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The pooled variance is an estimate of the fixed common variance underlying various populations that have different means. We are given a set of sample variances s i 2 {\displaystyle s_{i}^{2}} , where the populations are indexed i = 1 , … , m {\displaystyle i=1,\ldots ,m} ,
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.
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 .
If the sum of squares were not normalized, its value would always be larger for the sample of 100 people than for the sample of 20 people. To scale the sum of squares, we divide it by the degrees of freedom, i.e., calculate the sum of squares per degree of freedom, or variance. Standard deviation, in turn, is the square root of the variance.
M1 and M2 can be interpreted in terms of variance of a multinomial distribution (Swanson 1976) (there called an "expanded binomial model"). M1 is the variance of the multinomial distribution and M2 is the ratio of the variance of the multinomial distribution to the variance of a binomial distribution.
Panel (data) analysis is a statistical method, widely used in social science, epidemiology, and econometrics to analyze two-dimensional (typically cross sectional and longitudinal) panel data. [1] The data are usually collected over time and over the same individuals and then a regression is run over these two dimensions.