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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 ...
There are some alternatives to conventional one-way analysis of variance, e.g.: Welch's heteroscedastic F test, Welch's heteroscedastic F test with trimmed means and Winsorized variances, Brown-Forsythe test, Alexander-Govern test, James second order test and Kruskal-Wallis test, available in onewaytests R
If the sample sizes in the two groups being compared are equal, Student's original t-test is highly robust to the presence of unequal variances. [20] Welch's t-test is insensitive to equality of the variances regardless of whether the sample sizes are similar.
The simplest application of this equation is in performing Welch's t-test. An improved equation was derived to reduce underestimating the effective degrees of freedom if the pooled sample variances have small degrees of freedom. Examples are jackknife and imputation-based variance estimates. [3]
He showed that under the usual departures (positive skew, unequal variances) "the F-test is conservative", and so it is less likely than it should be to find that a variable is significant. However, as either the sample size or the number of cells increases, "the power curves seem to converge to that based on the normal distribution".
In statistical quality control, the ¯ and s chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. [1] This is connected to traditional statistical quality control (SQC) and statistical process control (SPC).
The common example scenario for when a paired difference test is appropriate is when a single set of test subjects has something applied to them and the test is intended to check for an effect. Z-tests are appropriate for comparing means under stringent conditions regarding normality and a known standard deviation.
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 ...