# Thread: sample size - poisson dist'n?

1. ## sample size - poisson dist'n?

Hello,

I am designing a survey questionaire and need help estimating sample sizes.

The survey will ask the respondents about the number of a certain animal species seen in a given month. e.g., how many bears did you see?

Because this is count data (# of animals seen/person), I don't believe methods for normal distributions apply? (or do they?).

Can someone point me to an equation that will estimate the required sample size for these data?

(For the sake of an example, let's assume I want to estimate the mean with a margin of error of 5% and a 95% confidence interval. The population of people will vary, but lets use 200).

Thank you,
Shawn Morrison

2. Originally Posted by Ochotona
Hello,

I am designing a survey questionaire and need help estimating sample sizes.

The survey will ask the respondents about the number of a certain animal species seen in a given month. e.g., how many bears did you see?

Because this is count data (# of animals seen/person), I don't believe methods for normal distributions apply? (or do they?).

Can someone point me to an equation that will estimate the required sample size for these data?

(For the sake of an example, let's assume I want to estimate the mean with a margin of error of 5% and a 95% confidence interval. The population of people will vary, but lets use 200).

Thank you,
Shawn Morrison
There are at least three methods that I can think of for doing this:

1. Compute the distribution of mean number of sightings from a sample of size $N$, with mean number per sighter $\mu$, and then use that to determine the required sample size for the sort of mean number of sightings you are expecting (I suspect, but would have to do some research to confirm this, that with $N$ observers the distribution of the total number of sightings is Poisson with mean $N \mu$, where $\mu$ is the mean number of sightings from a single observer)

2. Generate approxinate distributions for the mean using a bootstrap technique.

3. Using the Chebyshev or Vysochanskiï-Petunin inequalities to give conservative estimates of the required sample size.

CB

3. Thank you - I'll try those ideas.