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The "68–95–99.7 rule" is often used to quickly get a rough probability estimate of something, given its standard deviation, if the population is assumed to be normal. It is also used as a simple test for outliers if the population is assumed normal, and as a normality test if the population is potentially not normal.
In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the calculation equals the true value.
As explained above, while s 2 is an unbiased estimator for the population variance, s is still a biased estimator for the population standard deviation, though markedly less biased than the uncorrected sample standard deviation. This estimator is commonly used and generally known simply as the "sample standard deviation".
A two-tailed test applied to the normal distribution. A one-tailed test, showing the p-value as the size of one tail. In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test ...
For instance, if estimating the effect of a drug on blood pressure with a 95% confidence interval that is six units wide, and the known standard deviation of blood pressure in the population is 15, the required sample size would be =, which would be rounded up to 97, since sample sizes must be integers and must meet or exceed the calculated ...
Statistical analyses involving means, weighted means, and regression coefficients all lead to statistics having this form. Quite often, textbook problems will treat the population standard deviation as if it were known and thereby avoid the need to use the Student's t distribution.
where ¯ is the sample mean, s is the sample standard deviation and n is the sample size. The degrees of freedom used in this test are n − 1. Although the parent population does not need to be normally distributed, the distribution of the population of sample means ¯ is assumed to be normal.
For a large sample from a normal distribution, 2.22Q n is approximately unbiased for the population standard deviation. For small or moderate samples, the expected value of Q n under a normal distribution depends markedly on the sample size, so finite-sample correction factors (obtained from a table or from simulations) are used to calibrate ...