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This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
Normally, however, only a subset is available, and the variance calculated from this is called the sample variance. The variance calculated from a sample is considered an estimate of the full population variance. There are multiple ways to calculate an estimate of the population variance, as discussed in the section below.
In statistics, Scheffé's method, named after American statistician Henry Scheffé, is a method for adjusting significance levels in a linear regression analysis to account for multiple comparisons. It is particularly useful in analysis of variance (a special case of regression analysis), and in constructing simultaneous confidence bands for ...
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA compares the amount of variation between the group means to the amount of variation within each group.
For two jointly distributed real-valued random variables and with finite second moments, the covariance is defined as the expected value (or mean) of the product of their deviations from their individual expected values: [3] [4]: 119
In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing.It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood.
Because of the reciprocity of estimator-variance and Fisher information, minimizing the variance corresponds to maximizing the information. When the linear (or linearized) statistical model has several parameters, the mean of the parameter estimator is a vector and its variance is a matrix. The inverse of the variance matrix is called the ...