# Little's MCAR test: why must missing values be random?

When we have data with a lot of missing values, as I see it, the missing values are likely to be observed with some systematic properties. Maybe some sex is more likely to not answer a question and leave it blank, compared to the opposite sex, and so on. I'm just wondering, why exactly is it necessary to test for the randomness of the missing values? I'm looking at Little's paper and I see no mention of why this is important.

Will not lack of randomness help us in determining how to "fill in the missing values", if that is desired?

## 2 Answers

When the missing data follows MCAR (Missing Complitely at Random) pattern, the estimates obtained are not biased (since the lost of information is uniformely distributed among all the variables and levels). The only drawback of this situation is the reduction of statistical power due to the lost of cases. Hence, this can be easily overcome by increasing the sample size.

On the contrary, when the missing data pattern is not MCAR (and thus, the probability of missing depends on either the observed data or the unobserverd data), bias may appear in the estimates. Dealing with this second situation is trickier since it can not be overcame by adding more observations . In this case, imputation procedures must be considered.

• You mention estimates obtained, and that they are not biased in case of MCAR. What estimates are these? And I'm not certain what drawback you are talking about, is there a drawback if your missing data is MCAR? Why? – Erosennin Jan 27 '17 at 13:46

If you have good reason on theoretical grounds for supposing that the missing values are not MCAR then there is absolutely no reason to test for MCAR. So in that case you would carry out usually multiple imputation. If you have good reason to believe on theoretical grounds that it is in fact MCAR (the technician dropped the test tubes, someone unplugged the freezer, the interviewer's computer was struck by lightning) then there is no point testing either, just do a complete cases analysis and curse your bad luck.

• So, if you want to "fill in" the missing values, how you do this depends on your missing values being MCAR or not? – Erosennin Jan 27 '17 at 13:41
• I think it is more "whether" than "how". How you do imputation depends on many other things too. – mdewey Jan 28 '17 at 13:32