of items should be determined by the breadth of the domain being tested, as well as practical constraints like the quality of the items available, time limits, and cost. Constraints that limit the length of a test will underestimate the magnitude of alpha. Eliminating such constraints could result in a substantially higher estimate of alpha, but one would be hard-pressed to say it is artificially high; indeed, it is likely to be more accurate.

If the number of items on a test were to approach infinity, coefficient alpha would approach 1.00. This is unlikely to happen in the real world. But tests of narrowly-defined content/constructs may result in scores that can be reliably estimated with just a few good items, while broad or diffuse ones may require many items to produce reliable scores.Drbb01 (talk) 21:11, 27 May 2012 (UTC)

Sijtsma's paper

I know this is a primary source and not to be directly used, but there is a possibility this article is very flawed if the arguments put forward in "On the use, the misuse, and the very limited usefulness of cronbachs alpha" by Klaas Sijtsma in 2009 are true. Basically this measurement should not be used because many other better metrics exist. I guess we must wait to see if it gets picked up in secondary sources... --TimSC (talk) 20:11, 3 October 2012 (UTC)

Negative alpha and theoretical alpha

I'm no expert but a sentence like "theoretically alpha should vary from 0 to 1 but empirically it can be anything smaller than 1" (I'm paraphrasing here) just can't be right. So I changed it, it got changed back by an IP and I changed it again to something that at least makes sense but might or might not be what the IP/original author meant and it might or might not even be factually correct. I'm also under the impression that the "Definition" section discusses things that go far beyond the definition of alpha (and are more like the derivation of alpha) which ultimately lead to this whole confusion. I'm sorry I can't be more constructive but: please, somebody, fix this! --Mudd1 (talk) 22:22, 27 January 2013 (UTC)

Intelligence citations bibliography for updating this and other articles

You may find it helpful while reading or editing articles to look at a bibliography of Intelligence Citations, posted 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 these 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. You can help other Wikipedians by suggesting new sources through comments on that page. It will be extremely helpful for articles on human intelligence to edit them according to the Wikipedia standards for reliable sources for medicine-related articles, as it is important to get these issues as well verified as possible. -- WeijiBaikeBianji (talk, how I edit) 02:02, 2 September 2013 (UTC)

'Ideal' Cronbach's alpha levels

Under 'Internal Consistency', the Wikipedia page currently states (2018/01/16) that an alpha level of .90 or above is 'Excellent'. However, the literature is in dispute about this, with many sources saying that a value above .90 is not ideal, as it indicates that many of the items may be redundant. While some agree with the Wiki page, and state that .90-.95+ is best, others state that anything outside of .70-.80 is not ideal. 2001:388:608C:4950:6DCE:17C8:2BB:211F (talk) 05:50, 16 January 2018 (UTC)

In general, values like alpha (or rho_T properly) should not be misunderstood at cutoff values. Such values give indications that help to discuss issues. But you should not kick out an item if the alpha value is 0.69 and retain the one with 0.71, just because you believe 0.7 should be understood as a cutoff value. The same applies for the upper end. Check for example what these authors, the editors of a leading management journal, have to say about "cutoff values": Guide, V., & Ketokivi, M. (2015). Notes from the Editors: Redefining Some Methodological Criteria for the Journal. Journal of Operations Management, 37 https://doi.org/10.1016/S0272-6963(15)00056-X 130.226.41.9 (talk) 14:52, 2 February 2018 (UTC)

Moving this article to tau-equivalent reliability

I suggest to move this article to tau-equivalent reliability. "Cronbach's alpha" is a term from the psychometric stone age. Good journals don't use the term anymore, but only $\rho _{T}$ and tau-equivalent reliability. 80.71.142.166 (talk) 07:03, 7 February 2018 (UTC)

Tone

This article reads like a mathematics textbook, not a Wikipedia article. Please see Wikipedia:What_Wikipedia_is_not#Wikipedia_is_not_a_manual,_guidebook,_textbook,_or_scientific_journal. It also addresses the readers and makes use of "we" and "you". Please see MOS:YOU.

It should be completely rewritten.

Ira

Ira Leviton (talk) 23:38, 30 July 2020 (UTC)

I agree with Ira; as a non-statistician, this page was pretty much impossible to understand. A simple narrative example of Cronbach's Alpha in use would be very helpful

KA

2603:8080:1440:356:9108:4680:5BEE:C89A (talk) 23:24, 6 March 2021 (UTC)

over items holding occasion fixed

The current wording here is too obscure, and so it should be improved --Backinstadiums (talk) 10:02, 18 March 2022 (UTC)

"Common misconceptions" section is misleading

It is unclear at first whether headings stated as facts are in fact true or false. These headings should be rewritten for clarity. For example, "The value of Cronbach's alpha ranges between zero and one" could be "Cronbach's alpha is not restricted to values between zero and one" (that seems to be the message of the text, but I'm not familiar with the subject). Elleh3113 (talk) 19:21, 9 March 2023 (UTC)

Prerequisites are not prerequisites

The prerequisites section suggests the conditions are nessecary to use the coefficient. Strictly speaking these are not prerequisites of the coefficient's use, they are conditions under which the coefficient gives an accurate measure of reliability. As per one of the sources cited in that section (Cortina, Jose M., 1993), perfect tau-equivalence is "seldom, if ever achieved", which would imply the coefficient is seldom, if ever, useable.

Per its relatively common misuse, there is clearly a need to discourage its inappropriate use (or perhaps, to keep better in line with policy, to explain clearly and early in the article the conditions under which its use is appropriate), but I think this section could do with a rewrite.

Ideally, it would include a list of the most important conditions for its accuracy, a statement that without these conditions it is unlikely to accurately measure reliability, and finally a non-list of some of the less-important conditions which affect accuracy (Georgia Spiliotopoulou (2009) lists several, e.g. the existence of a central response tendency).

I may come back later and do this myself, but I thought should leave this here in case I forget to do so. Designated Maelstrom (talk) 15:29, 13 May 2023 (UTC)