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Math Help - clinical depression trial

  1. #1
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    clinical depression trial

    two clinical psychiatrists assessed five patients for depression, one using the Beck depression inventory and the other using the Hamilton rating scale for depression. the scores recorded for each scale are given in the following table:
     <br />
\begin{array}{c|ccccc}Scale&1&2&3&4&5\\\hline Beck&20&11&13&22&37\\Hamilton&22&14&10&17&31\\\hli  ne\end{array}<br />
    (a) are the two depression scales related? a regression analysis in R gave the following output:
     <br />
\begin{array}{ccc}\ &Estimate\ Std.&Error\\(Intercept)&3.7070&3.8433\\Beck&0.7327  &0.1704\end{array}<br />
    Residual standard error: 3.498 on 3 degrees of freedom

    Based on this analysis, perform a hypothesis test for association between the Hamilton and Beck scales

    (b) Kendall's \tau is a nonparametric measure of correlation based on concordant and discordant pairs. two points (x_{1},y_{1}) and (x_{2},y_{2}) are concordant if the signs of x_{2} - x_{1} and y_{2} - y_{1} match; otherwise they are discordant. for example, in this data, the pair (20, 22) and (11, 14) are concordant while the pair (20, 22) and (22, 17) are discordant.
    given the numbers of concordant and discordant pairs, c and d, respectively, Kendall's \tau is defined by
    \tau = \frac{c - d}{\frac{1}{2}n(n-1)}
    the difference divided by the total number of pairs. calculate the value of \tau for the relationship between the Hamilton and Beck scales in the data above.
    (c) based on the value from (b), use this approximation to perform a hypothesis test for association between the Hamilton and Beck scales based on Kendall's \tau.
    Last edited by wik_chick88; December 15th 2010 at 05:57 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by wik_chick88 View Post
    two clinical psychiatrists assessed five patients for depression, one using the Beck depression inventory and tyhe other using the Hamilton rating scale for depression. the scores recorded for each scale are given in the following table:
     <br />
\begin{array}{c|ccccc}Scale&1&2&3&4&5\\\hline Beck&20&11&13&22&37\\Hamilton&22&14&10&17&31\\\hli  ne\end{array}<br />
    (a) are the two depression scales related? a regression analysis in R gave the following output:
     <br />
\begin{array}{ccc}\ &Estimate\ Std.&Error\\(Intercept)&3.7070&3.8433\\Beck&0.7327  &0.1704\end{array}<br />
    Residual standard error: 3.498 on 3 degrees of freedom

    Based on this analysis, perform a hypothesis test for association between the Hamilton and Beck scales

    (b) Kendall's \tau is a nonparametric measure of correlation based on concordant and discordant pairs. two points (x_{1},y_{1}) and (x_{2},y_{2}) are concordant if the signs of x_{2} - x_{1} and y_{2} - y_{1} match; otherwise they are discordant. for example, in this data, the pair (20, 22) and (11, 14) are concordant while the pair (20, 22) and (22, 17) are discordant.
    given the numbers of concordant and discordant pairs, c and d, respectively, Kendall's \tau is defined by
    \tau = \frac{c - d}{\frac{1}{2}n(n-1)}
    the difference divided by the total number of pairs. calculate the value of \tau for the relationship between the Hamilton and Beck scales in the data above.
    (c) based on the value from (b), use this approximation to perform a hypothesis test for association between the Hamilton and Beck scales based on Kendall's \tau.
    Please post what you have already tried for this question.

    CB
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  3. #3
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    i have no idea where to even start?!
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