Determining Sample Size

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    Robert Martin

    I’ve been asked to determine the correct sample size to use in order to assess whether 3 criteria have been met
    for a particular invoice
    1.  Correct billing by a 3rd party administrator
    2.  Correct Bill Payment by a 3rd party bill payment vendor
    3.  Correct receipt of materials for the invoice in question.
    Our 3rd party adminstrator bills me in advance for services to be rendered (i.e. $185 mils)
    Payment is made in advance to that 3rd party administrator
    Through the course of operations the 3rd party administrator notifies me that they only paid out $165 mils and thus owe me $20mils.
    I want to audit this 3rd party administrator by checking their detail transactions against their billing to me.  There are approximately 8,000 transactions per week.
    How do I calculate a good representative sample in which to audit?


    Terry Brewer

    The UCLA Statistics Homepage has an excellent sample size calculator.  You can find it at  On the home page look for the “Publications” general heading and select “UCLA Statistic Calculators”.  From that page search down through the various calculators to “Sample Size Calculator”.
    It sounds like you wish to caculate the proportion of billings that are accurate (or inaccurate) in each of your three categories, so you should probably select the “proportions” tool.  Once there, leave poplation size at infinity.  Changing that variable does not make a lot of difference anyway.  “Max allowable difference” basically refers to what plus or minus error you are willing to allow.  Changing this variable makes a big difference in your end result.  I recommend a value of between 0.1 and 0.05 for your study (+/- 10% to +/-5%).  For confidence level, most people stay with 95%. Finally, if you have no previous proportion caclulations from previous studies, stick with the default population proportion.
     Your result will probably be in the mid hundreds.  For an ongoing study, I would suggest randomly selecting a few each day to get the target sample size for a month/quarter/etc. as required.  For a static study, choose your sample from across the desired time frame.



           The simple formula to calculate the sample size is
         n = Z^2 * p*(1-p)/(error)^2     for infinite or very large population
        If you have a finite population make the correction as below
            Sample size(for finite population ) = 1/{(1/n) + (1/N)}
            n= same as calculated by the above formula
              N = Population size
         Z = corresponding Normal value for confidence interval (assume Confiedence interval for example for 95% CI your Z = 1.96)
          p = Population proportions ( assume 0.5 as safer side)
          error = assume in % ( ex 5% etc)
    Hope this helps you
        If you need more clarifications pleas mail me at
          [email protected]

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