# Math Help - Stratified Sampling

1. ## Stratified Sampling

Here is the question:
When using stratified sampling, does everyone in the population have an equal chance of being selected?

My initial thought is that generally everyone does have an equal chance of being selected. But that is only true if everyone has the chance of being selected. By which I mean, it could be the case that one of the strata was so small that no one is chosen from that strata.
e.g. Choosing 100 people from a population of 100000 by stratified sampling with two strata: male and female. If there were only 20 males and 99980 females then 0 males would be chosen - so if you were a male you would have no chance of being selected.

Is this correct?
(Afterall, the method does mathematically give everyone an equal chance of being selected - the problem is that you cannot have a decimal number of people)

EDIT:
And 2ndly:
A secretary of a club with 120 branches and wants to collect a representative sample. She has a complete list of members classified by branches. She selects 4 branches at random and then 10 members at random from those 4 branches.
1. Would all members be equally likely to be chosen? Explain
2. Under what unlikely circumstances would all members be equally likely to be chosen?

I have few ideas on this question. Any help?

2. Originally Posted by Niall2
Here is the question:
When using stratified sampling, does everyone in the population have an equal chance of being selected?
Not in general, it depends on how the sizes of the samples for the strata are chosen.

If the strata sample sizes are proportional to the strata's representation in the population then eveyone would have an equal chance of being selected. But to reduce the variance of the the result often the sample size for strata are set proportional to the expected SD of the strata.

RonL

3. Originally Posted by Niall2
And 2ndly:
A secretary of a club with 120 branches and wants to collect a representative sample. She has a complete list of members classified by branches. She selects 4 branches at random and then 10 members at random from those 4 branches.
1. Would all members be equally likely to be chosen? Explain
2. Under what unlikely circumstances would all members be equally likely to be chosen?

I have few ideas on this question. Any help?
Suppose all the branches but one had 10 members, and the other had 1000 members, would all members
have an equal chance of being selected?

RonL

4. Originally Posted by CaptainBlack
Suppose all the branches but one had 10 members, and the other had 1000 members, would all members
have an equal chance of being selected?

RonL
I see.
So the unlikely circumstance in which they all had the same chance of being chosen is if all the branches had the same number of people?

5. Originally Posted by Niall2
I see.
So the unlikely circumstance in which they all had the same chance of being chosen is if all the branches had the same number of people?
Yes

RonL