Finding out whether a word occurs significantly more often in one text or corpus than in another is an important question in analysing corpora. As noted by Kilgarriff (Language is never, ever, ever, random, Corpus Linguistics and Linguistic Theory, 2005; 1(2): 263-76.), the use of the X2 and log-likelihood ratio tests is problematic in this context, as they are based on the assumption that all samples are statistically independent of each other. However, words within a text are not independent. As pointed out in Kilgarriff (Comparing corpora, International Journal of Corpus Linguistics, 2001; 6(1): 1-37) and Paquot and Bestgen (Distinctive words in academic writing: a comparison of three statistical tests for keyword extraction. In Jucker, A., Schreier, D., and Hundt, M. (eds), Corpora: Pragmatics and Discourse. Amsterdam: Rodopi, 2009, pp. 247-69), it is possible to represent the data differently and employ other tests, such that we assume independence at the level of texts rather than individual words. This allows us to account for the distribution of words within a corpus. In this article we compare the significance estimates of various statistical tests in a controlled resampling experiment and in a practical setting, studying differences between texts produced by male and female fiction writers in the British National Corpus. We find that the choice of the test, and hence data representation, matters. We conclude that significance testing can be used to find consequential differences between corpora, but that assuming independence between all words may lead to overestimating the significance of the observed differences, especially for poorly dispersed words. We recommend the use of the t-test, Wilcoxon ranksum test, or bootstrap test for comparing word frequencies across corpora.