# Correlation between interval and ordinal data

I am performing analysis to establish the correlation between personality (self-rated) and competency performance (line manager rated).

The personality domains are the 'Big 5' and have been created through administration of a questionnaire which respondents reply to on a Likert Scale. Each domain has circa 9 items in the scale, from which a composite (mean) score is produced for each domain. I have deliberated long and hard with regards to whether this is classed as interval or ordinal; finally arriving at the former (interval). The data is normally distributed as you would expect.

The performance data is line manager ratings on competency performance - this is clearly ordinal. Oddly, the data here is normally distributed also; this may be due to sample size...more likely it is due to being a 3-point rating scale with a large amount of 'mid-ratings' (2).

How then do I go about performing correlation analysis when I have 1 set of data that are ordinal and the other that are interval?

I appreciate that due to the competency ratings issue noted about, there is unlikely to be any great correlation of significance - but I want to know the appropriate techniques and methods I ought to follow so I can learn and justify the findings.

• Please search this site for correlation interval ordinal. There has been a heap of posts about it already. Feb 6, 2017 at 14:21

The 3-point scale can obviously not be normally distributed. More likely: you have a rather small number of samples $n$ and therefore your test of deviation from normality has not enough power.