george.varkey

Dear Suresh, Thanks for input. Appreciate that. With respect to 11 & 12 above, 11. Yes, *Raosoft calculations are inaccurate*. They +do not+ consider the power values when they recommend a sample size. You can use Minitab and show that if you set the power of test at 50%, you will get the same answers as recommended by Raosoft. You don't have to do the manual calculations by hand. Of course, you are welcome to use the excel spreadsheet that I provided if you don't have access to Minitab. *This is not the same as 50% response accuracy.* That refers to the null hypothesis Ho: p = 50% (where p stands for proportion and not the p-value). A. So I take it that raosoft just doesnt bother about Power. The Response accuracy referred in raosoft is our expected proportion p = 0.95 ? Can I assume that since SLA is fixed at 98% accuracy, we may input p=0.98 and redo the sample calculation? However your statement "This is not the same as 50% response accuracy" is with ref to the Minitab or your sample calculator ? (have not tried yours yet) "That refers to the null hypothesis Ho: p = 50%" is with ref to Raosoft calculator? 12. If sampling is done with replacement, then it follows a binomial distribution and if sampling is done without replacement, then if follows a hypergeometric distribution. So, the question you need to ask is does the % accuracy numbers change as you sample the data. This is a moot point usually, when the population sizes are very large and both of these distributions will give you similar answers. As you have correctly pointed out, the formulas are using normal approximations anyway. I also derived my formulas that I used in the excel spreadsheet using the normal approximation. A. In the case of sampling audits for corrective actions, you are only searching for erroneous records, and you SHOULD'NT count the same error twice in the day/ monthly for reconciliation. Hence this has to be without replacement case : hence Hypergeometric. The present case of Audit by Fowzieh for large population sizes will apply even for much smaller sizes say more than 30 too, whence the Hypergeometric will always be used for "without replacement" . Please comment. Thanks George Varkey

Dear All : Fowzieh / VK / Suresh Jayaram There is something wrong in accepting these sampling conclusions : Please comment on the individual observations : 1. Fowzieh says it’s the prevalent practice to do daily internal audit + weekly external audit by client themselves. So I guess by the time the users actually correct them, we are into the 2nd/ 3rd week. 2. Having decided to do that, the reporting pattern is already “pre-defined” a priori as “daily” . Hence our Pop N = 4000 (Daily volume basis) , and 3. we SHOULD NOT reckon the monthly N = 80,000 to calculate Sample size. We therefore cannot select n = 1785/ 21 to arrive at QA’s daily audit schedule target !! 4. Audit target MUST be 1254 for the QA iff you do a constant daily N of 4000 ! 5. Fowzieh, since your daily production (data entry) is fluctuating ( 4000 ± something) your Sample size itself is going to be a Variable. - – - 6. You may need to track the (historical) daily volumes on an Attributes Control Chart based on another sampling size n0 (p chart for proportions non-conforming) , arrive at an average p value, provided your current process is stable in operations. 7. Fowzieh : As an aside, in response to your comments vide point #10 above wherein you “track” those errors, are you going any further, say following any Control charts in your operations?? 8. Then you may use this average p (from Control chart ) and input this info into the www.roasoft Hypergeometric/ Normal formula to derive an average Daily sample size which could be more apt than considering the previous sample figure of n= 1254 9. In other words the sampling requirements arise on account of 2 reasons/ purposes : (a.) sample size n0 to prepare the p-Control chart (not being done?) (b.) sample size n to just get random records for audit purposes ONLY. (being attempted now ? ) 10. This query of Sampling is not that simple as it looks. VK / Suresh , kindly whet if the above line of thinking is ok (based on Control charts) , or we may simply do all this on approximations. ( ie. upto point #4 ) Inviting comments from everyone please. George Varkey

Fowzieh / Suresh Pl clarify : 1. You decided to do daily audits now after seeing the sample size requirements of 1254, or was it the prevalent practice ? 2. Pl elaborate on this : “if I had non-production resource/ non-revenue generating resource ( QA ) do the audit” Otherwise is it a self-validation by you daily? 3. Or you directly doing the data-entry yourselves, and correcting them on-line (ie. Live – in this case its not audit ! ), or checking them at end of day (this is extra-audit)? 4. Are you now concluding that since monthly audit sample size being n=1785 (N= 80,000), you are now opting for this in lieu of daily audit n= 1254 (N= 4000)? 5. If that being so, you will be postponing your corrective actions till end of month? . I don’t know the implications of such delay from customer perspective , or cost implications, etc… Pl clarify the nature of transactions ; this may be a huge COPQ issue. 6. the sample sizes were generated assuming your response expectation accuracy is 95% (as per VK) , with 95% CI. and with ±1% Error margin. Remember customer SLA is 98% desired. He wants this to be your min.response level, in which case your margin of error should be ± 2% ( NOT ± 1% as per VK assumptions) . VK to clarify this, please. Am I missing something here? If 98% is min desired, then customer could expects ( 100% to 98%), ie 99% ±1% 7. In view of pt 6 above sample sizes will change 8. Fowzieh, you mentioned your team accuracy now is 99.6%, pretty good, then your sample sizes will come down? 9. At the end of the day , I still don’t get it why should you do a monthly audit because of your high volumes ? 10. Fowzieh : How do you search and track your Data entry errors whether on a daily or monthly basis? Do you red tag them for later corrections 11. Mr. Suresh : you mentioned the Calculator did the sampling at 50% “power”. Is this the 50% response accuracy referred above? (later changed to 95% per VK). You mentioned “If you desire a higher power of test (1-beta), you need to use a formula that includes power in the sample size calculations” . Does this imply the raosoft formula does not build-in (1-beta) power , and we have to resort to manual formula calculations? 12. Regarding the distributions, it is Hypergeometric not Binomial but ultimately the Normal approx are being used in the formula : Comments Regards George Varkey

Dear VK, This is my first response to this forum. (I did the GB in Frb 2005 at Chennai, if you recall). Some observations to you and Fowzieh : 1. Why should you be doing a monthly data entry audit (at end of month I suppose) if you are handling such high transactions? 2. If so, How could you cope up with timely data corrections and taking timely CAPA actions to solve those defective records 3. Surely you would prefer to do the CAPA on a daily basis with less transactions (4000) and daily sample lots (even if higher at 1254 records). Surely you want to correct any defectives at least by the next day (hopefully) isnt? 4. VK, you didnt comment on the type of data distributions in this case : is it binomial, or a hypergeometric application, since sample sizes are huge. The referrred Calculator assumes which type in these cases? (HG, B or Normal approximations?) Awaiting your inputs and clarifications George Varkey Chennai