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When dealing with missing data and Little's missing completely at random test, it's widely considered that if the test has a significance level of P>0.05 the data can be considered as MCAR.

But, I can't find a single paper that confirms that interpretation. All the papers just say that their values are higher than 0.05 so their data set is good and can reject the null hypothesis etc etc but they never confirm that where they got that "0.05" value. I was searching for hours. I found the following paper of Little (1988) http://www.jstor.org/stable/2290157

I couldn't find anything in that paper that it states about significance (P) of greater than 0.05 can be considered as data completely missing at random. Am I looking for the wrong key words? can anyone help me? Are there any research papers that confirm this?

UPDATE: In a nutshell, I'm asking, I need evidence by research papers of "P>0.05 can be considered as the data is missing completely at random"

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  • $\begingroup$ @peter: please ask in which part you're not clear to put the question on hold? anyone who are familiar with little's missing completely at random statistical test (MCAR) will understand it by a matter of minutes, although they might not have an answer as I'm also finding papers for hours. But, I don't see why did you put this on hold by saying it's not clear? $\endgroup$ – Pretty_Girl Aug 28 '16 at 14:00
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    $\begingroup$ I am familiar with MCAR and I don't understand the question. The whole thing is unclear, sorry. The first sentence says "little's missing" that is no part of MCAR. You then say that some analysis shows p > 0.05 but you don't say what analysis. Then you say that p > 0.05 means you can reject the null (whatever it is, you didn't say) but it's just the opposite. The whole question just doesn't make sense. Your update does not help, $\endgroup$ – Peter Flom - Reinstate Monica Aug 28 '16 at 14:05
  • $\begingroup$ @PeterFlom: to be more simple, say, I got a data set which has several missing data points, so I ran a MCAR in SPSS "Little's MCAR test: Chi-Square = 74.354, DF = 60, Sig. = .124". there is a widely used parameter that if you got a "sig." of greater than 0.05, the missing values can be considered as "random". But, I can't find any research paper that confirms that. $\endgroup$ – Pretty_Girl Aug 28 '16 at 14:13
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    $\begingroup$ Oh. OK. That makes sense. You should edit your question. For one thing, you should capitalize Little. The way you have it, it is a word not a name. Correct punctuation and grammar aids clarity. $\endgroup$ – Peter Flom - Reinstate Monica Aug 28 '16 at 15:00
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You're right to be skeptical. The whole business of interpreting a significance test's failure to reject a null hypothesis as evidence for the null hypothesis is illegitimate. It just means that on the particular metric your test considered, the data you have isn't extremely unlikely under the null hypothesis.

Furthermore, missingness completely at random is a strong assumption and should not be made merely on the basis of quantitative analyses of the data at hand (after all, the question is what's missing from what you have), but also on the qualitative question of how you think the data came to be missing.

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Paul Allison's discussion of MCAR in his Sage monograph, Missing Data, has one of the clearest explanations of MCAR in the literature. For instance on p. 3, regarding a test of the MCAR mechanism hypothesis, he writes:

The data on Y are said to be missing completely at random if the probability of missing data on Y is unrelated to the value of Y itself or to the values of any other variables in the data set...it's easy to test this by dividing the sample into those who (...are vs those who are not missing...) and then testing for a mean difference. If there are, in fact, no systematic differences on the fully observed variables between those with data present and those with missing data, then the data are said to be observed at random. On the other hand, just because the data passes this test does not mean that the MCAR assumption is satisfied. Still there must be no relationship between missingness on a particular variable and the values of that variable...

So, to @Kodiologist's point, the assumptions for MCAR are strong and a simple test does not, in and of itself, satisfy those assumptions. They merely lend evidence in its support.

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