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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, Welch's t-test, or unequal variances t-test, is a two-sample location test which is used to test the (null) hypothesis that two populations have equal means. It is named for its creator, Bernard Lewis Welch , and is an adaptation of Student's t -test , [ 1 ] and is more reliable when the two samples have unequal variances and ...
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 s i 2 is the unbiased estimator of the variance of each of the two samples with n i = number of participants in group i (i = 1 or 2). In this case ( s Δ ¯ ) 2 {\displaystyle (s_{\bar {\Delta }})^{2}} is not a pooled variance.
In statistical hypothesis testing, a two-sample test is a test performed on the data of two random samples, each independently obtained from a different given population. The purpose of the test is to determine whether the difference between these two populations is statistically significant .
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 ...
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. The two-pass algorithm computes this variance estimate correctly, but the naïve algorithm returns 29.333333333333332 instead of 30.
The following 57 pages are in this category, out of 57 total. ... Pooled variance; Principle of marginality; R. Random effects model; Repeated measures design;