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Propagation of uncertainty. In statistics, propagation of uncertainty (or propagation of error) is the effect of variables ' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement ...
Unbiased estimation of standard deviation. 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 ...
The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.
It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic:
Degrees of freedom (statistics) In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. [1] Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a ...
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Reduced chi-squared statistic. In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating [1] and variance of unit weight in the context of weighted least squares. [2][3] Its square root is called regression standard error, [4 ...