Which, upon inserting the data for this particular example, is equivalent to rejecting: 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.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/or unequal sample sizes. Examples for the Unpaired t-test There are many applications for the independent t-test, it is an important test e.g. For the example in hand, the value of the test statistic is: If you want to compare two different groups, whether they come from one sample or two samples, you use an unpaired t-test.
Therefore, it seems reasonable to use the test statistic:įor testing the null hypothesis \(H_0:\mu=\mu_0\) against any of the possible alternative hypotheses \(H_A:\mu \neq \mu_0\), \(H_A:\mu\mu_0\). In earlier versions, TTEST is the formula. Distribution-free two-sample comparisons in the case of heterogeneous variances. In most cases, however, the two standard deviations are. If the two samples have identical standard deviations, the df for the Welch t test will be identical to the df for the standard t test. In recent versions, T.TEST is introduced. Hence, the neglect of the unequal variance t-test illustrated above is a. The df for the unequal variance t test is computed by a complicated formula that takes into account the discrepancy between the two standard deviations. In general, we know that if the data are normally distributed, then:įollows a \(t\)-distribution with \(n-1\) degrees of freedom. Two-sample unequal variance examines whether the variance of means between two sets is unequal. The null hypothesis is \(H_0:\mu=120\), and because there is no specific direction implied, the alternative hypothesis is \(H_A:\mu\ne 120\).
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