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help for kapssi                                       (Author:  David Harrison)
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Sample size calculations for kappa

    Two unique raters, two ratings:

        kapssi kappa, { se(#) | diff(#) [level(#)] | n(#) } p1(#) [ p2(#)
               round ]

    Two or more (non-unique) raters, two ratings:

        kapssi kappa, { se(#) | diff(#) [level(#)] | n(#) } p(#) [ m(#) round
               ]


Description

    kapssi estimates required sample size for estimating the kappa-statistic
    of inter-rater reliability for a binary outcome (having postulated value
    kappa) with given standard error, or the standard error for a given
    sample size.  If n() is specified, kapssi computes standard error;
    otherwise it computes sample size.  kapssi is an immediate command; all
    of its arguments are numbers (see help immed).

    For two raters, the results are the same as produced by sskdlg or sskapp
    (except for rounding; see round option below), based on the asymptotic
    variance presented by Fleiss, Cohen and Everitt (1969).  Results for more
    than two raters are based on the asymptotic variance for the
    Fleiss-Cuzick estimator of kappa presented by Zou & Donner (2004) in the
    case of equal numbers of ratings for each subject.


Options

    se(#) specifies the standard error of kappa.

    diff(#) specifies the half width of the confidence interval for kappa as
        an alternative to the standard error.

    level(#) specifies the significance level for the confidence interval;
        the default is obtained from set level (see help level), usually
        level(95).

    n(#) specifies the sample size for which to calculate standard error.

    p1(#) specifies the proportion of positive results reported by rater 1
        (of two raters).

    p2(#) specifies the proportion of positive results reported by rater 2
        (of two raters); if p2 is not specified it is assumed to be equal to
        p1.

    p(#) specifies the overall proportion of positive results (multiple
        raters).

    m(#) specifies the number of raters; the default is m(2).

    round specifies that the sample size is to be rounded to the nearest
        integer; the default is to round up using the function ceil(). This
        allows reproducability of results for two raters produced by sskdlg
        or sskapp which both have this behaviour.


Examples

    Two raters.  Compute sample size given standard error:

        . kapssi .8, se(.1) p(.1)

    Compute sample size given half width of confidence interval:

        . kapssi .6, diff(.2) p1(.15) p2(.12) round

    This is equivalent to:

        . sskapp, p1(.15) p2(.12) diff(.2) kapp(.6)

    More than two raters.  Compute sample size:

        . kapssi .75, se(.12) p(.05) m(3)

    Compute standard error for given sample size:

        . kapssi .8, n(100) p(.12) m(4)


References

    Fleiss, J. L., Cohen, J. and Everitt, B.S. 1969. Large sample standard
    errors of kappa and weighted kappa. Psychological Bulletin 72: 323-327.

    Zou, G. and Donner, A. 2004. Confidence interval estimation of the
    intraclass correlation coefficient for binary outcome data. Biometrics
    60: 807-811.


Maintainer

    David A. Harrison
    Intensive Care National Audit & Research Centre
    david@icnarc.org


Also see

    Online:  help for kappa, sskdlg, sskapp, immed