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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 ...
From the t-test, the difference between the group means is 6-2=4. From the regression, the slope is also 4 indicating that a 1-unit change in drug dose (from 0 to 1) gives a 4-unit change in mean word recall (from 2 to 6). The t-test p-value for the difference in means, and the regression p-value for the slope, are both 0.00805. The methods ...
Test name Scaling Assumptions Data Samples Exact Special case of Application conditions One sample t-test: interval: normal: univariate: 1: No [8]: Location test: Unpaired t-test: interval
To design a test, Šidák correction may be applied, as in the case of finitely many t-test. However, when N ( n ) → ∞ as n → ∞ {\displaystyle N(n)\rightarrow \infty {\text{ as }}n\rightarrow \infty } , the Šidák correction for t-test may not achieve the level we want, that is, the true level of the test may not converges to the ...
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.
A follow-up paper showed that the classic paired t-test is a central Behrens–Fisher problem with a non-zero population correlation coefficient and derived its corresponding probability density function by solving its associated non-central Behrens–Fisher problem with a nonzero population correlation coefficient. [14]
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 .
The Šidák correction is derived by assuming that the individual tests are independent. Let the significance threshold for each test be α 1 {\displaystyle \alpha _{1}} ; then the probability that at least one of the tests is significant under this threshold is (1 - the probability that none of them are significant).