How to test relationship between Likert scale and continuous variable

Question

I wanted to analyze Likert data from a survey on customer perception based on various attributes (strongly disagree, disagree, neither, agree, strongly disagree). I wanted to show if there is some association or relationship with continuous variables (ex: attrition rate). Hypothesis is that customers rating highly on several attributes have better metrics (ex: higher engagement rate, lower turnover rate, etc). Any help on test, analysis approach, visualisation would be appreciated.

Answer 1

If this is your first look at the dataset, I'd suggest keeping it simple to start:

1. Think of your Likert scale as 5 data-bins, and compute the individual mean (and maybe standard deviation) for each continuous variable of interest, for each bin.

2. Then, look for the following properties of the result:

   1. Is there evidence of monotonicity between the Likert values and the averages in the bins, i.e. as you move up the Likert scale do the averages of your metrics of interest increase, or do they hop around randomly? (Don't get hung up on results being linear here. You're only looking to see, as we move up the scale, does the average value of variable X also move up [or down]).

   2. Is there evidence of a big change anywhere in the middle the scale, e.g. are the 3's closer to 4's in their average values, or closer to the 2's?

   3. Is there evidence of flattening, at the ends of the scale, e.g. are the 4's very different from the 5's or about the same? Same question applies to the 1's and 2's.

From here, you can start to determine whether further analysis should concentrate on the differences between the top and bottom of the scale, e.g. between the agrees and the disagrees, or on the differences at the ends, e.g. between the agrees and the strongly agrees, etc.