Linked Questions

1
vote
0answers
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% ...
229
votes
12answers
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 ...
58
votes
3answers
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 ...
27
votes
1answer
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? $$SE = \frac{SD}{\sqrt{N}}$$
11
votes
3answers
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 ...
9
votes
2answers
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 ...
1
vote
1answer
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 ...
0
votes
1answer
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
0
votes
0answers
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 ...
1
vote
0answers
55 views

Relationship between measurement precision and the precision of the mean of repeated measurements [closed]

Measurement precision can be improved by measuring the same quantity multiple times and taking the average. In other words, the average of several measurements of the same thing is more likely to be ...
2
votes
0answers
35 views

Unbiased Estimator of the Standard Deviation of the Sample Standard Deviation

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 ...