19 Alternatives to the t-Test
Sometimes we cannot run a t-test because our data do not meet the assumptions.
Alternative to Independent Samples t-Test – Mann-Whitney U
If you have a small sample and you are concerned about meeting the normality assumption, you can use the Mann-Whitney U test. This is the non-parametric equivalent to the independent samples t-test. I will not go into specifics, but the idea behind the Mann-Whitney U test is that you take all the values (regardless of group) and rank them. You then sum the ranks across groups and calculate your U statistic and p-value. You interpret the p-value like you normally would, but there are differences in how we report the results because this statistic is based on the median not the mean.
It is very easy to conduct this test in jamovi – when you select the independent samples t-test, simply check the box to run the Mann-Whitney U test. You will interpret the p-value in the same way, but note that we report the median, not the mean. With the harpo data, the results look like this:
We would report the results as follows: using the Mann-Whitney U test, there was a statistically significant difference in grades between Anastasia’s students (Mdn = 76, n = 15) and Bernadette’s students (Mdn = 69, n = 18), U = 79.50, p = .046, = .41.
Alternative to Dependent Samples t-Test – Wilcoxon Rank
If we have dependent samples and fail to meet the assumption of normality, especially when we are concerned about small sample sizes, then we perform the Wilcoxon rank test in stead. This is one of the options available after selecting to do Paired Samples t-test in jamovi. If we run this test with the Chico data we get the following output:
We could report the results as follows: using Wilcoxon rank test, students’ test scores were significantly higher at the second test (Mdn = 59.70) than at the first test (Mdn = 57.70), W = 2.00, p < .001, = .98.
The note about tied values is not necessary to discuss. It is just telling us one participant had identical values for both test1 and test2 (student15). You can check this yourself in the dataset.
