Is paired t-test robust to violation of 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 . . .
What if normality is violated in t-test?
If the assumption of normality is violated, or outliers are present, then the t test may not be the most powerful test available, and this could mean the difference between detecting a true difference or not. A nonparametric test or employing a transformation may result in a more powerful test.
Is there an alternative to the paired sample t-test?
If any of these assumptions are violated, a different test should be used. An alternative to the paired sample t-test is the Wilcoxon signed-rank Test . The data used in this example can be found on our GitHub page. The data set is fictitious and contains blood pressure readings before and after an intervention.
How can you tell if your data violate paired t test assumptions?
Outliers may appear as anomalous points in a graph of the paired differences against their mean. A boxplot or normal probability plot of the paired differences can also reveal lack of symmetry and suspected outliers. If the number of paired differences is small, it may be difficult to detect assumption violations.
Is the two sample t-test assumes normality?
So, as constructed, the two-sample t-test assumes normality of the variable X in the two groups. On the face of it then, we would worry if, upon inspection of our data, say using histograms, we were to find that our data looked non-normal.
When to reject null hypothesis in paired sample t test?
If the p-value is less than what is tested at, most commonly 0.05, one can reject the null hypothesis. In order for the paired sample t-test results to be trusted, the following assumptions need to be met: