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In general, with a normally-distributed sample mean, Ẋ, and with a known value for the standard deviation, σ, a 100(1-α)% confidence interval for the true μ is formed by taking Ẋ ± e, with e = z 1-α/2 (σ/n 1/2), where z 1-α/2 is the 100(1-α/2)% cumulative value of the standard normal curve, and n is the number of data values in that ...
These values are used to calculate an E value for the estimate and a standard deviation (SD) as L-estimators, where: E = (a + 4m + b) / 6 SD = (b − a) / 6. E is a weighted average which takes into account both the most optimistic and most pessimistic estimates provided. SD measures the variability or uncertainty in the estimate.
If one makes the parametric assumption that the underlying distribution is a normal distribution, and has a sample set {X 1, ..., X n}, then confidence intervals and credible intervals may be used to estimate the population mean μ and population standard deviation σ of the underlying population, while prediction intervals may be used to estimate the value of the next sample variable, X n+1.
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.
However, the sample standard deviation is not unbiased for the population standard deviation – see unbiased estimation of standard deviation. Further, for other distributions the sample mean and sample variance are not in general MVUEs – for a uniform distribution with unknown upper and lower bounds, the mid-range is the MVUE for the ...
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.
The table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4] The parameters used are:
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. [1] For example, the sample mean is a commonly used estimator of the population mean. There are point and interval ...