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% ...
69k views

### 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 ...
52k views

### 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? $$SE = \frac{SD}{\sqrt{N}}$$
4k views

### 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 ...
2k views

### 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 ...
2k views

### 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 ...