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Test for equality of proportions in matched samples (Cochran's Q)

        cochran varlist [weight] [if exp] [in range] [, detail ]


    by ... : may be used with cochran; see help by.

    fweights are allowed with cochran; see help weights.


Description

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

    The chi-squared calculated by 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 mcc. An exact significance probability
    will be reported in this case.


Options

    detail specifies to display the proportions and counts (i.e. number of
        nonzero outcomes).


Saved Results

    Scalars:

    r(N)         number of cases
    r(chi2)      Cochran's Q
    r(df)        degrees of freedom
    r(p)         p-value
    r(p_exact)   exact p-value (if only two proportions are compared)

    Matrices:

    r(T)         proportions and counts


Methods and Formulas

    Cochran's Q is defined as

             c * (c-1) * sum_j ( T_j - T_bar )^2
        Q = -------------------------------------
             c * sum_i ( u_i ) - sum_i ( u_i^2 )

    where c is the number columns (= number of proportions = number of
    variables), T_j is the number of nonzero outcomes in the jth column,
    T_bar is the mean number of nonzero outcomes (i.e. the proportion of
    nonzero outcomes) per column, and u_i is the number of nonzero outcomes
    in the ith row (= number of nonzero outcomes in the ith observarion).

    For large samples, Q is chi-square distributed with (c-1) degrees of
    freedom.


Reference

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


Author

    Ben Jann, ETH Zurich, jann@soz.gess.ethz.ch


Also see