Talk:Mean squared error

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[edit] INCONSISTENT ARTICLE TITLE

There is another article published on Wikipedia and titled "Root mean square error". Notice the use of the adjective "square", rather than "squared".

For the sake of consistency, I suggest to use "square" everywhere, including the title of this article, and indicate in the text that "squared" can be also used:

Symbol	Preferred name	Other name
SS	Sum of squares
MS	Mean square	("Mean squared" is not correct)
RMS	Root mean square	("Root mean squared" is not correct")
MSE	Mean square error	Mean squared error
RMSE	Root mean square error	Root mean squared error
MSD	Mean square deviation	Mean squared deviation
RMSD	Root mean square deviation	Root mean squared deviation

A disambiguation is also necessary.

[edit] MSE

The article does not give explicit formulae of the MSE for the estimators in the example. Could someone fill this in?

Someone has suggested that the page for Root mean square deviation (RMSD) be merged with mean squared error. I do not think that it makes sense to do this for several reasons: 1. MSE is a measure of error, whereas RMSD method for comparing two biological structures. 2. RMSD is used almost exclusively in the context of protein folding, whereas MSE is used to describe statistics 3. Merging the articles would result in losing the meaning of the RMSD article.

Note that root mean squared deviation is different than root mean squared error.

• My two cents: --DanielPenfield 17:40, 1 November 2006 (UTC)

1. RMSE = estimator of average error, RMSD = estimator of average distance. They're measuring the same thing: differences or variation.
2. RMSD is used in disciplines other than bioinformatics/biostatistics—try googling RMSD and "electrical engineering", for example.
3. Merging the articles should preserve the RMSD tie-in.

• My opinion: -- PdL -- January 11 2007 (UTC)

1. D in RMSD typically stands for "deviation", not for "distance". The distance and the difference between two scalar values are not exactly the same thing: the distance is the absolute value of the difference.
2. Deviation is the difference between the real value of a variable and its estimated or expected or predicted or "desired" value (for instance, the mean).
3. On the other hand, "error" is the difference between an estimated value of a variable and its real value. There are errors "of estimate" as well as errors "of measurement", and they are all with respect to the (often unknown) real value of the variable.
4. I conclude that a deviation is the additive opposite of an error. I agree that both words indicate differences, but they have not exactly the same meaning, and it is inappropriate to use theme as synonims.

[edit] Content

Sweeping critique: This article is pretty useless to anyone but a math major.

Specific suggestion: If someone agrees with me on the following statement, then it would be helpful if added into the article--

"MSE is also sometimes called the variance; RMSE is also sometimes called the standard deviation."

I'm pretty sure that's correct, but I won't add it without confirmation.

• Agreed that the article could be made more friendly to those of use who haven't studied statistical theory. BTW, MSE and RMSE estimate the variance and standard deviation. To equate them would be inaccurate. --DanielPenfield 17:40, 1 November 2006 (UTC)

"MSE is also sometimes called the variance; RMSE is also sometimes called the standard deviation." Well, the MSE is a random variable itself that needs to be estimated. It's not just a number. If it has been estimated, it gives a measures of the variation of an estimator with repect to a known parameter. But it is not the variance as it also accounts for the bias of the estimator. Squim 10:59, 24 December 2006 (UTC)