Unfortunately, it’s the first time that I learnt that Likert scale cannot be used together with t-test.
According to my favorite Stat Wiki by Prof. Koji Yatani,
Roughly speaking, there are two cases in which you want to use non-parametric test:
- Ordinal data: If your data are ordinal (like the results from Likert-scale questions), you should use non-parametric tests.
- Non-normal data: You cannot assume the normality of data.
It seems kind of rare to see non-parametric test used in HCI papers.
Fortunately, many of the parametric tests are fairly robust against the non-normality, so you can try parametric tests unless you think you really need to do non-parametric tests.
There are also some ways (e.g., data transformation) to allow you to use parametric test with your non-normal data.
You can find more details about statistical tests for checking the normality and data transformation in a separate page.
Here are a list of options:
Data transformation is a powerful tool when the data don’t look like forming a normal distribution
One common test for checking the normality is Shapiro-Wilk test.
The null hypothesis of Shapiro-Wilk test is that the samples are taken from a normal distribution. So, if the p value is less than 0.05, you reject the hypothesis, and thinks that the samples are not taken from a normal distribution.
Another test you can use for checking the normality is Kolmogorov-Smirnov test. This test basically checks whether two datasets are taken from the same distribution, but it can be used for comparing one dataset against an ideal distribution (int this case, a normal distribution).