Too Noisy at the Bottom: Why Gries’ (2008, 2020) Dispersion Measures Cannot Identify Unbiased Distributions of Words

ABSTRACT

Gries (2008, 2021) defined two dispersion measures able to alert corpus analysts to words that have a problematically limited distribution. Gries (2010, 2022) posited that these measures may additionally be relevant to language development research, as the learnability of a pattern may be predicted by the evenness of its distribution in corpora. However, both measures work by comparing vectors of observed and expected frequencies in partitioned corpora and this method cannot determine that a word is evenly distributed because it cannot distinguish the random noise inherent to an unbiased process from substantial non-random bias. An additional concern with the 2008 measure is raised: the 2008 measure is Manhattan distance scaled to the unit interval and, as such, it is extremely sensitive to the number of corpus parts because this choice sets the dimensionality of the measure space. In sum, this short analysis presents evidence that these measures should not be used to declare a pattern evenly distributed as neither can tell the difference between statistical noise and systematic bias.

Disclosure Statement

No potential conflict of interest was reported by the author.

Notes

1. N = f is the meaningful limit on corpus parts for DP. N > f requires we posit fractional occurrences of words in E – a condition which cannot be observed in O – while expanding O with elements = 0 which pins it to the surfaces of the measured space ensuring high DP. When N > f is used (e.g. Biber et al., 2016, p. 460), analysts are measuring only the expanding volume of the space, not dispersion.