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Welch–Satterthwaite equation

Index Welch–Satterthwaite equation

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, corresponding to the pooled variance. [1]

11 relations: Behrens–Fisher problem, Chi-squared distribution, Degrees of freedom (statistics), Linear combination, Pooled variance, Probability distribution, Propagation of uncertainty, Statistical inference, Statistics, Variance, Welch's t-test.

Behrens–Fisher problem

In statistics, the Behrens–Fisher problem, named after Walter Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples.

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Chi-squared distribution

No description.

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Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

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Linear combination

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).

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Pooled variance

In statistics, pooled variance (also known as combined, composite, or overall variance) 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.

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Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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Propagation of uncertainty

In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them.

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Statistical inference

Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution.

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Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

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Welch's t-test

In statistics, Welch's t-test, or unequal variances t-test, is a two-sample location test which is used to test the hypothesis that two populations have equal means.

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Pooled degree of freedom, Pooled degrees of freedom, Satterthwaite-Welch, Satterthwaite–Welch, Welch-Satterthwaite, Welch-Satterthwaite equation, Welch–Satterthwaite.

References

[1] https://en.wikipedia.org/wiki/Welch–Satterthwaite_equation

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