The existence of negative correlation between linguistic measures across languages

1 Introduction

The aim of this paper is to propose a procedure to evaluate the possible existence of negative correlation between different linguistic measures. The procedure is based on simultaneous-equation regressions, which is a statistical technique that is widely used in other social sciences. The analysis is performed using a cross-linguistic perspective, and the measures used are three language ratios: phonemes per syllable, syllables per word and words per clause.

The three abovementioned ratios can be seen as indicators of different levels of language complexity. This concept is linked to the idea that a language becomes more complex when “the number of parts in a system” increases, ^[1] and it assumes that complexity is measurable using indicators for different language dimensions (e. g., phonology, morphology, syntax).

A complexity trade-off is a situation in which a higher level of complexity for a certain language component appears in correspondence to a lower level of complexity for another component. As each of the ratios that we consider can be interpreted as a measure that represents a different language domain, then a negative relationship between two of those ratios can be read as a signal of a complexity trade-off between two different language components.

In order to evaluate the relationships between phonemes per syllable, syllables per word and words per clause, we use a single text available in several languages. That text is the fable known as “The North Wind and the Sun”, which is a story recommended by the International Phonetic Association (IPA) to illustrate the phonetics of different languages and dialects. Having that text for a considerable number of languages, we have selected a sample of 50 cases and calculated the corresponding ratios.

The simplest way to analyze the existence of correlation in a context like the one described is to calculate standard (Pearson) correlation coefficients between the different ratios. We also calculate the so-called “partial correlation coefficients”, which have the advantage of using information about the three ratios at the same time. Alternatively, we run regressions in which each language ratio is supposed to depend on other variables (e. g., the other ratios, plus some categorical variables related to geographic and genetic factors). Those regressions are run at the same time, as a system of simultaneous equations, and their results are used to compute new partial correlation coefficients. Those coefficients are compared among themselves, and they are related to previous results that appear in the literature.

The rest of this article is organized as follows. In Section 2 we review the literature about cross-linguistic analyses of correlation, especially the one in which we find results about possible relationships between different measures of complexity. In Section 3 we explain the main characteristics of the dataset that we have assembled, based on the transcriptions for “The North Wind and the Sun” that appear in IPA (1999) and other related sources. In Section 4 we provide a theoretical foundation for our analysis, based on a synergetic linguistics’ approach. In Section 5 we apply regression techniques to our dataset, and find some results that can be compared with the ones from the existing literature. Finally, in Section 6 we make some concluding remarks.

2 Review of the literature

The literature about quantitative analysis of cross-linguistic correlations is not particularly large, but it is considerably diverse. The branch of that literature which is closer to the type of analysis that we perform in this article is the one that began with Fenk-Oczlon and Fenk (1985). That literature analyzes the possible existence of correlation between different language sub-systems using actual text analysis, and it does so by calculating several linguistic ratios (phonemes per syllable, syllables per word, phonemes per word, words per clause, etc.). In Fenk-Oczlon and Fenk (1993), for example, we find a correlation analysis of those ratios that comes from translations of a number of simple German sentences into 33 different languages, while in Fenk-Oczlon and Fenk (2005) there is an additional analysis in which some of those ratios are correlated with theoretical variables (e. g., number of cases, tendency to postpositions, order of object and verb). They end up with a set of conclusions that imply negative correlation between many of the analyzed variables, and some of them turn out to be statistically significant.

Another branch of the literature, which leads to results that are similar to Fenk-Oczlon and Fenk’s, is the one that relates word length to measures of phonological complexity. This literature begins with a paper by Nettle (1995), which finds a strong negative correlation between phoneme inventory size and phonemes per word, and is later continued by studies such as Wichmann et al. (2011), which uses an alternative measure of phonological complexity and a much larger dataset (while also controlling for geographic and genetic factors). Another contribution that is worth noting is the one by Oh et al. (2013), which calculates correlations between syllables per word and two measures of “information density” (which are ratios between the number of syllables and the number of words in the same text translated to different languages, using Vietnamese as an external reference). These authors find a highly significant negative correlation between syllabic information density and number of syllables per word.

Other articles, such as Shosted (2006), study the possible existence of negative correlation between linguistic phenomena using purely theoretical (or “typological”) variables. In that paper, the author compares the number of possible syllable types in a sample of 32 languages with the number of inflectional categories of the verbs in those languages, and his analysis ends up with the conclusion that no statistically significant correlation can be found. In the same line of research, Nichols (2009) analyzes five language domains (phonology, inflectional synthesis, classification, syntax and lexicon), using a sample of 68 languages. While she finds no significant negative correlation between any of those five domains, she does find a significant positive correlation between her measure of morphological synthesis and her measure of syntactic structure.

In many cases, this literature considers the measures that it uses as indicators of language complexity, and therefore interprets its correlation coefficients as evidence for or against the existence of complexity trade-offs. Part of the quantitative linguistic literature has also found phenomena related to negative correlation between different dimensions of actual text complexity using other statistical tools, such as spectral analysis. Moscoso (2011), for example, has detected the existence of a certain “universal shape” of languages related to the absence of repetition in very short scales and the abundance of repetition in very long scales, with a relatively flat regime for intermediate scales. As those scales can be loosely related to the concepts of word, sentence and discourse, those relationships (that are studied for relatively large corpora and applied to a sample of 15 languages) reveal a negative correlation between morphological and syntactic structure.

Other approaches to this problem restrict themselves to a particular language subsystem. Maddieson (2007), for example, measures phonological complexity using three different indicators: inventory size (of both consonants and vowels), tone systems, and elaboration of the syllable inventory. He also looks for relationships between those measures, but he only finds a significant positive correlation between consonant inventory and syllable structure, and a (less significant) negative correlation between syllable structure and tone complexity. Moran and Blasi (2014), conversely, find a relatively large negative correlation between vowel inventory size and number of phonemes per word, in a study in which this last concept is measured using the same word lists used by Wichmann et al. (2011).

