It's all in the question, really. This topic must have been raised and discussed before, but I can't seem to find a good reference just yet. I'm writing this paper where I make the case for a distinct construction (based, among other arguments, on the fact that its frequency has been increasing significantly over the years). But the still (arguably) low raw figures make the reviewers tick. I argue that the numbers in question are *not* low (especially because they now represent 17.5% of the uses of the main lexical at the heart of that construction). But I was hoping maybe there would be references that precisely discuss this issue, and especially that 'low' figures are still relevant (i.e. 'frequent enough') if they constitute a significant portion of an item's distribution. Any idea? Thanks!
Dear Benoit,
a seemingly simple question - but not really easy to answer. First of all, for statistical measurements, people will tell you that occurrence figures below five are too low. This makes sense: 1 occurrence out of three is 33.3% (nearly double the figure you give) but a single further occurrence makes this 2/3 while a single absence brings 0%. So, first of all: the basis has to be large enough so that a single occurence cannot completely change the figures. Beyond that, raw figures, in particularly when really large, can be equally deceptive: is a phenomenon valid when there are enough occurences - but what if it turns out thsat this is due to a single producer overusing it? Or it being confined to one particular text type? - That, in itself, is an interesting finding but cannot be generalised.
I would suggest to undertake a log-liklihood test to see if your figures really indicate anything of interest - it also helps to support your argument if it does! Here is an easy-to-use tool: https://ucrel.lancs.ac.uk/llwizard.html
best of luck!
While not a direct answer to your question, Gries & Ellis (2015) and the notion of dispersion may be useful here, as a low frequent but widely dispersed construction is more likely to be conventionalized than one that is only used by one speaker or in a very restricted context.
Further, it may be useful to take a look at studies that report word recognition and lexical decision tasks, as word frequency is often taken as a predictive factor. You won't get a hard cut-off point from them, but they do suggest that very low frequencies -- in the ball park of 1-10 w./million -- may not be entrenched (see e.g., Kinoshita 2006 and citations therein).
Dear Michael Pace-Sigge and Barthe Bloom,
Many thanks for your helpful comments! I'll look into the different options you mention. I've also received further references from colleagues. I'll make sure to take all of that into account when thinking about this. (The notion of 'threshold' really is what I have in mind, I suppose. So I'll definitely think about this and see how I can apply what you mention to my data.)
Thanks again!
Benoît
Dear Benoît,
I guess that the idea of applying statistical measures to constructions proposed by Michael Pace-Sigge is definitely a good one. I had the same problem and one of the reviewers suggested using log-likelihood instead of raw frequency in order to hedge against deceptive patterns of occurrence. In this regard, I highly recommend the books Statistics in Corpus Linguistics: A Practical Guide by Vaclav Brezina (2018) and The Statistics of Word Cooccurrences: Word Pairs and Collocations by Stefan Evert (2005). While reworking my paper, I created a log-likelihood calculator in MS Excel to assess the strength of collocation - all you need to do is to insert the frequency of node and collocate in the corpus as well as the frequency of their co-occurrence. If you want to test it out, I'd be glad to share and provide some additional commentaries. I hope that one day I'll be able to turn it into a proper desktop application.
I have the same problem when I study the lexicalisation of new phrases. The minimum quantitative threshold is hard to identify. Did you try to compare the figures with more "conventional" constructions to see how big the gap is? In my case it all depends on the corpus I choose. For instance, with a new phrase like "Haters gonna hate", the BNC says 0 and figures are rather low on many corpora but on corpora like iWeb or NOW, they're higher than very famous proverbs. May I ask what construction you are studying? Maybe it's a domain-specific one, or a pro-tem one, or one in the process of lexicalisation? Is it a "young" one?
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