I recently received this question:
I have scale which I want to run Chronbach’s alpha on. One response category for all items is ‘not applicable’. I want to run Chronbach’s alpha requiring that at least 50% of the items must be answered for the scale to be defined. Where this is the case then I want all missing values on that scale replaced by the average of the non-missing items on that scale. Is this reasonable? How would I do this in SPSS?
In RELIABILITY, the SPSS command for running a Cronbach’s alpha, the only options for Missing Data are to include or exclude User-Defined missing data. And by exclude, they mean listwise deletion.
So the only way to include cases with more than 50% observed data would be to impute them in a separate step before you run the reliability analysis.
And while you could impute the mean, I highly recommend you do not. While mean imputation maintains the mean of each separate variable, it does not maintain the relationships among variables.
In fact, with a lot of imputed values all right at the mean, the correlations with other variables become much lower. And since scale reliability entirely depends on correlations among the values in your scale, you will severely underestimate your scale reliability if you have more than a few cases with missing data.
Since you’re doing a Cronbach’s alpha, you could do a single imputation that is based on other variables–a regression or an EM imputaton. This kind of imputation will preserve the relationship among the variables on your scale without inflating them.
The general downside of single imputation is that SPSS will think that the imputed values were true, observed values. It will therefore underestimate standard errors.
But Cronbach’s alpha doesn’t have a standard error and is not involved in a hypothesis test. So for this purpose, the downside isn’t a big deal.
If you were doing a hypothesis test or doing any statistical analysis based on p-values, the best option, is to conduct a Multiple Imputation on the missing values. It’s often the only good one if you have more than about 10% of data missing (that’s 10% of all values, not of cases)
Both the single and multiple imputation techniques are available in SPSS Missing Values Analysis module. Multiple imputation was added in version 17, but single imputation is available in earlier versions.