Solved – scale score, yes/no question, t-test

I have scores from a likert scale questionnaire and have summed them up into one variable. I also have a yes/no question (the same participants that answered the questionnaire). Now I want to perform a t-test. What kind of t-test do I perform? Do I have to calculate the mean for each participant for the likert scale (compute variable thingy…) before the t-test and use that new variable in the t-test (as in, not the summed variable)? Do I have to do anything to the yes/no variable before performing the t-test? The yes/no variable would be the group variable.

Statistically challenged

Your research set-up:

Independent variable: Yes / No

Dependent variable: mean of the Likert scale

My answer:

Then you would use a two sample t-test to compare them.

My concern:

Now what is the far more important aspect of your question:

The Likert scale produces ordinal data that do not satisfy the requirement of equal spacing that would be required to calculate a meaningful mean. Therefore, you may not use the mean. Instead you should use the mode or the median. A test capable of comparing those is not the t test but the Wilcoxon rank sum test. In the social sciences it is common practice to use the mean but it is fundamentally wrong. For very large data sets and a very fine Likert scale (e.g. 0-15) you sort of may use a mean with caution. But it is not the best option. There are millions of great explanations of the Wilcoxon tests, so it might be easy to get an idea of how it works.

I know this is not what you wanted to hear, but it is very important 🙂

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