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Context: In the realm of Paid Search Marketing. Current reporting does not provide event level data only aggregate totals with different segments.  Want to compare distributions/test statistical significance of A/B test results.  Did not want to assume that data followed normal distribution or know STDEV for data so came with this approach. 

My Question: I am going to use the average "CPA" or "CTR" for a date range, and generate an observation for each conversion based off the average for a time range.  Is this statistically sound way if I want to generate raw data? Would I have wonky distributions because of the multiple averages?  Just want a gutcheck if I'm completely off base.  

My Aggregate data looks like below:

Day Cost Acquisition CPA or CTR
   1                     40                           2              $20
   2                     75                           3              $25

Observation data I generate looks like below:

Day Acquisition
                                     1                          $20
                                     1                          $20
                                     2                          $25
                                     2                          $25 
                                     2                          $25

I really appreciate your help with this question! An important project to me at work.  

  

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