I am creating an indicator for social development which includes variables of health, education and economy.
Since I have many variables, I decided to remove some of them based on dominion expertise and then check for collinearity (with a correlation matrix). In that way, I checked that the variables used were not redundant and thus do not provide more weight to a certain dimension. There is no significant number of variables with Pearson's coefficient above 0.8, which I praise as 'good'.
I have also run the Cronbach's alpha and been provided with an alpha=0.9 for the variables used. According to Nunnally's cut-off that is an acceptable Cronbach's alpha. I am not sure about the meaning of this, as I see it very similar to a Pearson's coefficient - and wonder whether both results might be contradicting-.