Background: I'm analyzing correlation between two behavioural types (boldness and aggression). Boldness values are continuous (range: 2 to 1195) and it's unit of measurement is in seconds (latencies). Aggression are ordinal ranks (ranked from 1 to 6, where 1<2<3 and so on..). Higher boldness scores mean the individual is less bold because it takes longer to resume activity. Higher aggression score means the individual is more aggressive. First, I ran a bayesian bivariate regression (MCMCglmm) to partition the variances into among- and within- individual differences, and then checked for covariance between boldness and aggression (the two response variables). I got a significant positive correlation which actually means that boldness and aggression are negatively correlated because increasing boldness values are deemed less bold.
Next, to make the results more intuitive, I reversed the boldness scores so that higher boldness scores indicate higher boldness. Since the boldness range is from 2 to 1195, I subtracted each boldness value from 1197 so that the new variable (lets call it Rboldness) also has a range from 2 to 1195 but in the reverse direction. The variances between boldness and Rboldness is the same, but the mean has changed. The distribution also changed from a right skew (boldness) to left skew (Rboldness) after log transformation.
The Question: The problem is that the strength of the correlation reduces from 0.5 to 0.3 after reversing the boldness scores (Rboldness). Being a purist, I'm not very comfortable in using ordinal ranks as a response variable, so I also analysed the data by collapsing the aggression ranks (1 to 6) into two meaningful and relevant categories (ordinal scores 1-4 coded as 0 and scores 5&6 coded as 1) and ran a binomial bivariate mixed model. The binomial model resulted in a significant correlation coefficient (Figure 1) before reversing boldness scores (r = 0.6) but the correlation becomes insignificant (Figure 2) after reversing the boldness values (Rboldness). Can anyone please inform why the correlation becomes insignificant after reversing one continuous variable? Many thanks in advance!