Now I'm reading Applied Missing Data Analysis by Craig K. Enders ,and I try to understand why we do Little's MCAR test ? .
On page 17 he wrote the following :
In truth, testing whether an entire collection of variables is consistent with MCAR is probably not that useful because some of the variables in a data set are likely to be missing in a systematic fashion. Furthermore finding evidence for or against MCAR does not change the recommendation to use maximum likelihood or multiple imputation. However, identifying individual variables that are not MCAR is potentially useful because there may be a relationship between these variables and the probability of missingness.
From this citation it is clear for me why we test MCAR by Univariate T-Test .
The confusion began , when I read page 19 , he wrote the following :
Little (1988) proposed a multivariate extension of the t-test approach that simultaneously evaluates mean differences on every variable in the data set. Unlike univariate t tests, Little’s procedure is a global test of MCAR that applies to the entire data set.
My question is , why we need to test MCAR on the entire datset , if it is recommended to use maximum likelihood or multiple imputation ,which in turn assume either MCAR or MAR mechanism .And as he wrote the useful thing we can get from testing MCAR is to identify the individual variables that are not MCAR that means the main reason for implementing the t-test approach is to identify auxiliary variables that you can later adjust for in the missing data handling procedure since by Little's MCAR test we can not get that ? .