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Main Question or Discussion Point
I have low counting stats and need to subtract background, account for efficiency, and divide by volume. How do I combine the asymmetrical (Poisson) errors?
That isn't a description of an experiment. As far as I know, it isn't a description of a specific problem in statistics.How do I subtract a Poisson background from a Poisson sample and propagate the error associated with each?
Estimation and "proving a difference" are technically two different statistical tasks. Statistics doesn't actually "prove" a difference. There are statistical procedures that make a decision about whether a difference in two situations exists, but these procedures are not proofs. These are regarded as "evidence". They are not a mathematical proof.I am counting the number of particles in 60 fields of view on a scope. I count three pieces of a filter for a sample and three pieces of a filter for a control. All of my counts in 60 fields of view are <50 and Poisson distributed.
The standard way of testing for significant difference is:I want to eventually test the hypothesis that one sample is is greater than the controls. And if two samples are different from each other. This I am ok with- but I have to show all of my calculations for how I can mathematically prove the values are different.
I have small counts in 60 fields of view on a scope and I was propagating error following Gaussian error propagation- which I now know is wrong. But what do I do with these asymmetrical error bars when I want to know sample (+/- error) minus control (+/- error)?
You can't calculate the probability that the null hypothesis is true.From that number, you can calculate the probability of the null hypothesis being true.
Sorry, sloppy formulation. I was going to be more specific, but I suddenly remembered that the data are assumed to follow a Poisson distribution - and I did not quite remember how to deal with that.You can't calculate the probability that the null hypothesis is true.