@ Denise Dal Lago ,

Apply Kearl Pearson's correlation and then apply t test for testing the significance of calculated value of correlation coefficient to be obtained.

Thanks Dhritikesh Chakrabarty .

I was considering to run a non-parametric correlation given the biased distribution of the data and the nature of the variable (ordinal). In any case, would this take into consideration the floor effect?

Thanks

This doesn't sound totally trivial, but I cannot recommend to use Pearson correlation ( as Dhritikesh Chakrabarty did) , since this may already be a bad choice with ordinal variables without zero inflation.

Ordinal variables do not need to follow a distribtion, therefore how do you come to the conclusion that the data are zero inflated and not only the true amount of zeros? Zero inflated models assume two different data generating processes and not only one.

Nevertheless, the easiest way would be to treat the zeros as part of one data generating process and you could use an ordinal correlation. But the typical ones like Spearman or Kendall's tau may be problematic with a lot of ties.

Another option would be polychoric correlation, but here you assume that the underlying data generating process for the ordinal variable is a latent normally distributed variable. In psychology this is quite reasonable (my field), but this is something you have to decide.

Maybe my choice would be an ordered logistic regression, to predict your ordinal variable with your metric variable.

I have have heard about zero inflated logistic and zero inflated probit regression (uses a normal cdf instead of the logistic function), but havent seen it and I do not know if there are any packages (I am using R) for this.

Many thanks Rainer Duesing.

I'm a bit unsure about running a regression since I don't have predictors based on my theory. Therefore, I plan to start with a correlational analysis. I appreciate your suggestion about the polychoric correlation. However, since I have one ordinal and one continuous variable, would it be more appropriate to run a polyserial correlation instead?

1) Yes you are completely right! A polyserial instead of a polychoric would be appropriate, if the underlying distribution assumptions are plausible. I was wrong, since I typically work with ordinal variables only. Sorry, and thanks for correcting!

2) In my opinion, in a 2 variable case, it does not matter if you chose a regression or correlation approach. It is about how much one variable changes when the other changes. The choice of DV and IV is quite arbitrary. For example, in the bivariate OLS regression context, the standardized regression coeffcient matches exactly the Pearson correlation (cave: confidence intervals differ!). Therefore, I would chose a method that helps to understand the data and that's why I prefer regression over correlation. But this might only a subjective view.

Many thanks!! This has been extremely helpful!