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In statistics, pooled variance (also known as combined variance, composite variance, or overall variance, and written ) is a method for estimating variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same. The numerical estimate resulting from ...
In statistics and uncertainty analysis, the Welch–Satterthwaite equation is used to calculate an approximation to the effective degrees of freedom of a linear combination of independent sample variances, also known as the pooled degrees of freedom, [1] [2] corresponding to the pooled variance.
Student's t-test assumes that the sample means being compared for two populations are normally distributed, and that the populations have equal variances.Welch's t-test is designed for unequal population variances, but the assumption of normality is maintained. [1]
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.
where ¯ is the sample mean and ^ is the unbiased sample variance. Since the right hand side of the second equality exactly matches the characterization of a noncentral t -distribution as described above, T has a noncentral t -distribution with n −1 degrees of freedom and noncentrality parameter n θ / σ {\displaystyle {\sqrt {n}}\theta ...
A pooled analysis is a statistical technique for combining the results of multiple epidemiological studies. It is one of three types of literature reviews frequently used in epidemiology, along with meta-analysis and traditional narrative reviews .
However, the sample size required for the sample means to converge to normality depends on the skewness of the distribution of the original data. The sample can vary from 30 to 100 or higher values depending on the skewness. [23] [24] F For non-normal data, the distribution of the sample variance may deviate substantially from a χ 2 distribution.
The parametric equivalent of the Kruskal–Wallis test is the one-way analysis of variance (ANOVA). A significant Kruskal–Wallis test indicates that at least one sample stochastically dominates one other sample. The test does not identify where this stochastic dominance occurs or for how many pairs of groups stochastic dominance obtains.