{smcl} {* 27oct2004}{...} {hline} help for {hi:cochran} {hline} {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}