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Math Help - Stratified Sampling

  1. #1
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    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?
    Last edited by Niall2; March 16th 2008 at 12:42 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Niall2 View Post
    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
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  3. #3
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    Quote Originally Posted by Niall2 View Post
    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
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  4. #4
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    Quote Originally Posted by CaptainBlack View Post
    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?
    Last edited by Niall2; March 17th 2008 at 09:35 AM. Reason: spelling
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by Niall2 View Post
    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
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