Non parametric test for semi-quantitative data.

#1
Hi everyone, I have a question about the sample size for paired comparison test. I want to compare multiple measurements from 2 machines, in order to demonstrate that there is no significant difference between these 2. Each day I can run these 2 machines in the same condition, so for each day I will have a pair of data from these 2 machines.

1. The first measurement I want to test is a semi-quantitative measurement, which have a limit of quantification (below that limit, the machine is not capable to give the exact result). Historically, we have around 13 data, which are all below this limit. For the testing, I want to consider this limit our acceptance criteria. But I don't know how many runs minimum I need to have.

2. The second measurement I want to test is a count data. Since we don't have a acceptance criteria, I am thinking about a non-parametric test for paired data. In that case, how many runs minimum I need to have?

Thanks for the help.
S.
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#2
If you run the machines at the same time using the sample batches of material (split the materials) adn if you randomly mix the operators between machines, you will only need to run the machines for 5 days, using all of the results for each machine each day. Then if all 5 of 1 machine’s results are better than all 5 of the results of the other machine then you will have an alpha of 5% that the machines are different from each other (subject to any othet confounding). This is a matched pair parametric test that use simple probability. It is like flipping a coin 5 times in a row and getting 5 heads. (Or 5 tails). It will work for all kinds of data.

We would need more details to give a more detailed answer...
 
#3
If you run the machines at the same time using the sample batches of material (split the materials) adn if you randomly mix the operators between machines, you will only need to run the machines for 5 days, using all of the results for each machine each day. Then if all 5 of 1 machine’s results are better than all 5 of the results of the other machine then you will have an alpha of 5% that the machines are different from each other (subject to any othet confounding). This is a matched pair parametric test that use simple probability. It is like flipping a coin 5 times in a row and getting 5 heads. (Or 5 tails). It will work for all kinds of data.

We would need more details to give a more detailed answer...
Thanks Bev D for the answer. I see your point here, so we consider that for each run, one machine has 50% chance of getting a better result than the other one (if we suppose that the 2 machines are similar). The fact that all my data are below the limit of quantification can be a problem? (some null results and some positive results w/o the exact value).
For each day, the 2 machines will be run by the same operator in the same condition, in short interval of time. What details do you need to give a more detailed answer? Sorry I am not yet familiar with all this.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#4
If one of your characteristics is so low that you only get zeros or a result below the limit of detection, why are you concerned if the machines are different on this characteristic? The test will tell you if there is a difference or if there isn’t...we never do a comparison test to prove one answer or the other we do it to know which answer is true.
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#6
2. The second measurement I want to test is a count data. Since we don't have a acceptance criteria, I am thinking about a non-parametric test for paired data. In that case, how many runs minimum I need to have?

Not having an acceptance criteria doesn't mean you need to shift to non-parametric tests. By the way, a good "guesstimate" for sample size is 25, given no other information.
 
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