# How can I test if there is a correlation between a score and a likert scale?

I'm having difficulty finding out what I can do with my data set. It comes from a french reading test that have 30 multiple choice questions.

For each of these questions:

1. I have the facility value for the items on the test, wich is the percentage of right answers to the questions.
2. I have the perception of the difficulty by the test takers, on a likert scale (Really easy, Easy, Medium, Hard, Really Hard).

Here is an example of what my data looks like: I want to know if there is a correlation between the facility value and the perceived facility of the items... In other words, if the easy questions are perceived as easy ones. I don't really know what to do with the data... Should I convert the scores of the likert scale? Should I do a "mean" for each item?

I recommend calculating Kendall's $\tau$. This effect size estimate is appropriate for ordinal data and permits nonparametric hypothesis testing if you're so inclined. No conversion of your data should be necessary if your Likert ratings are already stored in an ordered fashion. You can convert them to 1–5 if not and correlate these values with your percentage variable.
In , the command is cor(x,y,method='kendall') where x and y are your two variables. To perform a hypothesis test, just change cor to cor.test. I prefer to interpret $\tau$ on the scale of Pearson's r, as I am more familiar with that scale and expect most audiences to be as well. To convert $\tau$ (which is always smaller) to r, use $r = \sin\big(\tau\cdot\frac \pi 2 \big)$ as I mentioned in another answer.