Search results
Results From The WOW.Com Content Network
In the t-test comparing the means of two independent samples, the following assumptions should be met: The means of the two populations being compared should follow normal distributions . Under weak assumptions, this follows in large samples from the central limit theorem , even when the distribution of observations in each group is non-normal.
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 ...
One of the application of Student's t-test is to test the location of one sequence of independent and identically distributed random variables. If we want to test the locations of multiple sequences of such variables, Šidák correction should be applied in order to calibrate the level of the Student's t-test. Moreover, if we want to test the ...
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 analysis of variance that examines the influence of two different categorical independent variables on one dependent variable.
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. [56] When there are only two means to compare, the t-test and the ANOVA F-test are equivalent; the relation between ANOVA and t is given by F = t 2.
If the errors do not follow a multivariate normal distribution, generalized linear models may be used to relax assumptions about Y and U. The general linear model incorporates a number of different statistical models: ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The general linear model is a generalization of ...
For example, the test statistic might follow a Student's t distribution with known degrees of freedom, or a normal distribution with known mean and variance. Select a significance level (α), the maximum acceptable false positive rate. Common values are 5% and 1%. Compute from the observations the observed value t obs of the test statistic T.
Under the null hypothesis of no difference between population means (and assuming that standard ANOVA regularity assumptions are satisfied) the sums of squares have scaled chi-squared distributions, with the corresponding degrees of freedom. The F-test statistic is the ratio, after scaling by the degrees of freedom.