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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 ...
The test [26] deals with the famous Behrens–Fisher problem, i.e., comparing 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. The test is developed as an exact test that allows for unequal sample sizes and unequal ...
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 .
In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.Notionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations, where the test statistic used is the ratio of two sample variances. [1]
Typically, however, the one-way ANOVA is used to test for differences among at least three groups, since the two-group case can be covered by a t-test (Gosset, 1908). When there are only two means to compare, the t-test and the F-test are equivalent; the relation between ANOVA and t is given by F = t 2. An extension of one-way ANOVA is two-way ...
A paired difference test is designed for situations where there is dependence between pairs of measurements (in which case a test designed for comparing two independent samples would not be appropriate). That applies in a within-subjects study design, i.e., in a study where the same set of subjects undergo both of the conditions being compared.
Two-sample tests are appropriate for comparing two samples, typically experimental and control samples from a scientifically controlled experiment. Paired tests are appropriate for comparing two samples where it is impossible to control important variables. Rather than comparing two sets, members are paired between samples so the difference ...
Thus, the null hypothesis of equal variances is rejected and it is concluded that there is a difference between the variances in the population. Levene's test has been used in the past before a comparison of means to inform the decision on whether to use a pooled t-test or the Welch's t-test for two sample tests or analysis of variance or Welch ...