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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.
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.
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 .
Furthermore, the power of Welch's t-test comes close to that of Student's t-test, even when the population variances are equal and sample sizes are balanced. [2] Welch's t-test can be generalized to more than 2-samples, [7] which is more robust than one-way analysis of variance (ANOVA).
Based on this sample, the estimated population mean is 10, and the unbiased estimate of population variance is 30. Both the naïve algorithm and two-pass algorithm compute these values correctly. Next consider the sample ( 10 8 + 4 , 10 8 + 7 , 10 8 + 13 , 10 8 + 16 ), which gives rise to the same estimated variance as the first sample.
In statistics, one-way analysis of variance (or one-way ANOVA) is a technique to compare whether two or more samples' means are significantly different (using the F distribution). This analysis of variance technique requires a numeric response variable "Y" and a single explanatory variable "X", hence "one-way". [1] The ANOVA tests the null ...
Since it is a nonparametric method, the Kruskal–Wallis test does not assume a normal distribution of the residuals, unlike the analogous one-way analysis of variance. If the researcher can make the assumptions of an identically shaped and scaled distribution for all groups, except for any difference in medians, then the null hypothesis is ...
In estimating the population variance from a sample when the population mean is unknown, the uncorrected sample variance is the mean of the squares of deviations of sample values from the sample mean (i.e., using a multiplicative factor 1/n). In this case, the sample variance is a biased estimator of the population variance. Multiplying the ...