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I have several datasets containing hundreds of variables, measured at the same time point and with the same method.
Some of these variables have been measured more often and assume consistent values. Some were measured less often and have highly disperse values.

Example:

v1 2 1.8 1.5 1.9 2.1 1.78 1.95 2.0 2.1  
v2 2 100 -5.2  
v3 1 -1.3 -2 2.3  
v4 1 1.5 1.6 1.9 2.1 2.0 2.4 -1.1 2.3 1.5 1.6 1.9 1.8 1.6

I removed the outliers using adjboxStats in the robustbase package in R. I need an estimator that can tell me the value assumed by each variable during my experiment. Therefore, I calculated median and median absolute deviation (mad), since they are robust estimators not influenced by outliers.

I have been looking for days without success for a method which I could use to identify the variable that assume values to variable/disperse to be considered reliable. In other words, I'm looking for a method I could use to state that using that specific method I did not obtain consistent values for a specific variable.

For example in the above data I would say that I cannot trust the measurement performed for v2.

These data come from biological experiments, and having a variable with such huge difference, as v2, doesn't have sense. Therefore, it has to come from a methodological error. I would expect that all values of each variable are more or less similar. Therefore, if I have a variable that has values too different compared to a defined range (which is defined considering an accepted dispersion range) I will remove it. Maybe the range can be defined by and estimation of the "average" mad of all variables, or something like that. This could be an estimation of the variability I could expect and accept. But I would need a test to verify that.

I hope I managed to explain my problem.

Do you have any suggestion?

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  • $\begingroup$ I really don't think you can find any method that will universally say 'reliable' or 'not reliable'/'too variable'. This is because such a judgement varies from application to application and from person to person. My judgement will differ from yours. If you can specify properties that you want the result to have it might be possible to come up with some rule that could achieve it. $\endgroup$
    – Glen_b
    Jul 1, 2014 at 10:34
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    $\begingroup$ You just made my point perfectly. You are able to bring your subject area knowledge to say that one of the variables has some characteristic that doesn't make sense - but that's not inherent in the numbers. There are many contexts where those numbers make perfect sense. What makes it unreasonable for your situation is the context which exists outside the numbers; that simply isn't a characteristic of the numbers themselves. If you consider a number of such cases either side of the borderline, you'll likely be able to elucidate some rules (criteria) that help distinguish them. ... (ctd) $\endgroup$
    – Glen_b
    Jul 1, 2014 at 10:55
  • $\begingroup$ We might be able to help with identifying some criteria, but the choice of what is and isn't okay requires subject-expertise we won't have (or at least most of us won't) for your application. $\endgroup$
    – Glen_b
    Jul 1, 2014 at 10:57
  • $\begingroup$ Thanks. My problem is that form the biological point of view (these data come from biological experiments) having a variable with such huge difference, as v2, doesn't have sense. Therefore, it has to come from a methodological error. I was thinking something like considering a mad / median higher than 1 indicate that the differences among the values of that variable is higher than what I will obtain by chance. This means that I cannot be confided that the recorded value are the real biological value. Therefore, I cannot consider that variable. But I would need a test to verify that. $\endgroup$
    – efrem
    Jul 1, 2014 at 10:58
  • $\begingroup$ Yes you are right. In the case of these variables I would expect that all values are more or less similar. Therefore, if I have a variable that has values too different compared to a defined range I will remove it. Do you think these can help to find a good method? $\endgroup$
    – efrem
    Jul 1, 2014 at 11:01

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