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I am currently studying statistics and I have come across these terms about missing data mechanisms; MCAR, MAR and MNAR. I have a dataset with exactly one missing value and I can only think of that this missing value is MCAR.

My thought is that is the following:

It can't be MAR as we can not determine any pattern of missingness since we only have one missing value.

It can't be MNAR either as there is no reason why the missing value should be deleted/removed on purpose.

I think it is likely to be MCAR since it is completely random. It can be a human mistake, maybe the one who gathered the data just missed out on this single value.

I am new to these terms so this is my initial thought, can anybody confirm that I am on the right path or am I missing something?

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The properties of MAR, MCAR, and MNAR are not features of your dataset, but rather a feature of the data generating mechanism. Even if you have just one missing value, you could increase your sample size 100-fold, giving you an expected 100 missing observations - at that point you would have a robust case for estimating the missingness mechanism.

However, as you correctly noted, with just one missing case, you have no way to estimate the probability of missing or non-missing as a function of covariates. You could easily estimate an imputation probability model based on the complete data. In a reasonably well done study, it shouldn't matter what method is used: you're only potentially recovering some information from a single missing observation.

The point you should make is that, barring as suspicion of MNAR, you can (for most models) conduct a complete case analysis and obtain an unbiased and highly efficient result. Imputation and other missing data methods are only useful insofar as they recover a bit of the lost information.

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  • $\begingroup$ @restingquartH mean imputation is generally disregarded because, even in the cases where it's unbiased, it tends to be too optimistic - the SEs are not as big as they should be, so you're more likely to declare statistical tests as significant. This "data string" business sounds like a request for simple univariate stats on each variable. However, if someone asks for something that you're not clear on, you should ask them. $\endgroup$
    – AdamO
    Commented Dec 5, 2022 at 23:29

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