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The t-test p-value for the difference in means, and the regression p-value for the slope, are both 0.00805. The methods give identical results. This example shows that, for the special case of a simple linear regression where there is a single x-variable that has values 0 and 1, the t-test gives the same results as the linear regression. The ...
The problem of multiple comparisons received increased attention in the 1950s with the work of statisticians such as Tukey and Scheffé. Over the ensuing decades, many procedures were developed to address the problem. In 1996, the first international conference on multiple comparison procedures took place in Tel Aviv. [3]
In addition to causing numerical problems, imperfect collinearity makes precise estimation of variables difficult. In other words, highly correlated variables lead to poor estimates and large standard errors. As an example, say that we notice Alice wears her boots whenever it is raining and that there are only puddles when it rains.
The Student's t distribution plays a role in a number of widely used statistical analyses, including Student's t test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis.
With respect to FWER control, the Bonferroni correction can be conservative if there are a large number of tests and/or the test statistics are positively correlated. [9] Multiple-testing corrections, including the Bonferroni procedure, increase the probability of Type II errors when null hypotheses are false, i.e., they reduce statistical power.
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 ...
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.
In statistics, particularly in hypothesis testing, the Hotelling's T-squared distribution (T 2), proposed by Harold Hotelling, [1] is a multivariate probability distribution that is tightly related to the F-distribution and is most notable for arising as the distribution of a set of sample statistics that are natural generalizations of the statistics underlying the Student's t-distribution.