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Are t tests robust to non-normality?
the t-test is robust against non-normality; this test is in doubt only when there can be serious outliers (long-tailed distributions – note the finite variance assumption); or when sample sizes are small and distributions are far from normal. 10 / 20 Page 20 . . . exercise . . .
Is a paired t-test robust to violations of normality?
The paired samples and one- sample t-tests are perfectly robust to violations of normality at infinitely large sample sizes (Bradley, 1980 a,b; Scheffé, 1959) but at some unknown sample size this robustness begins to break down if the underlying population distribution is not precisely normal.
Is two-sample t test robust?
In the literature, one finds evidence that the two-sample t-test is robust with respect to departures from normality, and departures from homogeneity of variance (at least when sample sizes are equal or nearly equal).
How is the t test used in statistics?
The t-test and robustness to non-normality September 28, 2013 by Jonathan Bartlett The t-test is one of the most commonly used tests in statistics. The two-sample t-test allows us to test the null hypothesis that the population means of two groups are equal, based on samples from each of the two groups.
How does the Student t test compare two data sets?
Comparing the means of two data sets using the student t -test The Student t -test compares the mean of a data set (sample) of a new or modified assay to the sample mean of a reference assay. In the unpaired t- test the operator assumes that population distributions are normal (Gaussian), the SDs are equal, and the assays are independent.
Is the t-test valid when x does not follow a normal distribution?
In fact, as the sample size in the two groups gets large, the t-test is valid (i.e. the type 1 error rate is controlled at 5%) even when X doesn’t follow a normal distribution. I think the most direct route to seeing why this is so, is to recall that the t-test is based on the two groups means and .
What happens if the t-test assumes normality?
Of course if X isn’t normally distributed, even if the type 1 error rate for the t-test assuming normality is close to 5%, the test will not be optimally powerful. That is, there will exist alternative tests of the null hypothesis which have greater power to detect alternative hypotheses.