{smcl}
{* 27oct2004}{...}
{hline}
help for {hi:cochran}
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{title:Test for equality of proportions in matched samples (Cochran's Q)}

{p 8 15 2}
{cmd:cochran} {it:varlist} [{it:weight}] [{cmd:if} {it:exp}]
 [{cmd:in} {it:range}] [{cmd:,} {cmdab:d:etail} ]


{p 4 4 2} {cmd:by} {it:...} {cmd::} may be used with {cmd:cochran}; see help
{help by}.

{p 4 4 2} {cmd:fweight}s are allowed with {cmd:cochran}; see
help {help weights}.


{title:Description}

{p 4 4 2}{cmd:cochran} performs a test for equality of two or more proportions
in matched samples: Taking the 1-to-1 matching of observations into account,
{cmd:cochran} tests that the proportion of nonzero outcomes is constant for the
variables in {it:varlist}.

{p 4 4 2}The chi-squared calculated by {cmd:cochran} is known as Cochran's Q
(Cochran 1950). If only two proportions are compared, Cochran's Q is equal to
the McNemar chi-squared calculated by {help mcc}. An exact significance
probability will be reported in this case.


{title:Options}

{p 4 8 2} {cmd:detail} specifies to display the proportions and counts
(i.e. number of nonzero outcomes).


{title:Saved Results}

{p 4 4 2} Scalars:

{p 4 17 2} {cmd:r(N)}{space 9}number of cases{p_end}
{p 4 17 2} {cmd:r(chi2)}{space 6}Cochran's Q{p_end}
{p 4 17 2} {cmd:r(df)}{space 8}degrees of freedom{p_end}
{p 4 17 2} {cmd:r(p)}{space 9}p-value{p_end}
{p 4 17 2} {cmd:r(p_exact)}{space 3}exact p-value (if only two proportions are
compared)

{p 4 4 2} Matrices:

{p 4 17 2} {cmd:r(T)}{space 9}proportions and counts


{title:Methods and Formulas}

{p 4 4 2}Cochran's Q is defined as

             {it:c} * ({it:c}-1) * sum_{it:j} ( {it:T}_{it:j} - {it:T}_{it:bar} )^2
        {it:Q} = -------------------------------------
             {it:c} * sum_{it:i} ( {it:u}_{it:i} ) - sum_{it:i} ( {it:u}_{it:i}^2 )

{p 4 4 2}where {it:c} is the number columns (= number of proportions = number
of variables), {it:T}_{it:j} is the number of nonzero outcomes in the {it:j}th
column, {it:T}_{it:bar} is the mean number of nonzero outcomes (i.e. the
proportion of nonzero outcomes) per column, and {it:u}_{it:i} is the number of
nonzero outcomes in the {it:i}th row (= number of nonzero outcomes in the
{it:i}th observarion).

{p 4 4 2}For large samples, {it:Q} is chi-square distributed with ({it:c}-1)
degrees of freedom.


{title:Reference}

{p 4 8 2} Cochran, W. G. 1950. The Comparison of Percentages in Matched
Samples. {it:Biometrika} 37(3/4): 256-266.


{title:Author}

{p 4 4 2} Ben Jann, ETH Zurich, jann@soz.gess.ethz.ch


{title:Also see}

{p 4 13 2} Online:  help for {help mcc}