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I gave a questionary to 190 people to answer some questions. I want to check the correlation between the annual salary and how satisfy people are. So my two variables are annual salary and satisfaction. The data from annual salary are grouped into 6 categories: those without annual salary 0, 1-10,000 (10), 10,000-25,000 (25), 25,000-50,000 (50) , 50,000-75,000 (75), 75,000-100,000 (100) and above 100 (200). The satisfaction takes values form 0 to 10 (10 is very satisfied). My advisor suggested to do a regression but I found the $R^2$ = 0.01. I also tried to make a scatter plot but the data look strange.

Could you please suggest how to find the correlation between these two variables?

I attach an example of my excel spreadsheet with the data.

enter image description here

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    $\begingroup$ Please type your question as text, do not just post a photograph or screenshot (see here). In this case, we refer you to post data in a computer-readable format, facilitating for people to use your data to exemplify their answers! $\endgroup$
    – kjetil b halvorsen ♦
    Commented Dec 6, 2020 at 0:50
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    $\begingroup$ You seem to have ordinal data, not categorical. See stats.stackexchange.com/questions/289066/… $\endgroup$
    – kjetil b halvorsen ♦
    Commented Dec 6, 2020 at 0:52
  • $\begingroup$ Why is it such a problem that you wound up with $R^2=0.01?$ This tells me that salary is a very weak predictor of satisfaction at work. I could believe that big earners are stressed and unhappy, not just thrilled to be making a lot of money (and the reverse for modest earners). I think your method of treating satisfaction as a numerical variable (instead of ordinal) is a mistake, but nothing says that salary has to be a good predictor of satisfaction. $\endgroup$
    – Dave
    Commented Dec 6, 2020 at 1:00
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    $\begingroup$ Consider searching the site & reading some of the existing threads. How to assess the correlation between categorical variables has been covered several times. $\endgroup$
    – gung - Reinstate Monica
    Commented Dec 6, 2020 at 1:14

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For categorical variables, you won't get a correlation coefficient per se, but there is a statistical test that will allow you to see if the two variables are independent, and in this case, you should use: Chi-squared test of independence.

To get out of a value for how strong the association between the two variables is, you can use a Cramér's V

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