Does anyone know...

[Emily]

... if there is a term for the standard deviation from the standard deviation?

 

[Jorsoft]

Yes, it's called the standard deviation

 

[Chankama]

... if there is a term for the standard deviation from the standard deviation?

hmm.. nothing that is used in "mainstream" language. There "might" be a term from a definition stand-point. But, nothing I've run across which is used regularly.

Just to clarify, you are asking if there is a term for the "standard deviation" in a set of standard deviations.

As jorsoft said, it is "still" a standard deviation - obviously. But, the context is different. In refernece to the "original random variables", you can't just call it a "standard deviation" IMO..

For example, if you have N normally distributed random variables, whose s.d. is sampled from another normal random variable of s.d. /delta,

X1 ~ N(0, /delta_1^2)
X2 ~ N(0, /delta_2^2)
...
XN ~ N(0, /delta_N^2)

where

delta_i ~ N(0, /delta^2), i = 1 to N

Given, X1 ... XN, you want to know "what" to call /delta wrt X1 ... XN

 

[Vormund]

Just curious...when/where/how would this be used? I can't think of a real-world application...maybe I'm just tired...but...

 

[Chankama]

I just edited and posted one.

 

[Emily]

Re: Re: Does anyone know...

Just to clarify, you are asking if there is a term for the "standard deviation" in a set of standard deviations.

Hmm... I think I'm thinking of something different than you are. I mean in a set where you have a standard deviation, the standard deviation that members of that same set are from the standard deviation.

Um, ok, that wasn't worded much better. Say you have a set with a mean x and a standard deviation sigma, so on average, members of the set are sigma away from x. The standard deviation of the standard deviation would be how much members of the set deviate from being sigma away from x.

EDIT: The standard deviation of a set of deviations from a standard deviation? That might be a better way to say it.

Xula: I need it for an algorithm that analyzes seismograms to distinguish an earthquake from noise. (It needs to analyze the seismogram in real time, so it has to keep re-calculating the standard deviation and then once it deviates abnormally from that standard deviation, it's an earthquake.) I'm not 100% sure it's what I need to use, but I'm sort of curious if it exists anyway.

 

[Chankama]

hmm. I wouldn't really call it a "standard deviation of standard deviations"....

So essentially you have a model for Earth quake data, where M denotes the model and M' denotes the estimate.

M_mean' = E[X] ------------------ M_mean prime
M_s.d' = sqrt( E{ (X-M_mean' )^2 } ) -------- M_s.d prime

So, by some modelling, you derive some concrete values for M_mean and M_s.d .

Now, you want to know whether M_mean' and M_s.d' are "similar" to M_mean and M_s.d or different. If it's "similar", then you say ok, this is not "too" different from my model for it not being an earthquake. If it is, then you say "yeah it is an earthquake"..

Now, how do we establish a notion of "similar"?...

WHy don't you take a look at Hypothesis Testing?.. I think, it would be appropriate for this problem.

http://en.wikipedia.org/wiki/Hypothesis_testing

The hypothesis must be stated in mathematical/statistical terms that make it possible to calculate the probability of possible samples assuming the hypothesis is correct. For example: The mean response to treatment being tested is equal to the mean response to the placebo in the control group. Both responses have the normal distribution with this unknown mean and the same known standard deviation ... (value).

The above quote is "testing" the mean. In your case, it'll be the s.d.

 

[LoTeX]

Re: Re: Re: Does anyone know...

I need it for an algorithm that analyzes seismograms to distinguish an earthquake from noise.

Wouldn't it be easier just to run with the animals?

 

[Chankama]

The standard deviation of the standard deviation would be how much members of the set deviate from being sigma away from x.

I think what you are trying to say is that..

"s.d. of s.d." would be a measure of how much the [standard deviations] (SD) deviate from the "expected" standard deviation (ESD). The ESD is the true expectation in a sense.

All the other SD instances are dependant on your "current" measurement vectors. They might be "off" by chance - which is always possible when you have a limited dataset. Or it might be statistically significant - given a certain threshold. The threshold can be lower and lower as the # of data that you use to create the SD increases.

That being said, Hypothesis Testing is your ideal choice IMO.

 

[Emily]

I'm still not sure we're on the same page, so I calculated the standard deviation from the standard deviation:

The set is:
{37, 53, 28, 2, 16, 112}
avg=41.3333333
s.d. = 35.39

Then I made the set of how far each number varies from the standard deviation (how far each number's distance from the mean deviates from the standard deviation):
{31.0567, 26.723, 22.0567, 3.943, 10.0567, 35.2767}
avg = 21.5188
s.d. = 11.16477 <--- This is the number I'm looking for - how much, on average, each number's distance from the mean varies from the average distance from the mean

Thanks for the hypothesis testing link - I'll look at it and see if it'll help me out.