# How to find out if there is any correlation between a yes/no question and Likert scale data?

I have used a survey to research willingness to pay regarding virtual goods in videogames. For this, I have asked the respondents a couple of questions via Likert scale, to get their opinions on certain statements. I then asked them if they had ever purchased virtual goods before.

In this case, I want to see if satisfaction with the game leads to a higher likeliness of purchasing virtual goods. How would I go about testing this statistically? My first idea was to convert my Likert data to numerical values, E. G. from strongly disagree = 1 to strongly agree = 5. However I can't seem to find which type of test I should use to then see if there is any correlation between a higher satisfaction value and buying virtual goods.

You could use logistic regression. If you represent your likert, that is ordinal, predictor with numerical codes $$1,2, \dotsc$$, then use also a quadratic term to represent possible nonlinearity in the effects, or maybe even with a spline.