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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.
Here, = is the degrees of freedom associated with the i-th variance estimate. The statistic is approximately from the t -distribution since we have an approximation of the chi-square distribution . This approximation is better done when both N 1 {\displaystyle N_{1}} and N 2 {\displaystyle N_{2}} are larger than 5.
where = = and = is the pooled estimate for the variance. The test statistic has approximately a χ k − 1 2 {\displaystyle \chi _{k-1}^{2}} distribution. Thus, the null hypothesis is rejected if χ 2 > χ k − 1 , α 2 {\displaystyle \chi ^{2}>\chi _{k-1,\alpha }^{2}} (where χ k − 1 , α 2 {\displaystyle \chi _{k-1,\alpha }^{2}} is the ...
The power of this test is similar to that of Boschloo's test in many scenarios. In some cases, the -Unpooled test has greater power, with differences ranging from 1 to 5 percentage points. However, in some other cases, Boschloo's test has noticeably greater power, with differences up to 68 percentage points.
Pooled OLS [clarification needed] can be used to derive unbiased and consistent estimates of parameters even when time constant attributes are present, but random effects will be more efficient. Random effects model is a feasible generalised least squares technique which is asymptotically more efficient than Pooled OLS when time constant ...
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.
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 .