I have an environmental science issue where I'm trying to see if there is a correlation between some qualitative and quantitative data. (Hopefully I'm posting this in the right place).

Basically at my work we have ecological contractors who assess whether particular natural areas have high, medium or low vulnerability this is the qualitative data.

The quantitative data consists of looking at the shape each site based on a formula which compares the shape of each site to the reference shape of a circle which is the most compact shape and thus in theory is least vulnerable. This is the Diversity index. If a site has a diversity index of 1.3 this means that the shape of the site has 30% more perimeter than a circle of the same area.

I want to see if there is a positive correlation or not between the contractors subjective judgment and the diversity index. However, I don't think I can simply look at pearson's correlation coefficient or spearman's rank coefficient but I'm not sure? (I have attached a spreadsheet with more details).

What I have done is to give a score of 1 to all the sites which were assessed as being low vulnerability. 2 to all sites which were assessed as medium vulnerability and a score of 3 to all sites which were assessed by the contractors as being high vulnerability sites.

Out of the 156 sites in the data set 100 sites were low vulnerability, 49 medium and 7 high vulnerability.

Therefore, I ranked all the sites by their diversity index from smallest (least vulnerable quantitatively) to largest (most vulnerable quantitatively). Next I gave the top 100 smallest a score a score of 1 (this is the column "Diversity Index standardized"), the next 49 I gave a score of 2 and 7 sites with the largest diversity index I gave a score of 3.

If I only knew the Diversity index but not the vulnerability score and I used the Diversity index to guess what the vulnerability score was. On average I can expect to get the right answer 33.33% of the time by chance.

If I get it right more than 33.33% of the time then there is likely to be a positive correlation?

I would have guessed 52% of the time correct (see spreadsheet). Is there a correlation here and how do I test if there is or not?

Thanks