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nbryan5
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?
nbryan5 said:How do I subtract a Poisson background from a Poisson sample and propagate the error associated with each?
nbryan5 said: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:nbryan5 said: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.Svein said:From that number, you can calculate the probability of the null hypothesis being true.
Stephen Tashi said:You can't calculate the probability that the null hypothesis is true.
The concept of combining Poisson error is a statistical method used to combine multiple independent measurements of a Poisson-distributed variable into a single estimate with a more precise measurement and a smaller margin of error. This is particularly useful in situations where a single measurement may not be enough to accurately represent the true value of the variable.
Combining Poisson error is important in scientific research because it allows for a more accurate and precise estimation of a variable's true value. This is especially useful in experiments or studies where the measurement of the variable may be prone to random error, and combining multiple measurements can help reduce the impact of this error on the overall results.
The assumptions of combining Poisson error include that the individual measurements are independent of each other, the variable being measured follows a Poisson distribution, and the measurements are made with the same error rate. If these assumptions are not met, the results of the combination may not be accurate.
Combining Poisson error involves taking the mean of the individual measurements and calculating the standard error using a formula that takes into account the number of measurements and the error rate. This results in a new estimate of the variable's true value with a smaller margin of error than any of the individual measurements.
Combining Poisson error should be used in situations where there are multiple independent measurements of a Poisson-distributed variable and a more precise estimate is desired. This can be in various fields of research, such as biology, physics, and social sciences, where the measurement of a variable can be challenging and prone to random error.