This is a very important question. Researchers should examin the pattern and volume of the missing data before doing the final analyses. runing descriptive statistics can show where are the missings, so the researcher can look at the cases and the variables and observe any pattern or volume of missings. for example, if the same question has a large amount of missings, then there is a possible problem in this question that the participants did not understand, or did not like, or the question was unclear by wording or typing.

Usually Missing at random is better than non random because at random means that the missings is distributed over the different variables in small scale and can be replaced by many methods {Replacing missing is an Art and it take long time to be mentioned here}. however, if the missing is estimated to be too much, and this too much depends on the sample size and the type of the study, then missing becomes a serious problem.

You might want to research "response propensity" groups.  

This is a very important question. Researchers should examin the pattern and volume of the missing data before doing the final analyses. runing descriptive statistics can show where are the missings, so the researcher can look at the cases and the variables and observe any pattern or volume of missings. for example, if the same question has a large amount of missings, then there is a possible problem in this question that the participants did not understand, or did not like, or the question was unclear by wording or typing.

Usually Missing at random is better than non random because at random means that the missings is distributed over the different variables in small scale and can be replaced by many methods {Replacing missing is an Art and it take long time to be mentioned here}. however, if the missing is estimated to be too much, and this too much depends on the sample size and the type of the study, then missing becomes a serious problem.

Thank you Prof. Muayyad Ahmad,

How  I should identify missing data mechanism when my dataset has only one variable? In my dataset each data is a measurement of an attribute in several outputs of a machine.  I do not have several questions to analyze answers to them.

I doubt that the dataset has only one variable!!!

I wish you can elaborate more on your data set with the variables and number of cases..etc.

I monitor industrial processes. I am interested to find pattern of data. To do so I monitor how recorded measurements of a single quality characteristic (such as weight) change in several products while passing a specific step in production line. I need around 20 data samples to decide about the pattern. However, sometimes a part of data is missing. If the data is "missing not at random", we need to stop the process

Hi Razieh,

According to your data description, it is difficult to state what missingness mechanism is affecting your data. If you are monitoring the industrial processes, can you investigate deeply why the information was not acquired? 

For example, sometimes the information is not been recorded because an employee made a mistake and "hides" the information that is potentially dangerous for his position. This situation characterizes the MNAR mechanism. 

I hope that helps. 

Perhaps you are doing something like a Shewhart control chart, and once in a while the datum is not collected.  If so, and if you have no other data to estimate what that datum should have been, then you just don't know if the process appears to be within the bounds selected at that point.  

Thanks Fabio,

Yes, the problem is that I do not know when MNAR. Let's assume I expect 20 data but 5 of them are not recorded and i know the order and the place of missing values. Do you know any statistical test that can determine the probability of randomness by the missing data order?

Yes James, it is like Shewhart control chart. ".. the datum is not collected" However, I have "....other data to estimate what that datum should have been" the problem is the reason behind missingness of data may be not ignorable and i afraid the missing data be the critical data in control chart.

Razieh -

So you have 20 distinct sources, with one input datum each, on each occasion?  When looking at the current change, the 20, say 'respondents,' each may have had a response on the last occasion, call that N =  20, but say only 18 responded this time, call that n = 18, and say correspondingly that you then have 18 y-values and 20 x-values, in this hypothetical example.  Then you could graph y and x on a scatterplot.  The predicted y-values corresponding to the two missing values could be found, and you could also get the corresponding estimated variance of the prediction errors.

In the case of linear regression through the origin, you could make use of the following, though for totals, so divide by N for the means:

Section 5, Option 1, page 10 in

 https://www.researchgate.net/publication/261474159_Some_Proposed_Optional_Estimators_for_Totals_and_their_Relative_Standard_Errors_for_a_set_of_Weekly_Quasi-Cutoff_Sample_Establishment_Surveys

There you look at variance of the prediction error for the total  (not individuals, as they are not additive). But all you might need to use below may be the two predicted values, bx1 and bx2, as explained below.

In your control chart, I assume you look at a standard error based on the distribution of the 20 responses.  If two (in this example) were imputed, by looking at how the other 18 changed from the previous period, then we are getting information from them which should inflate or deflate the standard error based on which were the 18 that reported.  If the two that varied the most from the others last time did not report, the predictions will carry this over to avoid underestimating the new standard error.  This is still just an estimate, but it could help account for nonignorable nonresponse if the missing data that tended to behave differently were from the same two sources between those two periods.

On the other hand, if your 20 observations are all from the same source, and you don't have any other information, you may not be able to do better than assume ignorable nonresponse.  However, you may be able to find some information to show otherwise, but that would depend upon further details of the operation, so you may need to go back and think that over.

I hope that at least some of this is relevant to your problem and/or helps give you an idea.

Cheers - Jim 

Article Some Proposed Optional Estimators for Totals and their Relat...

Dear Jim, Thank you for taking the time to share all of that great information and your article with me. Your advice is extremely helpful.