Dr. Yusuf Ziya Ozcan Department of Sociology Middle East Technical University Ankara 06531 Turkey
Phone: 90 312 210 3133 Fax: 90 312 210 1284 ----- Original Message ----- From: "Rich Ulrich" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Monday, November 24, 2003 7:42 PM Subject: Re: [edstat] small sample size > On 24 Nov 2003 07:47:39 -0800, [EMAIL PROTECTED] (Find_Housing) wrote: > > > Hi! > > > > I came accross this statistics issue and am hoping to get some > > suggestions from here. As part of our experiment design we have a need > > to statistically quantify the number of bacteria in a bag of medium. > > The goal is to be able to say that the bag is bacteria-free after > > evaluating some sampels taken from the bag. > > This problem becomes easier when it is stated right. > Your goal is to say that the bag is *practically* bacteria-free; > it need to be bacteria-free for *practical* purposes. > > How small is small enough? The super-pasteurized milk > can 'keep' at room temperature because the total count > in a quart has been reduced to dozens of organisms or less. > >From there, it will take months for the growth to become hazardous. > > What is your limit? Are you groping blindly, or is there > something formally stated? > > > The size of the total medium is 50 ml for the bag and the volume of > > sample taken for evaluation is 0.5 ml. > > Okay, there could be 100 samples. Here is amplification of > my point above, to show that proving 'zero' is impractical. > > If you test 50 samples, what is the chance that exactly 1 > of the original 100 samples had 1 bacterium? => 50%. > There is only a 50-50 chance that you would have picked > the 'bad' one in your sample. This is something that works > out pretty generally: If you want to prove that something is > zero, and the alternative is one, then you don't even make > much progress by "random sampling" until you have > sampled a large portion. > > What can save infinite sampling, for one thing, is sampling > that is *not* random but has a biased chance. > > What you really need for your application, though, is > a small, non-zero amount that is acceptable. You can > only push the estimated proportion *toward* zero, if > you are making an accurate estimate. > > > > [ snip, detail not yet relevant] > > -- > 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/ . > ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
