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Nichols, Johanna (1992). Linguistic Diversity in Space and Time. Chicago: University of Chicago
Press.
— (2005). How many words do you need? A note on corpus and lexicon size. Electronic document.
http://emeld.org/school/classroom/text/lexicon-size.html
Nichols, Johanna & Balthasar Bickel (2005a). Locus of marking in the clause. In Haspelmath et
al. (eds.), 98–101.
— (2005b). Locus of marking: Whole-language typology. In Haspelmath et al. (eds.), 106–109.
Nichols, Johanna, David A. Peterson, & Jonathan Barnes (2004). Transitivizing and detransitivizing
languages. Linguistic Typology 8: 149–211.
Correlating phonological complexity: Data and validation
by IAN MADDIESON
1. Introduction
In a forthcoming paper I examine the patterns of correlation found in a large
sample of languages between several fairly simple indices of phonological
complexity. The indices examined all relate to phonological contrast and include
the number of contrastive consonant segments, the number of contrastive
vowel qualities, the total number of vowel nuclei, the presence of tonal contrast
and its degree of elaboration, and the complexity of permitted syllable
structure. Of course, other properties of phonological systems not considered
here, such as word structure templates or the degree of transparency in alternations,
also contribute to complexity. Across the language sample as a whole,
the analysis shows that of the ten possible pairwise comparisons between the
selected measures five show positive correlations, four show no correlation,
and one shows a negative correlation. The results are summarized in Table 1,
and discussed in more detail in Maddieson (forthcoming).
The data in Table 1 provide prima facie evidence against an apparently
widely-held belief among linguists that complexity in one sub-part of the grammar
of a language is likely to be compensated for by simplification in another.
Such a view seems to be based on the humanistic principle that all languages
Table 1. Direction of correlation between complexity measures
syllable complexity # consonants # V qualities # V nuclei
# consonants positive
# V qualities uncorrelated uncorrelated
# V nuclei uncorrelated uncorrelated positive
tone complexity negative positive positive positive
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Correlating phonological complexity 107
are to be held in equal esteem and are equally capable of serving the communicative
demands placed on them. In rejecting the notion of “primitive” languages
linguists seem to infer that a principle of equal complexity must apply.
As Akmajian et al. (1979: 4) put it “all known languages are at a similar level of
complexity and detail – there is no such thing as a primitive human language”.
From this point of view it might seem a logical further step to hypothesize that
languages will undergo adjustments to equalize their overall complexity across
different subsystems.
As far as phonology is concerned it seems to be widely believed (though
such beliefs are rarely expressed in print) that, for example, a language with a
large number of distinct consonants is likely to have a small number of vowels,
or that a language with an elaborated tone inventory will have a tendency to
simple syllable structure. These are two of the issues that the analyses summarized
in Table 1 were designed to examine. But the appropriate way to conduct
such an analysis of a sample of languages and what confidence to place in the
results remain very open questions for linguists. The focus of this contribution
will be on one of the correlations noted in the table, the positive correlation
between syllable complexity and size of consonant inventory, and on some of
the possible strategies to test its reliability. Before proceeding further it may be
worth emphasizing that this correlation is not an automatic consequence of any
necessity to have a large consonant inventory in order to make complex syllables.
A small inventory – and the smallest contains six consonants – could be
employed to create many varied strings of consonants in both onset and coda
positions of syllables. A complex syllable can be created from an inventory of
two consonants, as in English stoats (/stoUts/). With just these consonants even
more complex syllabic structures could easily be constructed, such as /stsotst/.
The manner of compilation of the language sample used will first be described,
then the global result for the correlation in question presented. The
remainder of the article will discuss various strategies for testing the validity of
the result. In this discussion the importance of identifying outliers when means
of numerical indices are being examined will emerge, as well as issues concerning
sampling procedures. Some initial steps towards the use of re-sampling
strategies will be proposed.
2. The language sample
The sample of languages analyzed in the present study is essentially an expanded
version of the UCLA Phonological Segment Inventory Database
(UPSID) sample described in Maddieson (1984). This was earlier extended
from 317 to 451 languages for a version distributed as an interactive database
(Maddieson & Precoda 1990). At both these stages, selection of languages for
inclusion was governed by a quota principle seeking maximum genetic diBrought
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108 Ian Maddieson
versity among extant languages (and those spoken recently enough to have
been described by linguistically sophisticated observers from direct experience).
More recently, the author’s participation in the World Atlas of Language
Structures (WALS) project (Haspelmath et al. (eds.) 2005) led to the merging of
the UPSID sample with the 200 languages chosen as the core sample for WALS.
Although genetic diversity was a major goal of the WALS sample, a number of
other factors also played a role in the selection, including the political importance
of a language, the availability of a full-length grammar, the presence of
the language in other typological samples and a desire for wide geographical
coverage. Due to overlapping membership of the UPSID and WALS samples
this resulted in a merged sample of about 520 languages. As part of a project to
more fully examine geographical distribution of phonological characteristics
of languages, this database is continuing to be enlarged, with the intention of
reaching a total of 1000 or so languages. At the time of writing the database
includes 621 languages, with the data for different languages at varying levels
of completeness.
The addition of more languages, and in particular the relaxation of the requirement
that no pair of closely related languages be included, changes the
representativity of the sample. On the one hand, including more languages
means of course that the range of diversity among languages has a greater
chance of being better represented. Naturally, properties that are rare in the
world’s languages are more likely to be found in at least one of the sample
languages as more and more are included. On the other hand, the relative frequency
with which particular characteristics are represented may be increasingly
distorted by factors such as the aim of including languages from geographical
areas that would otherwise be sparsely sampled, and the inequality
of availability of information on languages from different families and parts of
the world. These factors are likely to result in certain language families being
overrepresented in comparison with the numbers that would be included in the
kind of genetically stratified sample that is most often proposed as the foundation
of quantitative typological research (Bell 1978, see also discussions by
Perkins 2001, Cysouw forthcoming). Such concerns make it even more critical
to consider ways of testing how meaningful any particular result extracted from
the data is.
3. Overall correlation of syllable structure type and consonant inventory
size
The result that will be the focus of this article is the finding of a positive overall
correlation between the two parameters of syllable complexity and consonant
inventory size. Syllable complexity is a ranked categorial value based on
the maximally complex syllable type that is permitted in the language. It has
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Correlating phonological complexity 109
three values, Simple, Moderate, and Complex. The structure of onsets and of
codas are both taken into account in this evaluation, but nuclei are not considered
as contributing to syllable complexity. Languages with Simple syllable
structure are those which do not permit any elaboration of the onset beyond
a single consonant and do not permit any codas. In other words they permit
only (C)V syllables. Among languages in this category are Yoruba, Ju|’hoan,
Maori, and Guaraní. For example, verbs in Yoruba typically consist of a single
CV syllable, such as /bO/ ‘come’ or /
>
kpa/ ‘hit, kill’. Languages with a Moderate
level of syllabic complexity are those in which the coda may contain not
more than one consonant, and the onsets are limited to a single consonant or
a restricted set of two-consonant clusters having the most common structural
patterns, typically an obstruent followed by a glide or liquid (the 30 language
sample used in Maddieson (1992) had shown that simple codas and minimally
elaborated onsets tend to co-occur in languages). Among languages in this class
are Ewe, Dadibi, Nahuatl, Somali, Yanyuwa, Sundanese, Thai, and Mandarin.
Ewe and the New Guinea language Dadibi allow onsets with a glide or liquid
in second position, but no codas. Nahuatl, Somali, and Yanyuwa have no tautosyllabic
clusters, but allow a single coda consonant. Sundanese, Thai, and
Mandarin allow single codas as well as onset clusters with liquid or glide as
C2. In Mandarin the “medials” of the traditional analysis of Chinese syllables
are treated as glides in an onset cluster. The most complex Mandarin syllable
thus has a structure like that in words like /ljâN/ ‘bright’. Languages which
permit a wide range of onset clusters, or which permit clusters in the coda position
are classified as belonging to the Complex syllable category. Languages
in this class include Georgian, Lushootseed, Soqotri, and French. Some Georgian
examples of complex syllables are /prxiv/ ‘on foot’ and /vxetkt/ ‘we are
splitting’; Lushootseed examples include /sqibkw
’/ ‘octopus, squid’, /q’tsab/
‘lack’, /sxw
qw
’up/ ‘Green River’, and /sup’qs/ ‘hair seal’; French examples include
/stKikt/ ‘strict’, /klwatK/ ‘cloister’, and /tK4izm/ ‘truism’. It should be
noted that these classifications are only in terms of the maximal syllable elaboration
permitted, and languages may differ considerably in how frequently
the more complex patterns occur in the lexicon or in text. Recent international
loan vocabulary is excluded from evaluation of a language’s syllable complexity
category.
Languages in the Moderate class are considerably more frequent than either
of the other types. Of the 515 languages in the current sample for which values
of both syllable complexity and consonant inventory size are entered, 294 are
Moderate (57.1 %), while just 62 are Simple (12.0 %), and 159 are Complex
(30.9 %).
The relationship of syllable type to the number of consonants in the inventory
is examined in some detail here. The size of the inventory is a straightforward
numerical index – in the current sample ranging from a low of 6 to a
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110 Ian Maddieson
high of 128. For many languages the consonant inventory size is a relatively
uncontroversial datum, although there are plenty of cases which are open to
varying interpretations and for some languages the data may be unreliable. An
advantage of using a large sample of languages is that errors in either direction
are more likely to cancel each other out in an analysis of the aggregate. The
comparison of the two variables is performed in two ways, using either all the
515 available languages or excluding a small number with what are considered
to be outlier values for the number of consonants. An outlier is a value that is
far from the range of the majority of the data; as a rule of thumb an outlier is
often defined as a value more than two standard deviations from the mean. In
the entire sample the mean number of consonants per language is 22.72 with a
standard deviation of 10.65.
When the set of languages is divided by syllable category, there are on average
more consonants in the inventories of languages with complex syllable
structures than in languages with moderately complex syllable structures and
the least in languages with simple syllable structure. This result is shown graphically
in the left-hand panel of Figure 1. In an analysis of variance, syllable category
has a significant effect on consonant inventory size (F.2;512/ D 11:097,
p < :0001), but in a post-hoc comparison of means using Fisher’s PLSD (Protected
Least Significant Difference) test adjusted for unequal cell sizes the difference
between Moderate and Simple categories does not reach significance.
Since outlier values can have distorting effects on analyses based on means,
the analysis was repeated excluding those languages with consonant inventories
more than two standard deviations from the mean following the common
rule of thumb used to define outliers. This results in excluding the 18 languages
with 45 or more consonants, or about 3.5 % of the sample. Not surprisingly,
this exclusion results in lower means for the number of consonants, as shown
in the right-hand panel of Figure 1, with a particularly marked reduction in the
mean for Simple languages. Analysis of variance of this reduced set of languages
shows a highly significant effect of syllable type on size of consonant
inventory (F.2;494/ D 28:87, p < :0001). In this case all post-hoc comparison
of means are significant at p < :002 or better. Finding a significant difference
between Moderate and Simple categories is not due to exclusion of a disproportionate
number of outlier languages with Simple syllable structure. In fact,
only two languages are excluded from this category (3.2 %), compared to ten
removed from the Moderate category (3.4 %) and six from the Complex category
(3.8 %). However, since the number of Simple languages is the smallest
the exclusion of any language has a greater effect on the mean, and among
the languages excluded is Ju|’hoan, which has the second highest number of
consonants (92) of any language in the sample.
Since means can be misleading indicators of group differences if distributions
of values within the groups are non-normal, the data were also examined
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Correlating phonological complexity 111
15
17
19
21
23
25
27
Complex Moderate Simple
25.74
21.81
19.31
mean#ofconsonants
mean#ofconsonants
24.58
20.50
17.45
15
17
19
21
23
25
27
Complex Moderate Simple
Figure 1. Mean number of consonants by syllable complexity class. On the left, analysis with all
languages included; on the right with exclusion of languages with more than 44 consonants.
to see how well the three groups of languages meet the assumption of normality.
Histograms of the number of languages with given sizes of consonant
inventories for each syllable category are presented in Figure 2 together with
the values for skewness and kurtosis. Outliers, as defined above, are excluded
from these figures and calculations. A best fit to a normal distribution curve
is superimposed on each of the histograms. These plots show that the normal
fit is good for Complex and Moderate languages, and there are low values for
skewness and kurtosis in these groups. Skewness is a measure of how equally
the values are distributed above and below the mean, kurtosis a measure of
of how peaked the distribution is. In a perfectly normal distribution both are
zero; a value above 3 is usually considered excessive. A normal fit is somewhat
less appropriate for Simple languages. Nonetheless, the skewness and
kurtosis of this distribution are not excessive. The platykurtic (flat) peak is in
part attributable to the fact that the number of languages in this category is the
lowest.
Figure 2 also confirms that the “center of gravity” of the distribution is lower
as syllable structure is simpler. The midpoints of the distributions shown in
Figure 2 can be expressed by the medians, which increase with an increase in
syllable complexity. For the Complex languages the median number of consonants
in the inventory is 24, for Moderate languages the median is 20, and
for Simple language the median is 17. If outliers are included, the median for
Simple languages increases to 18, but the others do not change. For the entire
sample the median is 20 excluding outliers, which increases to 21 when the
outliers are included.
The analyses presented above demonstrate that in this large sample of languages
rather than complexity in syllable structure being compensated by simplicity
in consonant inventory, there is a tendency for consonant inventories to
be more elaborated in languages with increasing levels of syllabic complexity.
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112 Ian Maddieson
size of consonant inventory
numberoflanguages
Complex
0
2
4
6
8
10
12
14
5 10 15 20 25 30 35 40
Skewness = 0.446
Kurtosis = -0.245
Moderate
0
5
10
15
20
5 10 15 20 25 30 35 40
Skewness = 0.815
Kurtosis = 0.399
Simple
0
1
2
3
4
5
6
7
5 10 15 20 25 30 35 40
Skewness = 1.240
Kurtosis = 2.437
numberoflanguagesnumberoflanguages
Figure 2. Histograms of the number of languages with given consonant inventory size, by syllable
complexity category
It has been shown that the differences between the means of consonant inventory
size across the syllable complexity categories are significant, and that
it is appropriate to take the means as representing the within-group distribu-
tions.
This result is over the surveyed languages as a whole, but what does this
mean? Can the trend discovered be taken as general or does it reflect strong
but local tendencies – patterns that are particularly strong in certain areas or
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Correlating phonological complexity 113
language families? Are there imbalances in the sample which risk creating distortions
in the results?
4. Validation by areal sub-samples
Various methods have been suggested to test the generality and validity of results
in large language samples. One is to divide the sample on areal/genetic
lines and look for the repetition of a pattern across the divisions, either in the
aggregate of the languages in each division or within genetic units judged to
represent comparable historical depths to each other. This approach has been
particularly advocated by Dryer (e.g., 1989, 1992, 2003) and also widely employed
by Nichols (e.g., 1992). Dryer (1989) originally suggested using five divisions
(cf. Maddieson 1991) but in later work has used six. Nichols (1992) employed
a variety of groupings ranging from just three macro-areas to as many
as twelve smaller areal groups, as well as using alternate cross-cutting purely
genetic and contact-based groupings. In the present analysis six areal/genetic
groupings are used which are similar to Dryer’s but differ in some details.
The groups are based primarily on the continental landmasses and the major
language families which are indigenous to and “anchored” on these landmasses.
All members belonging to a given language family are assigned to a
single area even when the dispersion of the family crosses the areal divisions
employed. In other words, in cases where strictly geographical and genetic affiliations
are in conflict, the genetic relationship between languages are given
priority. The six groups and the number of languages in each group in the 515
language sample analyzed here are shown in Table 2.
The “Europe, West & South Asia” area covers Europe, Asia Minor, and the
Indian subcontinent as well as Siberia and the rest of Asian Russia. This is
home to several large language families such as Indo-European, Dravidian,
Altaic, and Uralic, as well as smaller groups such as the Caucasian families
and Chukchi-Kamchatkan and isolates like Basque and Burushaski. Japanese,
Korean, and Ainu are taken to be Altaic languages and so fall in this group
despite being outside the geographical limits. Creoles lexically based on IndoTable
2. Areal/genetic groupings
Area Number of languages in sample
Europe, West & South Asia 74
East & South-East Asia 102
Africa 125
North America 66
South & Central America 70
Australia & New Guinea 78
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114 Ian Maddieson
European languages are grouped with Indo-European for want of a better clas-
sification.
The “East & South-East Asia” area covers China, the Indo-Chinese peninsula,
and island Asia. The main language families are Sino-Tibetan, AustroAsiatic,
Tai-Kadai, and Austronesian. Since the Austronesian family is anchored
in this area, the many Austronesian languages spoken outside the area
(e.g., Malagasy, Iaai, Maori, Rapanui) are included in this group.
“Africa” is simply the African continent and its adjacent islands. All languages
in the large Niger-Congo, Nilo-Saharan and Afro-Asiatic families are
included in this group as well as the languages in the Southern African “Khoisan”
groups and the probable isolates Hadza and Sandawe. The main mismatch
with the geographical limits concerns those Afro-Asiatic languages spoken in
Asia Minor or adjoining areas of Europe, which are included in this group.
“North America” is geographically that part of the Americas north(-west)
of the Isthmus of Tehuantepec in southern Mexico. It includes Greenland and
the Aleutian islands and the major islands of the Caribbean. There are numerous
language families which are entirely indigenous to this geographical
area, including Na-Dene, Eskimo-Aleut, Uto-Aztecan, Algonquian, Tanoan,
Wakashan, Hokan, and Totonacan among others. Oto-Manguean, Mixe-Zoque,
and Huavean languages are also classed with the North American languages although
some are found at or just south(-east) of the Isthmus.
“South & Central America” is that part of the Americas to the south(-east)
of the Isthmus of Tehuantepec. This area includes the Yucatán peninsula of
Mexico as well as the countries traditionally considered to form Central and
South America. A number of well-recognized indigenous language families
such as Cariban, Arawakan, Chibchan, Je, Tupian, and Mayan are included
here as well as other languages and groups whose genetic affiliations are less
well understood.
The final area, labeled “Australia & New Guinea”, geographically covers
the area often referred to as Oceania in British usage, namely Australia, New
Zealand, and New Guinea and the other islands of Melanesia, as well as Micronesia
and Polynesia. Since many of the languages spoken in this area are
Austronesian languages and these are included in the East and South-East
Asia group, the only languages in this group are the indigenous languages
of Australia and the “Papuan” languages. Papuan is a cover term for all the
non-Austronesian languages of island Asia and Melanesia including the large
Trans-New Guinea family as well as other smaller groupings spoken in parts
of Indonesia, Papua New Guinea, and the Solomon Islands whose historical
relationships are not yet well understood.
Table 2 shows that the numbers of languages in the current sample from the
different areas are quite unequal. In particular, there are almost twice as many
languages from Africa as from North America. This specific imbalance reflects
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Correlating phonological complexity 115
Table 3. Numbers of languages in areal/genetic groups by syllable complexity category
Europe,West&
SouthAsia
East&
South-EastAsia
Africa
NorthAmerica
South&
CentralAmerica
Australia&
NewGuinea
Complex 55 20 24 35 10 15
Moderate 19 72 83 29 39 52
Simple 0 10 18 2 21 11
partly the fact that the African area has had more effort invested in compilation
of the sample at its present stage, but also the fact that a very large number
of languages have been recognized in Africa and most of them continue to
be spoken daily whereas many indigenous languages of North America were
already lost from daily use before being adequately described.
The breakdown of the languages in the sample by areal/genetic groupings
and syllable complexity category is given in Table 3. The table reveals salient
differences among the groupings in terms of relative frequency of the syllable
types. In four groups, Moderate languages are predominant, as in the entire
sample, but in the Europe, West & South Asia group and in North America
Complex languages are most frequent. No area has a majority of Simple languages,
but their proportion is greatest in South and Central America.
In order to examine the relationship between the two variables of interest in
each area a sufficent number of cases must occur in each cell of this table. Since
there are no cases of Simple syllable structure in the languages in the first area
(Europe, West & South Asia), and only two in North America, these areas must
be omitted from any area-by-area comparison involving all three syllable complexity
classes. The mean consonant inventory size by syllable category in the
remaining four groupings is shown in Figure 3. In the upper panel all languages
in the four groups are included, a total of 375, whereas in the lower panel outliers,
as defined earlier, are excluded. The exclusion removes two languages
from the East & South-East Asia group, one from Australia & New Guinea,
but eight from Africa. A two-way analysis of variance with area and syllable
category as main effects shows that there is, as expected, a highly significant
effect of area on consonant inventory size (F.3;363/ D 13:209, p < :0001),
with all pairwise comparisons being significant at better than p < :004 except
for that between South America and Australia & New Guinea, which are
not significantly different. Syllable category does not have a significant effect.
However, when outliers are excluded there is a significant main effect of sylBrought
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116 Ian Maddieson
meansizeofconsonant
inventory:alllanguages
meansizeofconsonant
inventory:outliersexcluded
0
5
10
15
20
25
30
Simple
Moderate
Complex
E, SE Asia Africa
C&SAmerica
Aust, N Guinea
Simple
Moderate
Complex
E, SE Asia Africa Aust, N Guinea
0
5
10
15
20
25
30
C&SAmerica
Figure 3. Histograms of mean consonant inventory size by syllable complexity category across
four areal/genetic language groupings. Upper panel: all languages included; lower panel: outliers
excluded.
lable complexity categories (F.2;351/ D 8:867, p < :0002). With the outliers
included both the East & South-East Asia and Africa groups show exceptions
to the monotonic decrease of mean consonant inventory with simpler syllable
type, and the Australia & New Guinea group shows virtually no difference
across the syllable complexity classes. When outliers are excluded, there are
no direct counterexamples to the pattern found in the overall results as shown
in Figure 1, and replicated most clearly in the Central & South American group
in Figure 3.
Moderate and Complex languages can be compared in the two remaining
areal groupings, as shown in Figure 4, on the left with outliers included, and
on the right with outliers excluded. Exclusion of outliers removes only one
language from the North American group, and five (all from Caucasian families)
from the Europe, West & South Asia grouping. In a two-way analysis of
variance, there is no significant difference in mean consonant inventory size
between these areas, but a highly significant difference between the Complex
and Moderate syllable categories, whether outliers are included or excluded (in
the latter case, F.1;128/ D 16:519, p < :0001).
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Correlating phonological complexity 117meansizeofconsonant
inventory:alllanguages
meansizeofconsonant
inventory:outliersexcluded
0
5
10
15
20
25
30
0
5
10
15
20
25
30
Moderate
Complex
N AmericaEurope,
W&S Asia
N AmericaEurope,
W&S Asia
Figure 4. Histograms of mean consonant inventory size by syllable complexity category for remaining
areal/genetic language groupings. Left panel: all languages included; right panel: outliers
excluded.
In summary, although the syllable complexity patterns are unequally distributed
among the areal/genetic groupings, there is good evidence that the
correlation between consonant inventory size and syllable complexity is not a
localized pattern. When the distorting effect of outliers is removed, Complex
languages have a saliently higher mean consonant inventory size than Moderate
ones in four of the six areas (in Europe, West & South Asia, Africa,
North America, and Central & South America), while in the remaining two
areas the means are roughly equal. In the three of the four areas in which Moderate
and Simple languages can be compared, the Moderate languages have
higher mean consonant inventory size than Simple ones (in East & South-East
Asia, Central & South America, and Australia & New Guinea), the exception
being Africa where Moderate and Simple language means are similar. It follows
from the foregoing that in each of these four areas Complex languages
have higher mean consonant inventory size than Simple ones. Of the ten possible
within-area comparisons between a given syllable complexity level and
the next lower-ranked level, seven show that mean consonant inventory size is
greater in the more complex syllable class, and in five of these the difference
is statistically significant (using Fisher’s PLSD, with significance levels ranging
from .0341 to .0016) despite the small number of cases in several of the
cells being compared. These statistically significant comparisons occur in five
different areas, Africa being the only area in which a significant difference is
not found. The remaining three within-area comparisons show roughly equal
mean numbers of consonants. No comparison shows a larger mean consonant
inventory size in the less complex syllable class.
In employing a within-area analysis procedure the analysis above is similar
in certain respects to the approach taken by Dryer, but it differs significantly
in not employing any subsetting by genera. Dryer looks for a “majority vote”
among genera rather than among languages in each area. A genus is loosely deBrought
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118 Ian Maddieson
fined as a genetic group “roughly comparable in time depth to the subfamilies
of Indo-European” (Dryer 1992: 83–84). Since Dryer is dealing with relations
between binary categories his method is to count the number of genera in which
a hypothetically related pair of values occurs and compare that with the number
where other pairings occur. If the languages in a genus are not uniform, the
genus will be counted more than once. Dealing with a numerical variable, as
in the present study, it is not possible to follow a directly analogous procedure.
However, given a classification into genera, it would be possible to calculate
the mean for each genus and then average these means, so that each genus
contributes equally to the areal mean. Alternatively, the consonant inventory
size variable could be divided into binary categories (languages above the median,
vs. those below) and a procedure similar to Dryer’s applied. Neither of
these steps have been pursued, in part because I am less confident than Dryer
(and less confident than I used to feel) that comparable genera can in fact be
established around the world on the basis of current knowledge.
The results in this section can be taken as sufficient to reject any suggestion
that the overall correlation found in the sample is the result of a particularly
strong trend in the languages of just one or two given areas or families which
swamps weaker contrary trends outside those groups. This strengthens the case
for rejecting the hypothesis of compensation between the two parameters being
compared. But can this result be taken to indicate that there is actually a general
trend for increase in syllabic complexity and elaboration of consonant inventory
to go together in natural spoken human languages? Although individual
languages vary a great deal in how the two parameters match up (and languages
with simple syllable structure but large consonant inventories or with complex
syllable structure and small consonant inventories certainly both occur), is it
reasonable to conclude that the paths of natural historical linguistic change are
in general more likely to create positively correlated patterns of complexity?
To support such a conclusion some of the well-known problems concerning
construction and analysis of large language samples (which led Dryer to adopt
the strategy he employs) must be confronted. These will be briefly discussed
in the following section. Various sub-sampling strategies designed to address
(some of) these problems will then be presented and their outcomes examined
in an attempt to evaluate if the general trend found in the aggregate data should
be considered a meaningful and reliable result.
5. Sampling and re-sampling strategies
The principal concern raised with large language samples has been over the
issue of independence of the entries selected. Independence has a number of
meanings in this context, and which of these aspects are relevant – and the extent
to which they raise concern – depends on how the sample is to be used. One
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Correlating phonological complexity 119
meaning concerns whether the chance of any given language being included in
the sample is independent of the chance of another language being included.
Random sampling can ensure independence of this kind. Given a list of the currently
extant (or recently spoken) languages, it should be possible to construct
a random sample of this population. However, there are two serious problems
in constructing such a sample. The first is that there is in fact no reliable list
of languages available, and no immediate possibility of this being constructed,
despite admirable attempts to approach this goal, notably in the compilation
of the Ethnologue, now in its fifteenth edition (Gordon (ed.) 2005). The difficulties
are twofold. First, knowledge of linguistic diversity “on the ground”
remains quite unequal across different areas of the world. Secondly, and perhaps
more critical, any enumeration of the number of languages depends on
the establishment and consistent application of criteria as to what constitutes a
separate language (if that is even possible). It seems apparent that in available
lists, quite uneven criteria have been applied. For example, the Ethnologue lists
a total of 35 Arabic languages, but just 14 Sinitic languages in China. Many observers
feel that Chinese subsumes a greater divergence of linguistic varieties
than Arabic.
Not only is there a dearth of knowledge about the number of languages in
existence, but biases are introduced into the information that is available by the
fact that linguists frequently tend to keep working in an area or language family
they know, so that related or adjacent languages are more likely to gain documentation.
Because not merely knowledge of the existence of some language
but the appropriate data on the language for the intended analysis is required,
this factor compromises the independence of the available sample points to
some difficult to quantify degree.
A second meaning of independence of samples concerns whether the data
value or values for a chosen sample language is or are independent of those
of other languages sampled. This factor is the one that has received the most
discussion, and has most influenced the efforts to design sampling strategies. A
pair of languages that descend from a common parent, or a pair whose speakers
have been in contact with each other over a period of time, are generally
assumed to be more likely to share features than a pair of languages not known
to have a common parent, nor to have been in contact. The importance given to
this sense of independence derives from the purpose for which most language
samples are assembled. Relatively few researchers in the domain of language
typology and universals are interested in the frequency or contingency relations
of properties as they are distributed across the universe of extant languages –
which is the universe that language samples can most realistically hope to represent.
Instead it is often hoped to provide a foundation to make, as Perkins
(2001: 423) puts it, “inferences about language, the general faculty of which
individual languages are instances”. It may be useful to conceptualize this goal
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120 Ian Maddieson
as a search for those patterns that would still hold true if the history of humankind
since the birth of language could be re-run multiple times with quite
different probablities for the survival and extinction of given languages over
the millennia. Since we only have one history to deal with, we cannot actually
compare multiple outcomes. Most typologists seem to feel that the best
that can be done is to structure the sample so that relatively high nodes in the
genetic trees of extant language families determine sampling strata (Nichols
2003 demurs in proposing a primarily areal sampling strategy – as used by
Shosted 2006). Beyond this general agreement, a variety of strategies has been
proposed, ranging from those whose selection criteria is a largely intuitive determination
of historical depth (Maddieson 1984, Bybee et al. 1994) to those
which use a computation of branching complexity of family trees (Rijkhoff &
Bakker 1998), and those which include prior tests for the association of variables
of interest before sample size is determined (Perkins 1989, Stephens &
Justeson 1984). Here we wish to suggest that sub-sampling and re-sampling
techniques should be more seriously considered by typologists, and we take a
few tentative steps in that direction.
Using a small randomly-drawn sub-sample from the larger sample may be
the best that can be done to approximate a random sample of languages. If
the sub-sample’s size is small it is likely to be constructed in a way that also
satisfies the desire for only largely unrelated and non-adjacent languages to be
included. The process can be repeated and an average result over a number of
trials obtained in a similar fashion to the way that jackknifing techniques are
used in cases where few (independent) data points are available. The purpose
is to estimate how great the chance variation contributed by sample structure
is, and to use this to determine the reliability of any result. The mean result
obtained by selecting five random sub-samples of 30 languages each is shown
in Figure 5. Random number variables were generated using a function in the
Statview program (SAS Institute 1992–1998) for the purpose and the list of
15
17
19
21
23
25
27
24.7
21.3
16.1
Complex Moderate Simple
mean#ofconsonants
Figure 5. Mean number of consonants by syllable category in five random samples of 30 languages
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Correlating phonological complexity 121
languages then sorted by ordering the random numbers and picking the 30
languages aligned with the lowest numbers. Outliers which would have been
picked by this process were excluded and the next language taken (exclusions
ranged from 0 to 2 in the 5 trials). Other than this, any language had an equal
chance of being selected, that is, no constraint against the same language occurring
in more than one sub-sample was enforced, nor was the selection “edited”
to meet any areal or genetic diversity criteria. Except for the fact that two of the
five sub-samples included just one North American language (against an expected
four or so), the sub-samples generally had a good balance across areas
and languages families. A monotonically decreasingly mean number of consonants
was found with decreasing syllable complexity. Across this relatively
small number of trials, the grand means of the Complex and Moderate sets are
both significantly different (by Fisher’s PLSD) from that of the Simple sets at
at least the .007 level. The individual sub-sample means for the Complex sets
range between 20.8 and 28.0 (s.d. 2.76), for the Moderate sets between 19.3
and 25.8 (s.d. 2.64), and for the Simple sets between 14.5 and 19.0 (s.d. 2.04).
This variation provides the estimate of the random component due to choice of
sampled languages.
However, there is a potentially serious flaw in the foregoing procedure. Because
of the small number of languages in the Simple syllable class in the
entire sample, only 2 to 4 Simple languages are included in each of the random
sub-samples, against 6 to 16 Complex and 10 to 22 Moderate languages.
Such a small number of data points is a poor basis for constructing a meaningful
average. A second method was therefore tried which constrained the subsamples
to include ten languages from each syllable category. The selection
within-category is random, giving a hybrid random-stratified sample. Outliers
(between 0 and 1 per sub-sample) were excluded as before, but no other modifications
to the random selections made. Mean results from five trials with this
constraint are shown in Figure 6. At least two languages from each area occur
in each sub-sample. Again, a monotonic decrease in mean consonant inventory
size with decreasing syllable complexity is found. The difference between the
Complex mean and both those of the Moderate and Simple sets is significant
(by Fisher’s PLSD) at at least the .02 level. The range for Complex sets is between
22.2 and 25.0 (s.d. 1.10), for Moderate sets between 14.4 and 21.7 (s.d.
2.86), and for Simple sets between 14.4 and 20.2 (s.d. 2.69). In this exercise,
a truer estimate of the variation contributed by choice of sampled languages
in the Simple category is probably obtained, and the more limited number of
Moderate languages in each sub-sample makes it less likely that this category
will simply converge to the overall mean of the whole sample.
Although re-sampling techniques would normally be carried out with a much
larger number of iterations, the limited analyses of sub-samples included here
suggest that the trend found in the overall sample for larger consonant inventory
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122 Ian Maddieson
mean#ofconsonants
24.4
19.4
17.2
Complex Moderate Simple
15
17
19
21
23
25
27
Figure 6. Mean number of consonants by syllable category in five random samples of 30 languages
constrained to include 10 languages of each syllable category
to co-occur with more complex syllabic possibilities is quite robust, and is not
dependent on a biased choice of sample languages. Of course, this finding only
relates directly to the universe of extant and recent languages. The extent to
which it might be projected to the universe of possible languages is another
debate altogether.
6. Summary
This paper makes two principal points. First, it presents a statistical finding:
that increasing syllable complexity shows an overall positive correlation with
increasing size of consonant inventory in modern spoken languages. Secondly,
it examines the reliability of this finding using several techniques, including
dividing the total sample into areal/genetic sets and using re-sampling. Though
re-sampling methods have been used increasingly often as an analytical tool
in other disciplines, their application in typological linguistic studies to date
appears negligible. It has also highlighted the need to consider the nature of
the variables being examined and the distribution of the values in any sample
used. In this case, the fact that one of the variables is a real number (an interval
scale) with a near-normal distribution opens up certain possibilities, such as
reliance on means, but closes off others. Major inequalities in the frequency
of languages across the syllable complexity categories needed to be taken into
account in designing appropriate tests.
Received: 19 August 2005 University of California at Berkeley
Revised: 16 March 2006
Correspondence address: Department of Linguistics, University of California at Berkeley,
Dwinelle Hall 1203, #2650, Berkeley CA 94720-2650, U.S.A.; e-mail: ianm@berkeley.edu
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Correlating phonological complexity 123
Acknowledgment: This work was supported by the National Science Foundation through grant
BCS-034578 to the author.
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