Poisson limit - are two smaller samples better than one large sample?

[bmiksch]

In a real world sampling situation, testing water with limited numbers of organisms, how do the probabilities of getting a positive test compare between, say, taking one 100 mL sample (twice as much sample) vs. two 50 mL samples, if the method of detection can detect as little as one organism in either sample?

Seems like the bigger sample has a better chance of having at least one organism in it, but the lower probability in the smaller sample is compensated for by taking two of them.

I think I should approach this by constructing an excel file which plots the poisson cumulative distribution as a function of the # of organisms (k), but for the two smaller samples I should use the square of the probability, like P(two samples) = 1 - [1 - P(one sample)]^2. Or is it just a 'wash' and so long as the total volume analyzed is equal the probabilities are the same?

Any advice appreciated.

[squareandrare]

I think they're the same. You should get the same p-values either way.

[Dason]

Technically if the poisson assumption is true then like squareandrare says there isn't really a difference. I'm not sure if two samples is good enough but there are cases where having lots of smaller samples would be nicer than one large sample because then you could actually test if the assumption of a poisson distribution is reasonable. I don't think it really makes much of a difference here though?

[bmiksch]

So here is what I came up with. Right? Wrong?

Excel Poisson(min # of organisms needed for detection = 1, variable mean as # of organisms in water increases, logic set to TRUE for cumulative distribution)

Column 1 = mean organism count per 400 mL sample from 0 - 5
Column 2 = 1-POISSON.DIST(1,mean,TRUE)
Column 3 = 1 - (1 - column 2)^2 Taking two 400 mL samples.
Column 4 = 1-POISSON.DIST(1,mean x 2,TRUE) Mean organism count in 800 mL = 2 x 400 mL

Plotted Column 1 vs. Columns 3 and 4, yielding graph. Shows slight difference, even preference for 1 800 mL sample.

Pretend this is homework but answer is real world application in food safety.