On 24 Nov 2003 11:29:40 -0800, [EMAIL PROTECTED] (Find_Housing) wrote: > Thank you Rich! > That's a very good point. > > Let's say, if 10 bacteria is acceptable for a bag of 50 ml blood. How > would you approach the problem?
If you are going to talk about a number so close to zero, I think I would approach it from the side of, "What can I believe, if the sample looks perfect?" Here is an approximate method, and I don't know whether you want 1-tailed or 2-tailed testing. Consider the 2x2 contingency table, and the chisquared test on the table. In one row, place the count of Bacteria 'observed' in testing, and in the other row, place the number which may exist, allowably but at the limit, in the untested part. Then in the second *column*, place two numbers which are large numbers, because they are to indicate the fixed-expectations, based on the fraction of the sample to be tested. For instance, if you spotted 0 bacteria, in a 10% sample: and hope for no more than 10 in the rest -- 0 for 1000 10 for 9000 .... Those yield a chi squared test value of 1.1; totally ordinary. You might check out the fact that the table has almost the same test value if you change the 1000/9000 to ten times as much, or (not quite as firmly) ten times as few. (I'm showing how to do computation with a computer program that is set up for the numerical entries. If you have one that takes fixed proportions, then you can merely put in those fractions.) For the table to be 'unusual', you need to escalate to 0 for 1000 35 for 9000 ... Those yield a chi square of 3.87 (p=.049) or 2.81 (p=.093) depending on whether you figure Yates's correction applies. But that indicates that '35' is in the ballpark of what you can have some confidence in, for a 10% sampling. If you want more assurance based on a zero count, you have to increase the size that is tested. If you sample, say, 20% 0 for 2000 20 for 8000 ... Those yield a chi squared of 4.97 or 3.78 -- so the *bigger* fraction involved in the testing shows that there must be a lower rate, plus, there is a smaller quantity (only 80%) where the other bacteria can reside. Does this do it? -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html "Taxes are the price we pay for civilization." . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
