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I am working on a project where we would like to take the ratio of two measurements A/B and subject these ratios to a ranking algorithm. The ratio is normalized prior to ranking (though the ranking/normalization are not that import to my question).

In most cases measurement A (the starting measurement) is a count with values greater than 1000. We expect an increase for measurement B for positive effects and a decrease in measurement B for negative effects.

Here is the issue, some of our starting counts are nearly zero which we believe is an artifact of experimental preparation. This of course leads to some really high ratios/scaling issues for these data points.

What is the best way to adjust these values in order to better understand the real role in our experiment?

One suggestion we received was to add 1000 to all counts (from measurement A and B) to scale the values and remove the bias of such a low starting count, is this a viable option? Thank you in advance for your assistance, let me know if I am not being clear enough.

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    $\begingroup$ There's a good rundown of missing data methods that might help get you started: stat.columbia.edu/~gelman/arm/missing.pdf $\endgroup$ Jan 8, 2015 at 15:17
  • $\begingroup$ And another approach that I haven't tried myself but comes from a very respected author and sounds good in the abstract: gking.harvard.edu/files/gking/files/measure.pdf $\endgroup$ Jan 8, 2015 at 15:21
  • $\begingroup$ Sorry, I wanted just to add paragraphs for clarity in the question -- but Stack Overflow only accepts edits if they are longer than 6 characters. So I also rephrased the problem description to 'A/B measurements'. Why did you call them 'B/A measurements', by the way? $\endgroup$
    – logc
    Jan 8, 2015 at 19:51
  • $\begingroup$ Thanks for the comments I will take a look at these links. B/A measurements was a typo...thanks for the fix. $\endgroup$
    – Dennis
    Jan 9, 2015 at 15:14

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Yes, the general idea is to add a baseline small count to every category. The technical term for this is Laplace smoothing. Really it's not so much of a hack, as encoding the idea that you think there is some (uniform?) prior distribution of the events occurring.

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  • $\begingroup$ Sean-Thank you for the response, much appreciated! I thought it seemed like an OK path forward but I did not have anything to base that on. Will read up on Laplace Smoothing. $\endgroup$
    – Dennis
    Jan 9, 2015 at 15:16
  • $\begingroup$ This is also a well known technique in compositional data analysis (data in the interior of a simplex), for handling zero-valued components. The idea is that, in many physical applications such as geology (where the methods were first developed), zeroes were more likely due to detector limitations than being true "structural" zeroes. So adding some small value to the zeroes allows analysts to apply log transforms to the composition without having missing values or infinities $\endgroup$ Jan 12, 2015 at 4:23

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