The sample coefficient alpha is affected by leptokurtic true score distributions, or skewed and/or kurtotic error score distributions. Therfore, I would like to found a alternative to Cronbach's alpha.
Correlations are relatively robust with regard to kurtosis, and the most likely effect is to restrict the range of the correlation so that it cannot reach a value of 1.0. That means that you would be under-estimating your correlations, leading to a conservative estimate for Alpha. So, if you have an Alpha value of .80 or above, that would be a strong indication that there is a high level of shared variance among your indicators.
Matthias Kohl, yes, anything that affects your correlations will affect your alpha. So, if your correlations have problems due to outliers, then so will your alpha.
“A Nonparametric Coefficient of Internal Consistency”, Robert R. Trippi and Robert B. Settle, Multivariate Behavioral Research, Vol. 4, No. 11, (October 1976) pp 419-424
I'm using SPSS, unfortunately it seems like it is not possible to get "robust Cronbach's alpha" as an output. David L Morgan , which program you suggest I use?
I do all my work with SPSS, so I can't help you with robust alpha.
In general, the limitations due to lack or normality will give you lower correlations that you would observe with normal data, so the estimate of alpha will be conservative. In other words, if it reaches a level of .80, it would almost certainly be higher if you had normally distributed variables.