the more correct way to approach reliability for ordinal data from a factor analytic point of view (like Cronbach's alpha does) is by using the matrix of tetrachoric or polychoric correlations to calculate alpha.
for all your psychometric needs! https://psychometroscar.wordpress.com/
I think I came up with a better way to measure internal consistency reliability based on L-comoment theory i.e.the L-correlation, which is a hybrid between the Pearson and Spearmen correlations......see here:
Advertise on Talk Stats