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Most two-sample t-tests are robust to all but large deviations from the assumptions. [22] For exactness, the t-test and Z-test require normality of the sample means, and the t-test additionally requires that the sample variance follows a scaled χ 2 distribution, and that the sample mean and sample variance be statistically independent ...
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 possibly unequal sample sizes. [ 2 ] [ 3 ] These tests are often referred to as "unpaired" or "independent samples" t -tests, as they are typically applied when the statistical ...
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 table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4] The parameters used are:
The program provides methods that are appropriate for matched and independent t-tests, [2] survival analysis, [5] matched [6] and unmatched [7] [8] studies of dichotomous events, the Mantel-Haenszel test, [9] and linear regression. [3] The program can generate graphs of the relationships between power, sample size and the detectable alternative ...
Lehr's [3] [4] (rough) rule of thumb says that the sample size (for each group) for the common case of a two-sided two-sample t-test with power 80% (=) and significance level = should be: , where is an estimate of the population variance and = the to-be-detected difference in the mean values of both samples.
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.
If there is interest in the marginal probability of obtaining a tail, only the number T out of the 100 flips that produced a tail needs to be recorded. But T can also be used as a test statistic in one of two ways: the exact sampling distribution of T under the null hypothesis is the binomial distribution with parameters 0.5 and 100.