Solved – Alternative to one-sample t-test when data is not normal

I have a variable whose values range between 1 for strongly disagree and 5 strongly agree. I want to test the hypothesis if the respondents (managers) agree on the new implemented procedure. So I want to check if the mean is 3.5, but the data is not normal so I cannot use a one-sample t-test. What can I use in this case?

Since the data is ordinal (not continuous) and does not follow a Normal distribution, I recommend using a Wilcoxon Rank Sum test (aka Mann–Whitney U test) instead of a t-test. Wilcoxon Rank Sum test is a nonparametric approach to the t-test.

You can find more information about the assumptions here:

In R, you can implement the test with the following commands. Example:

> fake_data <- rpois(n = 100, lambda = 5) > wilcox.test(x = fake_data, mu = 3.5)  Wilcoxon signed rank test with continuity correction  data:  fake_data V = 3986, p-value = 4.204e-07 alternative hypothesis: true location is not equal to 3.5  ## reject H_0: true location is equal to 3.5 

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