Dealing with missing data when both outcome and covariates are missing I have two categorical variables. There are missing values in both variables, and they do not necessarily occur simultaneously. 
For example, the data might look like this: 
ID     Rating     Status
 1      Good       Good
 2      -          Good
 3      OK         Bad
 4      OK         -
 5      -          -
 6      Bad        OK
I would like to see if there is an association between Rating and Status (Chi-squared test), what can I do about the missing values?
Thanks in advance.
 A: What I would do to assess the type of missingness is partition your results into four groups: complete cases, first answer blank, second answer blank, both answers blank.
In complete case set, look at the marginal distributions of $X_1$ and $X_2$, separately. Compare the marginal distribution of $X_1$ in the complete case category to the marginal distribution of $X_1$ where the second answer was blank. See if they're similar. (You could do some test if you'd like - perhaps chi-squared to compare the categories under missingness and completeness - if you want to more methodically make a decision.)
Repeat for $X_2$. If the distributions are similar, then it's evidence that your data are MCAR (missing completely at random) as missingness doesn't affect the marginal distributions. This will help you to assess what mission data method (likely imputation) you should use.
Hope this helps! Let me know if this is unclear.
A: If you just run a chi-square test in most software, it will throw out all of the cases with missing data on either variable. This is not ideal and is only statistically valid if your missing data are "missing completely at random" and this is hardly ever the case in real life. 
In other cases, I would recommend multiple imputation (http://www.stefvanbuuren.nl/mi/MI.html). This can be accomplished fairly easily in SAS, R, SPSS, and other software. It is basically a 3-step process: 1) Impute missing data, 2) conduct analyses on the multiple resulting datasets, 3) pool results. There is a bit of work required to learn the details of each step and how to do it in the software of your choice but Stef's website is helpful and lists many other helpful resources. 
Edited to add: you should also consider anything you know about WHY the data might be missing. If people who would have otherwise given Bad ratings were more likely to not provide a rating, then you want to look into methods for MNAR (missing not at random). Also try to include as much additional information as possible in your imputation model.
