sample again

[bartholomew]

Following my previous question I would like to ask another.

I know that the sample should be representative of the population.
But due to budget constraints the sample is smaller than it normally
would have been the case.

The target population is 1800.
80% White patients
20% non-white patients

As the sample has to be one hundred (suggested sampling method
is random stratified sampling) I fear that I might not see the picture
if I select only 20 Black patients.
Is it possible for the sample not to be proportionally representative?
I think it is, but do not know how many patients of each of the two groups
should be in the sample.

[WaldoMcFroog]

Firstly, you've going to have about +/- 9.5% margin of error on a 95% confidence level and you should declare this up front. Personally, I don't believe that your sample size is large enough to be trustworthy and any statistians reading your work will likely feel the same. Any trends could simply be the result of not having sufficient people surveyed.

You have two distinct sub-populations here - white and non-white. They are distinct - one cannot be in both, and collectively exhaustive - there are no other possibilities that a member of the population can be in, so that's good.

Random Stratified Sampling means that you have split out sub-groups (in your case White/Non-White) but within each one, you will pick the individuals to survey randomly. You have two choices:

1) Proportional Allocation - since you know your population is 20% non-white, you choose 20 individuals at random from the non-white members of the population.

2) Optimum allocation (or Disproportionate allocation) - Each stratum is proportionate to the standard deviation of the distribution of the variable. Larger samples are taken in the strata with the greatest variability to generate the least possible sampling variance. i.e. you have to know that this strata is going to be more varied, so need to include more. From what you've said, you don't know this, meaning 1) should be the preferred method.

This goes back to the size of sample again - it's not really big enough.

[Peter Pedant]

Hi BB me again

I wouldnt dream of adding to W McF'#s answer - but you deserve a medal for persistence.

There must be a statistician sort of near you, you can talk to ?

[Hamish]

What are you wanting to test? previously you mentioned looking for differances between two groups. Do you mean some on the drug and some on palcebo? or do you mean white vs black reactions?

If it is the latter I would have though you would need a 50:50 sample, but I'm no statastition (can't even speeel it!)