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Math Help - Pooling in the Chi-squared test?

  1. #1
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    Pooling in the Chi-squared test?

    Hi, please take a look at this exam paper:
    http://mei.org.uk/files/papers/s307ja_k39h9.pdf
    Please read question 4(a) on page 4 of the pdf
    Now scroll down to page 11 of the pdf to see the mark scheme answer.

    What I don't understand is why they've pooled the first two groups.
    Also, how do you determine how many degrees of freedom are lost? In other words, when you're looking at the table of values for the Chi-squared distribution, how do you know what row to read off? This seems to require knowledge of how many degrees of freedom are lost, can someone remind me of to determine this?
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  2. #2
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    Quote Originally Posted by AAKhan07 View Post
    Hi, please take a look at this exam paper:
    http://mei.org.uk/files/papers/s307ja_k39h9.pdf
    Please read question 4(a) on page 4 of the pdf
    Now scroll down to page 11 of the pdf to see the mark scheme answer.

    What I don't understand is why they've pooled the first two groups.
    Also, how do you determine how many degrees of freedom are lost? In other words, when you're looking at the table of values for the Chi-squared distribution, how do you know what row to read off? This seems to require knowledge of how many degrees of freedom are lost, can someone remind me of to determine this?
    What I don't understand is why they've pooled the first two groups.
    There's a rule of thumb that classes need to have an observed frequency of 5 or more to use the chi-squared test. One remedy is to pool. That's why the first two groups were pooled (because the first group has an observed frequency less than 5).

    Also, how do you determine how many degrees of freedom are lost?
    The degrees of freedom is equal to the number of classes (after pooling) minus the number of parameters estimated from the population to calculate the expected frequencies (in this case two - the mean and the standard deviation of the normal distribution) minus 1.

    Therefore in this question, df = 6 - 2 - 1 = 3.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    There's a rule of thumb that classes need to have an observed frequency of 5 or more to use the chi-squared test. One remedy is to pool. That's why the first two groups were pooled (because the first group has an observed frequency less than 5).

    Regarding this, does the data have to be put into classes?. For example if the question just gave 22.0, 22.5, 23.0, 23.5, 24.0, 24.5 etc, with their observed frequencies. it'll be useful to know if the chi-square test only uses data when you categorise each of them into classes.
    Last edited by mr fantastic; January 16th 2009 at 05:20 AM. Reason: Fixed the quote tags
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    Quote Originally Posted by mr fantastic View Post
    There's a rule of thumb that classes need to have an observed frequency of 5 or more to use the chi-squared test. One remedy is to pool. That's why the first two groups were pooled (because the first group has an observed frequency less than 5).
    Its the expected frequencies in a cell that needs to be more than 5 not the observed (and it is also that no more than 20% of the cells should have expected frequencies less than 5)

    .
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  5. #5
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    Quote Originally Posted by Constatine11 View Post
    Its the expected frequencies in a cell that needs to be more than 5 not the observed (and it is also that no more than 20% of the cells should have expected frequencies less than 5)

    .
    Thanks for that. My muddle.
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