This paper considers the mean and variance of the statistic ψ*, which among others is useful in measuring agreement between two raters. Under the assumption of independent random raters, the distribution of ψ* and a test of significance are given. As the G index of Holley and Guilford is a special case of ψ*, the results may be applied for this index as well.
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References
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Holley, J. W. and Guilford, J. P. (1964). A note on the G index of agreement. Educational and Psychological Measurement, 24, 749-753.
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Lienert, G. A. (1972). Note on tests concerning the G index of agreement. Educational and Psychological Measurement, 32, 281-288.
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Viernstein, N. (1990). A coefficient for measuring the agreement on bipolar rating scales. Educational and Psychological Measurement, 50, 273-278.
