Talk:Errors and residuals in statistics
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[edit] Additions by anon 193.206.152.72
This editor added a few paragraphs which seem to reflect a complete misunderstanding of the topic, perhaps due to confusion with a margin of error. I have moved them here in case anyone wants to discuss them further. The additions follow below. -- Avenue 11:56, 19 July 2006 (UTC)
- This is false! Error is the uncertainity on a measurement of a quantity.
- 1) It is always a positive number!!!!!
- 2) As an example, when I tell you the time 3:45 pm I have uncertainity on the last digit, so I'll have an error of plus/minus 1'
- 3) I can evaluate the error from the distribution of quantities, for example via "minimum square method".
- 4) In the case of the minimum height I have 2 kind of errors: the error on the measurement of each single height, and the error on the average height of the population. The first one is a consequence of the instruments I use to measure it: if I can resolve mm, I'll have plus/minus 1mm, if I resolve cm I'll have plus/minus 1cm etc... The second one is calculated with statistical methods from the distribution of the heights (minimum square method).
[edit] Variance cancelling
- The text says: "The σ appears in both the numerator and the denominator in those calculations and cancels. That is fortunate because in practice one would not know the value of σ2" -- but it is pretty unclear what calculations are being referred to since in the above equations this is not the case. --Richard Clegg 18:10, 24 July 2006 (UTC)
See Student's t-distribution, where one finds this:
The numerator has a normal distribution with standard deviation σ. The denominator is distributed as σ times a chi-distributed random variable with n − 1 degrees of freedom. So the standard deviation σ cancels, and the probability distribution of the expression above does not depend on σ. Michael Hardy 21:39, 24 July 2006 (UTC)
[edit] Cleanup?
I see on the article itself that it is tagged for cleanup, but I don't see any tags here. Nor, frankly, do I see what needs cleaning (the article looks good to me). I am new here, what am I missing?Plf515 11:46, 24 November 2006 (UTC)plf515
[edit] Simple Explanation
Is the following correct?:
- In mathematics, a residual is the error in a result. If we wish to find x such that f(x)=0, given an approximation, y of x, the residual is 0−f(y) and can be computed. The error is x−y; because x is unknown, the error cannot easily be computed.
As the article stands, it doesn't include residual outside of statistics (such as in approximation). If the above concise definition is correct, I'd like to add it near the top of this article. —Ben FrantzDale 21:31, 30 November 2006 (UTC)
