13 questions linked to/from Standard deviation of standard deviation
178 views

Confidence Interval on the standard deviation [duplicate]

Supposed we have $n = 15$ independent samples $X_1, X_2, ..., X_n$ from distribution $N(\mu, \sigma)$. Sample mean $\bar{X} = 2.4$ and sample variance $\hat{\sigma^2} = 0.55$ What's the 95% ...
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Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?

It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our ...
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Why is sample standard deviation a biased estimator of $\sigma$?

According to the Wikipedia article on unbiased estimation of standard deviation the sample SD $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$ is a biased estimator of the SD of the ...
74k views

Converting standard error to standard deviation?

Is it sensible to convert standard error to standard deviation? And if so, is this formula appropriate? $$SE = \frac{SD}{\sqrt{N}}$$
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How can I find the standard deviation of the sample standard deviation from a normal distribution?

Forgive me if I've missed something rather obvious. I'm a physicist with what is essentially a (histogram) distribution centered about a mean value that approximates to a Normal distribution. The ...
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Distribution of standard deviation

This question addressed the normal distribution, but I am wondering what is known about the distribution of the standard deviation of a sample of size n drawn from an arbitrary distribution. In ...
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Standard deviation of (assumed) normal distribution

Say I measure a system for $N$ periods of time $T$. In each of these time periods $T_i$, with $1 \leq i \leq N$, I get $M_i$ occurrences. I have reason to assume that the variable $M$ follows a ...
956 views

How to calculate the standard error of the variance of a data set

Given a data set of N points with sample mean $\overline{x} \pm \Delta\overline{x}$ (here $\Delta\overline{x}$ is the standard error of the mean given by $s/\sqrt{N}$) and sample variance $s^2$, I am ...
259 views

Standard deviation of standard deviation of autocorrelated timeseries

I'm trying to get an estimate of the error in my sample standard deviation (not a statistician at all, hope I'm using correct terminology). The timeseries is normally distributed and follows an AR1 ...
124 views

Error of the variance

I have a collection of $(x,y,z)$ data points. I want to compute the mean, $\mu$, and variance, $\sigma^2$, along each axis, as well as the errors on each. I know that the standard error of the mean ...
67 views

How to calculate standard errors of the sample standard deviation (in excel) [duplicate]

I have data on exchange rates, where I have calculated the mean and the standard deviation of the payoff. I am able to run a regression (payoff regressed on a constant) and get the standard error of ...
I'm looking for an unbiased estimator of the standard deviation $\text{SD}(s)$ of the sample standard deviation $s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \overline{x})^2}$. I have found this ...