Extending the Cochran rule

We first describe a number of inter-related issues that need to be considered by the researcher when comparing frequencies of linguistic features in two or more corpora. We then describe the chi-squared and log-likelihood tests used in previous research for the comparison of word frequencies. Our focus, in this paper, is on the issue of reliability of the statistical tests, and we describe simulation experiments to compare the reliability of the chisquared and log-likelihood statistics under conditions of different-sized corpora and probability of a word occurring in text. We observe that the Cochran rule provides a good guide to accuracy of both statistics in general, but in some cases it needs to be extended. We conclude by recommending higher cut-off values for the Cochran rule at the 5%, 1% and 0.1% levels. In order to extend applicability of the frequency comparisons to expected values of 1 or more, use of the log-likelihood statistic is preferred over the chi-squared statistic, at the 0.01% level. The trade-off for corpus linguists is that the new critical value is 15.13.