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WikiProject Mathematics (Rated C-class, Mid-importance)
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This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
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 Field: Probability and statistics

ossible heteroskedasticity of residuals can be find by using White's Heteroskedasticity Test on data. Heteroskedasticity problem can be avoided using Weighted Least Squares (WLS)-regression instead of Ordinary Least Squares (OLS)-regression.

added, gtx, Frank1101 19:47, 26 July 2006 (UTC)

sources not named[edit]

White (1980).

Could you expand on this comment? I am not sure what you are getting at. --Richard Clegg 13:02, 26 July 2006 (UTC)


quote: (There seems to be no standard agreed-upon spelling for these words; they are sometimes spelled homo- or heteroscedastic or -schedastic, depending on location and personal taste.)

schedastic: I have never seen this, is this a valid spelling? I'm not a native speaker... Gtx, Frank1101 21:34, 16 September 2006 (UTC)

We think it is good to mention alternate spellings. But the second sentence seems more like an observation rather than fact, and doesn't add to the discussion at hand. Unless its deemed relevant or links to American vs. British spellings is warranted, this could probably be cut out.

Ref.: (In America, it is usually spelled homoscedastic. It is an exception to the rule that American spellings are usually more faithful to the etymologies than British spellings.)

I would like to draw your attention to McCulloch, J. H.: "On Heteros*edasticity", Econometrica, vol. 53, no. 2, March 1985, pp. 403. The author explores the linguistic aspects, and makes it very clear that "Heteroskedasticity is therefore the proper English spelling." - 14:15, 2 January 2007 (UTC)

my econometrics book spells it heteroskedasticity as well 06:45, 13 April 2007 (UTC)
I haven't found the corresponding line yet but Peter Kennedy also made a clear statement and gives reliable sources in his book "A Guide to Econometrics" that "heteroskedasticity" with "k" is the correct spelling. -- MM-Stat (talk) 14:38, 1 February 2010 (UTC)

In Greene (5th, 6th, and 7th editions) and Wooldridge, and in statistical programs like Stata, R, and SAS, I have only seen it spelled heteroskedasticity (talk) 20:53, 24 January 2012 (UTC)

I'm looking at Greene 5th edition right now - it's spelled with "c". That said, every other book I can put my hands on right now (Wooldridge, Kennedy, Griffiths Hill & Judge, Cameron & Trivedi, Stock & Watson) spell it with a "k" except Greene and Gujarati & Porter. And both of those are newer editions of 25-year-old textbooks. DaveDixon (talk) 16:15, 19 April 2015 (UTC)
Just saw the table of contents for the 7th edition on Greene's web page: still spelt with "c". DaveDixon (talk) 19:05, 19 April 2015 (UTC)
(unsigned contribution) Paper explaining the preferred spelling: ( end unsigned contribution) Note that this is the McCulloch, in Econometrica, referred to above. Melcombe (talk) 17:19, 7 February 2012 (UTC)

All my life in college and university, I have always encountered in books and myself used only "heterosKedasticity" - came today to this article and was totally surprised by the spelling...


There's an article called heteroscedacity, which seems not a Yank-v-Brit difference, but a simple misspelling in any country. It seems a good bit less complete than this article, but maybe someone else would like to take a look to see if anything should be merged from it before it's redirected here. --Trovatore 07:00, 21 December 2005 (UTC)

I'm not so sure that spelling with a c is the incorrect version - it was certainly how I learned it. A literature search on PubMed for 'heteroscedastic' gives 82 results compared to only 10 for 'heteroskedastic', 'heteroscedasticity' gives 67 items whereas 'heteroskedasticity' gives 17. -- 18:41, 27 December 2005 (UTC)

The issue isn't c or no c. The c-vs-k thing is a Yank/Brit difference and falls under the usual rules (since this isn't specific to a country or culture, the first article written gets to keep its spelling). The misspelling is "heteroscedacity" (ends in -acity when it should end in -asticity). --Trovatore 18:59, 27 December 2005 (UTC)
Homoscedasticity exists, and is so spelt. Wikipedia is inconsistent, but this seems excessive. I prefer -sced- as the usual treatment of Greek names. Is there objection to moving this article? Septentrionalis 18:01, 6 October 2006 (UTC)
online link to that reference is here [1] Justinc (talk) 15:46, 15 November 2011 (UTC)
A search on yields 109,000 hits for "heteroskedasticity" (2330 since 2015) versus 95,700 for "heteroscedasticity" (2220 since 2015). Not decisive, but far different from the PubMed result. DaveDixon (talk) 16:21, 19 April 2015 (UTC)

Most of the links to here[edit]

Use the -k spelling. After years of statistics, this is the first place I've ever seen it spelled with a -c. Jarring, to say the least. 18:28, 2 December 2007 (UTC)

You haven't been around much. Michael Hardy (talk) 05:17, 20 August 2008 (UTC)

Seriously use -k. I refer you again to the Econometrica publication by McCulloch. I am certain that trumps all of your other banter. Brit, Yank, whoever will certainly agree that Econometrica knows what it is talking about in regards to statistics. (talk) 19:36, 29 March 2008 (UTC)

Improving the illustration[edit]

There is an illustration in the article showing an example of heteroscedasticity, and as someone new to the topic it would be helpful to my understanding if some (simple) formula for generating such a plot were provided in conjunction with the plotted output, along with the actual values of the variables along the x-axis (e.g. one colored line per variable, similarly colored in the formula). Similarly, the plot illustrated for homoscedasticity could be updated so that by comparison it's easy to see the difference in the variances of the variables affecting the output. —Preceding unsigned comment added by (talk) 18:47, 30 January 2008 (UTC)

clarified statement of importance[edit]

i have reworded the second paragraph for clarity: heteroskedasticity is not a significant concern *of* regression analysis (that connotes regression analysis is principally used to study heteroskedasticity); "bad effect" means the statistical tests are uninterpretable (rather than incalculable); the tests are uninterpretable *because* the statistical distributions used to calculate the area probabilities may no longer apply. (talk) —Preceding undated comment added 18:01, 24 September 2011 (UTC).

Heteroskedasticity does not cause bias[edit]

The presence of heteroskedasticity in a dataset does not cause OLS estimators to be bias, only inefficient. Should be changed.

I have changed the entry because this comment is completly true: OLS is still (conditionally) unbiased, consistent and asintotically normal under heteroskedaticity. —Preceding unsigned comment added by Heteroskedasticity (talkcontribs) 02:51, 21 April 2010 (UTC)

Rank correlation for testing heteroscedasticity?[edit]

On Feb 19th, 2010, somebody added the rank correlation as a test for chekcing heteroscedasticity. Anyone has any reference about how that is done? I am unable to find any such reference. Otherwise, I think this test should be deleted. —Preceding unsigned comment added by Samikrc (talkcontribs) 15:09, 25 June 2010 (UTC)

this page is far too specialized and unclear. Please revise (talk) 17:14, 5 November 2010 (UTC)

Clarification - check accuracy[edit]

The text used to read: "Most of the methods of detecting heteroscedasticity outlined above modified for use even when the data do not come from a normal distribution.". I changed it to " Most of the methods of detecting heteroscedasticity outlined above can be modified for use even when the data do not come from a normal distribution." - Please confirm that this is correct. --Slashme (talk) 13:59, 20 August 2013 (UTC)


Could some editor add etymology. What (most likely Greek) words are etymons of this word?

Just noticed the info was there. I separated it in a section so that it looks similar to many other articles in Wikipedia.