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In statistics, the Behrens–Fisher problem, named after Walter-Ulrich 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.
However, the studentized range distribution used to determine the level of significance of the differences considered in Tukey's test has vastly broader application: It is useful for researchers who have searched their collected data for remarkable differences between groups, but then cannot validly determine how significant their discovered ...
To use a finite difference method to approximate the solution to a problem, one must first discretize the problem's domain. This is usually done by dividing the domain into a uniform grid (see image). This means that finite-difference methods produce sets of discrete numerical approximations to the derivative, often in a "time-stepping" manner.
A paired difference test, better known as a paired comparison, is a type of location test that is used when comparing two sets of paired measurements to assess whether their population means differ. A paired difference test is designed for situations where there is dependence between pairs of measurements (in which case a test designed for ...
Fieller showed that if a and b are (possibly correlated) means of two samples with expectations and , and variances and and covariance , and if ,, are all known, then a (1 − α) confidence interval (m L, m U) for / is given by
In mathematics, the solution set of a system of equations or inequality is the set of all its solutions, that is the values that satisfy all equations and inequalities. [1] Also, the solution set or the truth set of a statement or a predicate is the set of all values that satisfy it. If there is no solution, the solution set is the empty set. [2]
The example discussed by Duncan in his 1955 paper is of a comparison of many means (i.e. 100), when one is interested only in two-mean and three-mean comparisons, and general p-mean comparisons (deciding whether there is some difference between p-means) are of no special interest (if p is 15 or more for example).
In an analogous way, one can obtain finite difference approximations to higher order derivatives and differential operators. For example, by using the above central difference formula for f ′(x + h / 2 ) and f ′(x − h / 2 ) and applying a central difference formula for the derivative of f ′ at x, we obtain the central difference approximation of the second derivative of f: