Atkinson on phoneme inventories in Science

[Matthew Dryer]

There are three problems that I am aware of with the Atkinson paper, one 
minor, two serious.  My primary concern is the hypothesis that there is 
a positive correlation between population size and size of phoneme 
inventory.  Since his further "out-of-Africa" claims assumes the former, 
it's not clear that he has anything interesting to say about this if the 
former turns out to be false.

First, he claims that phoneme inventories are relatively small in North 
America.  Maddieson's WALS data does not provide data on overall 
inventory size, only on consonant inventory, vowel inventory, and 
complexity of tones.  Atkinson's way of deriving overall inventory size 
is apparently to treat these three variables equally.  However, this is 
not what is normally understood by inventory size.
Languages in North America tend to have large consonant inventories and 
small vowel inventories, but large overall inventories since large 
consonant inventory tends to lead to large overall inventory.  This is 
not as serious a problem as the next two, because if there IS a 
correlation between population size and Atkinson's metric, then that 
would be interesting.

Second, in order to test any crosslinguistic hypothesis, one needs to 
have a sample that is unbiased with respect to the phenomena being 
examined.  In general, this is true for the WALS languages, as long as 
one controls for genealogy and area.  But the WALS languages are a 
highly biased sample as far as population size is concerned.  This is 
because there is a very strong correlation between population size and 
availability of grammatical descriptions, especially in Europe, Asia and 
Africa.  In fact, in constructing the 200-language sample for WALS, we 
deliberately chose languages with larger speaker populations in the 
sense that we deliberately chose languages for which data was more 
readily available.  This bias itself renders Atkinson's claims suspect, 
but his further claims about distance from Africa are rendered further 
suspect since the population bias in the sample is lower for languages 
further from Africa.

Third, although Atkinson controlled for non-independence within 
families, he did not control for non-independence within areas and 
because he failed to do so, his claims in terms of statistical 
significance are invalid.  One of the goals of the WALS atlas is to show 
areal patterns.  One has only to look at Maddieson's WALS map for size 
of consonant inventories to see that there is a large area in northwest 
North America with large consonant inventories (with languages from many 
different families) and a similar area in southeast Asia (again with 
languages from many different families) and a large area in northern 
South America with small consonant inventories (again with languages 
from many different language families) and similarly for New Guinea.  In 
other words, size of inventory can be an areal phenomenon.

I have argued in many places that unless a correlation is found 
independently in all parts of the world (in my method, the six 
continental areas I use), then we cannot conclude that it is real.  Bill 
Croft says "I asked a couple of physicists with whom I collaborate about 
what to think of global correlations when those correlations are not 
found in most or all of the subpopulations that the data may be 
partitioned into (areal, phylogenetic, etc.). They both stated that a 
global correlation is statistically valid even if the same correlation 
does not exist in all the partitioned subpopulations."  But the big 
problem with the Atkinson paper and others like it is precisely that 
nonlinguists who are experts on statistics do not understand the 
peculiar nature of crosslinguistic data.  It is obviously the case in 
general that correlations over a domain can be valid even if they are 
not found in all subdomains.  But I argued in my 1989 paper on large 
linguistic areas that the only way to determine whether there is a 
global correlation is see whether it is true in all areas of the world. 
  This is actually something of an overstatement; there are other ways 
to control for areal factors.  But as a rule of thumb, if something is 
not found in all areas or most areas, one should be very suspicious that 
the apparent global correlation is simply an artifact of not controlling 
for area.

Bill's additional statement "One of them further added that another 
possible reason is that the subpopulation samples may be too small to 
provide a significant correlation one way or the other" also betrays a 
lack of awareness on the part of these physicists of the problem 
presented by areal phenomena.  With crosslinguistic typological data, it 
is to all intents and purposes LOGICALLY impossible to test for 
statistical significance WITHIN linguistic areas because there are such 
strong areal patterns within large areas that one cannot find enough 
independent cases to remotely approach statistical significance.  We 
cannot, for example, determine whether there is a correlation between 
population size and phoneme inventory size within Africa on the basis 
of, say, three languages.  But the areal patterns within Africa are such 
that one cannot find more than three or so languages that are 
genealogically and areally independent.  Linguists should be very wary 
of seeking the advice of nonlinguists regarding statistics.

Matthew

Bill Croft wrote:
> Atkinson argues for the existence of two correlations in a global sample 
> of phoneme inventories: a correlation between size of phoneme inventory 
> and distance from Africa, and a correlation between size of phoneme 
> inventory and size of the population of the speech community. Atkinson 
> needs the latter, phoneme-population correlation to justify his 
> founder-effect explanation for the former correlation. The 
> phoneme-population correlation was also identified by Hay and Bauer 
> (2007). (Hay and Bauer also test Pericliev's [2004] data and found, pace 
> Pericliev, that the correlation is also strong in his sample [Hay and 
> Bauer 2007:397].) Johanna Nichols reports in her post a tentative result 
> from her sample: she reports that the global correlation is present, but 
> a division of the sample into large areas shows that the correlation 
> does not exist, or is even negative, in some of the areas. On this 
> basis, Johanna writes, "If there is really a correlation between 
> population size and phoneme inventory size (or anything else), it should 
> hold within areas as well as worldwide." She concludes that the global 
> phoneme-population correlation is an artifact of population sizes in 
> Eurasia and Africa, and areality in Africa plus neighboring regions.
> 
> Interestingly, with Dunn et al., the shoe is on the other foot with 
> respect to global correlations and correlations in subpopulations. Here 
> it is Dunn et al. who argue against the global word-order correlations 
> manifested in Greenbergian word order universals. Dunn et al. argue that 
> a correlation between various pairs of word orders are supported in some 
> language families but not others. Hence word-order correlations are 
> lineage-specific (and culture-specific) rather than universal in the 
> Greenbergian sense. Dunn et al. divide the global sample into 
> phylogenetic subpopulations rather than areal subpopulations, but the 
> point is the same. (There are two differences between Dunn et al.'s 
> analysis and the Greenberg universals: the Greenberg universals are 
> synchronic, while Dunn et al's data is a sample of diachronic word order 
> changes; and the model that Dunn et al. tests is not the model implied 
> by Greenbergian universals. While these differences are important, as I 
> argued in my post on their paper, I believe they aren't relevant to the 
> point being made here.) And in the case of Dunn et al., Matthew Dryer 
> argued in a post that the lineage-specific correlations are random 
> effects and the globally identified Greenbergian word-order correlations 
> are real.
> 
> I asked a couple of physicists with whom I collaborate about what to 
> think of global correlations when those correlations are not found in 
> most or all of the subpopulations that the data may be partitioned into 
> (areal, phylogenetic, etc.). They both stated that a global correlation 
> is statistically valid even if the same correlation does not exist in 
> all the partitioned subpopulations. This situation may arise when 
> negative correlations or noncorrelations in some subpopulations are more 
> than compensated for by positive correlations in other subpopulations, 
> so that the global effect is a positive correlation. (One of them 
> further added that another possible reason is that the subpopulation 
> samples may be too small to provide a significant correlation one way or 
> the other.) When pressed further about why a global correlation would 
> not lead to the same correlations in (large enough) subpopulations, the 
> response was that, in the simplest case, X is dependent not only on Y 
> but also on a factor Z that varies considerably from subpopulation to 
> subpopulation; and that one would expect the same correlations in the 
> subpopulations if and only if most of the observed variation in X is due 
> to Y. In fact, this is not the case for the phoneme-population 
> correlation: Atkinson shows that language family membership, which 
> clearly varies by region, accounts for the greatest amount of variance 
> for phoneme inventory size. But the other correlations still hold 
> globally when combined with this factor (Atkinson, supplementary 
> materials, pp. 5-6). So it appears that the global phoneme-population 
> and word-order correlations are valid, that is, there is a factor (or 
> factors) Y that needs to be accounted for; but there is apparently also 
> a factor or factors Z that lead to areal- and/or phylogeny-specific 
> differences in the linguistic patterns.
> 
> Of course, correlation is not causation, as we all know. We have to find 
> an explanatory framework that allows us to say that when X correlates 
> with Y (and Z), there is a causal connection between X and Y (and Z). 
> One problem with the global phoneme-population correlation is that there 
> is no satisfactory explanation for it: even the linguists who found the 
> correlation have only a few suggestions that they do not consider to be 
> strong enough to offer as an explanation. Conversely, there is no 
> obvious explanation why word-order correlations might be lineage- or 
> culture-specific. For example, no cultural reason easily comes to mind 
> why Proto-Indo-Europeans and their descendants couple verb-object and 
> adposition-noun order, but Proto-Uto-Aztecans and their descendants do 
> not. Nor is there an obvious culture-specific nonlinguistic behavior 
> that might be causally connected to word-order patterns in the way that 
> spatial cognition has been shown to be connected to linguistic spatial 
> frames of reference by Levinson and his colleagues.
> 
> Bill
> 
> Hay, Jennifer and Laurie Bauer. 2007. Phoneme inventory size and 
> population size. Language 83.388-400.
> 
> Pericliev, Vladimir. 2004. There is no correlation between the size of a 
> community speaking a language and the size of the phonological inventory 
> of that language. Linguistic Typology 8.376-83.