SAMPLE SIZE DETERMINATION

[#1]

Hi,

I was wondering if there is a way to determine the sample size as a function of %CV (Coefficient of Variation) by using JMP 17.

[#2]

Hi @DFereidouni : So that we may respond appropriately, can you provide more context and expand on exactly what you are trying to do?  Additionally:

   1. Is this a power calculation? One sample, two sample, k samples?

   2. Is the assumed distribution lognormal? Normal?

   3. What is the hypothesis (null and alternative) you want to test?

[#3]

I have an analytical test method with 17% CV as intermediate precision. The goal is to qualify a new lot of control material for this test method and I want to know how many test/run needs to be done by considering the variability. the current lot has a range of 2.1-6.2 ng/mL

1-  One sample test

2- Normal distribution

3- H0: the data-set have a cv value < 17 

[#4]

Hi @DFereidouni : OK, you want to show (with some level of confidence, say 95%) that CV <= 17%.  so H0 is actually CV > 17%, and your alternative hypothesis, Ha, is CV <= 17%; Ha is always what are are trying to show.

In the context of your clarifying answers, the answer to your query is "no, there is no JMP platform built for that". That's not to say that it is undoable in JMP. But it would likely take simulation. As part of that you may find the  following script useful.

https://community.jmp.com/t5/JMP-Scripts/Confidence-Interval-for-the-Coefficient-of-Variation-CV/ta-...

i.e., if the upper bound of the 90% confidence interval is < 17, then you would reject H0: CV>17 in favor of Ha: CV<=17 at 95% confidence. But that confidence interval is used once you have the data. So you could simulate data (based on some sample size, for an assumed mean and SD where 100*SD/mean < 17), then use that interval to see if the upper bound is less than 17. If so, that run gets counted as a "success".  Then run 1000's of such simulations while keeping track of the number of simulation runs that result in "success".  Power is then = (number of successes/number of simulations) for that mean, SD, and sample size. Then repeat that simulation for different sample sizes. Then, you'd have power as a function of sample size (for that assumed mean and SD). A sample size might then be chosen such that power if high enough (often > 80%, but you may choose something higher). There is a lot to think about here. The above script uses the method recommended by Vangel.

Vangel, Mark G. (1996) Confidence Intervals for a Normal Coefficient of Variation, The American Statistician 15(1) 21-26.

See (3) here if you can't find the Vangel article.

https://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/coefvacl.htm

Or, you could make your own confidence interval calculations (via Vangel) and see how the width of the interval changes as a function of n (sample size). Then choose n large enough such that the width of the interval is no more than some predetermined value, or until you get diminished return in precision (width of interval) for increasing the sample size further. These are subjective considerations that there are no hard and fast rules for.  

As I said...there is a lot to think about here. 

[#5]

Hi @DFereidouni : As a follow up to my comments above: 

You say "H0: the data-set have a cv value < 17". From that, I can infer that your question really is about the calculated CV from the sample. So, you aren't really asking about testing any kind of hypothesis about the population CV. If you are interested in the value you actually calculate from the sample, and what is an "adequate" sample size for that calculation, then the second option I described above may be your best choice.