Talk:True variance

message: Hi Michael,
please do not deface my site with ugly stop signs without stating your case. Say what your objections are and let's work together to make this entry I just finished writing better. Cruise 02:35, 24 August 2005 (UTC)
replies: text: That is true. Michael Hardy 22:15, 3 September 2005 (UTC)
replies: text: No, that's wrong.  There are good reasons for this usage, but User:Cruise seems to want to keep them out of the article. Michael Hardy 22:15, 3 September 2005 (UTC)

text: I don't think so. Michael Hardy 22:15, 3 September 2005 (UTC)

text: To some extent I hope my case is made by my recent edits.  There's more to do; I'll be back. Michael Hardy 19:27, 24 August 2005 (UTC)

message: Maybe this article should be improved by deleting it.
What the hell is going on here?  The "true variance" differs from the "unbiased variance" only in the denominator????  Someone who got an "F" in a statistics course would write that; it's hard to imagine anyone else doing so.
Here is the truth: the expression with n − 1 in the denominator that is a conventional unbiased estimate of a population variance is based on an i.i.d. random sample.  The "true" variance, more properly called the "population variance" is based on the whole population.  It is absurd to simply change the denominator in the population variance and call it "unbiased variance". Michael Hardy 22:26, 3 September 2005 (UTC)
thread_title: Deletion?

message: The current version of the article is simply incorrect and confusing. In general the concept of "true variance" cannot be defined in terms of finite sums (that would only work for finite populations). For example, if you're sampling from a population that follows a Cauchy distribution, you can sample till you're blue in the face, and you'd still be wrong: any finite sample will necessarily have a sample variance, and based on that you can try to estimate the population variance using a biased or unbiased estimator. But whatever you do, you will be wrong, because the true variance of the population is undefined.  Hence it is necessary to make a strict distinction between (a) the underlying population, which may not have a well-defined variance, skewness, etc.; (b) the mean, variance, etc. of a finite sample from that population; and (c) various estimators of the population moments, which may or may not involve sample moments. I've tried to say as much in my comments above.  There should be at least some pointer to a discussion of these issues, and the article should make explicit any assumptions it makes for purposes of exposition. For example, if this article is only about finite populations, it should say so and point to a more general discussion. --MarkSweep✍ 03:15, 4 September 2005 (UTC)
thread_title: Factual accuracy dispute

message: Hi Mark, Your article on variance describes this concept from the standpoint of the sampling theory. This article describes the concept of variance from the standpoint of data analysis. There is nothing wrong with either your approach, or with this approach. They just reflect different points of view. David Cruise 05:04, 4 September 2005 (UTC)
thread_title: Different points of view

message: Hi Michael and Mark,
Last night I was thinking about the core nature of this controversy and this morning I subscribed all equations in the article and made explicit that those definitions are not the abstract definitions of true or unbiased variances, but the computational definitions of true variance for the variable X, unbiased variance for the variable .... Michael, I also noticed your edits for the matrix subtraction entry, and I thank you for your help.
As you can see from this discussion page, it appears that it is only the three of us who care about these issues anyway, I propose to burry the hatchet, link each other's works, and let the reader decide if he/she needs more information on the theoretical or computational facet of statistics, the discipline we love and care about.
Yours,
David Cruise 17:56, 5 September 2005 (UTC)
replies: text: Hello.  I'll return to this article before the end of the week, but probably not today ....... Michael Hardy 20:57, 6 September 2005 (UTC)
thread_title: Working together

message: Hi Mark,
Thank you for your comments; they are constructive, incisive and helpful. The key point you make is that if this article is only about finite populations, it should say so. Today I elaborated on this point in the preamble to the article and it reads much better. David Cruise 12:32, 9 September 2005 (UTC)
thread_title: About infinity and eternity

message: As the lag time is up, I deleted the disputed tab. Cruise 19:24, 18 September 2005 (UTC)
thread_title: Lag Time

message: After reading everything above I hate to open this up again.  But this article is really a problem.  I have created an article titled population variance which follows the conventional terminology and conceptual framework of statistics.  Since the true variance article explicitly defines "true variance" to be something different from "population variance" as conventionally defined, this is not simply an attempt to create a parallel page on the same topic.  In principle, these could go on as two separate pages since they are describing different things.  The fact remains that this article has several problems.  To name two, it contains no reference that explicitly corroborates this use of the term "true variance."  Most problematically, it suggests that changing a factor from n-1 to n makes something "true" even if it based on sample. Skbkekas (talk) 20:44, 16 May 2009 (UTC)
replies: text: I just replaced the lead of the article on variance, so far without any complaints (but it's Labor Day weekend in the US so maybe no one's paying attention until Tuesday).  Without having yet seen this article on "true variance" I drew the distinction between variance itself and its estimation in the third paragraph of my lede.  While I do think it's reasonable to have a separate article on estimation theory, I'm not sold on the need for a separate article distinguishing variance from estimated variance.  In any event "true variance" is simply variance; it is what Variance is about, and I deliberately chose the two examples for my lede in the hope that it would be clear that they were examples of true variance and not merely of an estimation thereof.  One can certainly estimate die and root statistics with millions of Monte Carlo runs as a check on theory, but let's not put us theorists out of work right now in today's unforgiving labour market, especially on Labor Day.  I do not see what purpose this article serves that is not better served by the variance article.  True Variance is a Wisconsin-based progressive rock group, let's leave it that way.  --Vaughan Pratt (talk) 06:19, 7 September 2009 (UTC)
replies: text: Oops, ignore that rant, sorry, I just noticed the merge is now history.  --Vaughan Pratt (talk) 07:23, 7 September 2009 (UTC)
thread_title: Merger proposal