Standard error for unweighted kappa:
Method 1 is the simple estimate proposed by Cohen in his original paper on kappa:
Cohen, J. A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 213-220, 1960.
Formulaic and computational details for Method 1 can be viewed online in the Google Books preview of
Sheskin, D. Handbook of Parametric and Nonparametric Statistical Procedures. 3rd ed., CRM Press, 2004.
Method 2 is the more complex estimate described in
Fleiss, J.L., Cohen, J., and Everitt, B.S. Large sample standard errors of kappa and weighted kappa. Psychological Bulletin, 72, 323-327, 1969.
Formulaic and computational details for Method 2 can be viewed online in the Google Books preview of
Fleiss, J.L., et al. Statistical Methods for Rates and Proportions, New York, John Wiley & Sons, 2003.