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  • 1.  Confidence Intervals for Targets

    Posted 03-08-2013 14:33
    This message has been cross posted to the following eGroups: Statistical Consulting Section and Statistics in Marketing Section .
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    Hello,

    Just to clarify my question...
    I have data for 2012 but not for 2013 and we would like to tell the stores to increase their overall OSAT scores by .5 for 2013.

    So, the question around the confidence level is: what would the target have to be in order to have 80% confidence that the growth has been at least 0.5?

    1st attempt: 
        1) I found the confidence interval for the population mean from a random sample. 
        2) Increased each store's score by .5 then found the confidence interval for the population which is .5 above the original data
        3) The 2013 "proposed" confidence interval overlaps with the 2012 confidence interval

    I also tried to create bootstrap confidence intervals but my intervals still overlap.


    How do I find the 2013 mean so that they don't overlap and the distance between the intervals is 0.5?

    Thanks,
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    Kenita Hall
    Analytical Consultant
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  • 2.  RE:Confidence Intervals for Targets

    Posted 03-08-2013 15:15
    Hi Kenita,

    You will have to have one more piece of information, which is the correlation between the 2012 and 2013 scores (say, X1 and X2) within each store.  If you assume (X1,X2) follows a bivariate normal distribution, then the answer depends on the distribution of X2-X1, which is univariate normal with a variance depending on the correlation between X1 and X2.

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    Junfeng Sun
    Mathematical Statistician
    NIH
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  • 3.  RE:Confidence Intervals for Targets

    Posted 03-09-2013 06:46

    Hi Kenita,

    I believe that the fundamental problem is that stores are being told to attempt to raise their scores by 0.5, but the result is measured with a standard deviation of 0.7, if I understood your framing of the problem.  I.e., the measurement error is larger than the targeted change in score. 

    I don't see how it makes sense to tell the stores to achieve a measured improvement well above 0.5, so it is certain that their improvement was at least 0.5.

    I would recommend working on improving the measurement of the scores so the standard deviation of the measurement is small relative to the proposed change.  You may also want to verify that the standard deviation of the measured score is truly as large as you've estimated.

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    Best regards,
    Michael Morton
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  • 4.  RE:Confidence Intervals for Targets

    Posted 03-09-2013 13:23
    Kenita,

    I'm finding this rather confusing.  The confidence interval is for estimating a fixed population quantity such as a population mean.  What quantity are you estimating?  Are you just interested in whether last year's target + .5 falls in the CI for the 2012 mean?  If so, a simple approach is to test the hypothesis that the 2012 mean is greater than last year's target + .5.  Make sure your clients are not interpreting a CI or a hypothesis test for the population mean as a prediction interval for individual stores, which requires a different procedure.

    Sometimes it sounds like you want to know if you need to increase the target by more than .5 to be sure of success, and that you believe stores can change their OSAT scores at will.  This doesn't seem reasonable to me.

    To estimate future means it helps to have data on change.  Do you have multiple time points in your sample?  If you had an estimate of the 2012 mean and an estimate of change or slope, you could get an estimate for the 2013 mean and test if it is greater than the old target + .5.

    Good luck,
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    William Stewart
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