In this paper, we will focus on the correlation between three linguistic ratios (phonemes per syllable, syllables per word, and words per clause) using empirical measures derived from actual texts, and those measures will be subject to statistical analysis to determine the possible existence of negative correlation between them. As each of these ratios can be seen as an indicator of a certain type of complexity, their correlations also have an interpretation related to the existence of complexity trade-offs.

Another important feature of this paper has to do with its level of statistical sophistication. Contrary to previous studies that restrict themselves to product–moment correlation coefficients, we also use partial correlation coefficients calculated in different ways. With that approach, we control for factors such as the interaction of the proposed indicators and the effect of geographic and genetic factors, in a context of simultaneous-equation system estimations.

3 The North Wind and the Sun

The fable of the North Wind and the Sun, attributed to Aesop, is a text that has been used for many decades by the International Phonetic Association as a “specimen” or model to illustrate the sounds of languages, and also the phonetic symbols that are suitable to describe those sounds. It is therefore a unique case of a short text for which specialists in the phonetics of different languages have analyzed the sounds, the phonemes, the syllables and the words of the languages and dialects under study. For example, the (Standard Southern British) English version of “The North Wind and the Sun” that appears in Roach (2004) is the following:

The North Wind and the Sun were disputing which was the stronger, when a traveller came along wrapped in a warm cloak. They agreed that the one who first succeeded in making the traveller take his cloak off should be considered stronger than the other. Then the North Wind blew as hard as he could, but the more he blew the more closely did the traveller fold his cloak around him, and at last the North Wind gave up the attempt. Then the Sun shone out warmly, and immediately the traveller took off his cloak. And so the North Wind was obliged to confess that the Sun was the stronger of the two.

and its corresponding phonemic transcription is this:

ðə nɔ:θ wɪnd ən ðə sʌn wə dɪspju:tɪŋ wɪtʃ wəz ðə strɒŋgə | wən ə trævlə keɪm əlɒŋ ræpt ɪn ə wɔ:m kləʊk || ðəɪ əgri:d ðət ðə wʌn hu fɜ:st səksi:dɪd ɪn meɪkɪŋ ðə trævlə teɪk hɪz kləʊk ɒf ʃʊd bi kənsɪdəd strɒŋgə ðən ði ʌðə || ðən ðə nɔ:θ wɪnd blu: əz hɑ:d əz i kʊd | bət ðə mɔ: hi blu: ðə mɔ: kləʊsli dɪd ðə trævlə fəʊld hɪz kləʊk əraʊnd hɪm | ænd ət lɑ:st ðə nɔ:θ wɪnd geɪv ʌp ði ətempt || ðən ðə sʌn ʃɒn aʊt wɔ:mli | ænd əmi:diətli ðə trævlə tʊk ɒf ɪz kləʊk || n səʊ ðə nɔ:θ wɪn wəz əblaɪdʒd tu kənfes ðət ðə sʌn wəz ðə strɒŋgr əv ðə tu: ||

If we count the number of clauses, words, syllables and phonemes in this text, we find that it has 9 clauses, ^[2] 113 words, 143 syllables and 383 phonemes. This allows to calculate the average number of phonemes per syllable (equal to 2.6783), syllables per word (equal to 1.2655), and words per clause (equal to 12.56). The same exercise can be performed for other available languages. For example, the Japanese version of “The North Wind and the Sun” (Okada 1999) has a lower number of phonemes per syllable (equal to 1.9559) but a higher number of syllables per word (equal to 2.5506). That figure is even larger in the Tamil version (Keane 2004), where there are 3.1899 syllables per word but only 8.78 words per clause.

The systematic computation of the phoneme/syllable, syllable/word and word/clause ratios for different versions of “The North Wind and the Sun” can be a useful source to compare the value of those measures across languages, and to capture the possible existence of correlation between them. In order to perform that analysis, we selected a sample of 50 languages for which we found versions of the abovementioned text in either the Handbook of the International Phonetic Association (IPA 1999) or in the series of “Illustrations of the IPA”, published by the Journal of the International Phonetic Association (see Figure 1).

Figure 1:

Location of the languages included in the sample.

The sample assembled consists of ten languages from each of the five areas in which we divided the world: America (Sahaptin, Apache, Chickasaw, Seri, Trique, Zapotec, Quichua, Shiwilu, Yine and Mapudungun), Europe (Portuguese, Spanish, Basque, French, Irish, English, German, Russian, Hungarian and Greek), Africa (Tashlhiyt, Temne, Kabiye, Igbo, Hausa, Dinka, Nara, Amharic, Sandawe and Bemba), West Asia (Georgian, Turkish, Hebrew, Arabic, Persian, Tajik, Nepali, Hindi, Bengali and Tamil) and East Asia (Japanese, Korean, Mandarin, Cantonese, Burmese, Thai, Vietnamese, Malay, Tausug and Arrernte). ^[3] This sample is basically the same one that we used in another paper about a different topic (Coloma 2015), and covers 26 different language families.

Table 1 shows the main descriptive statistics of our dataset for the calculated linguistic ratios, in terms of their maximum, minimum and average values, together with their standard deviations (both at an aggregate level and within each of the areas). ^[4] In it, we can observe that, on average, the number of phonemes per syllable in the whole dataset is 2.3004, but that ratio ranges from a minimum of 1.7115 (which corresponds to Igbo, a Niger-Congo language spoken in Nigeria) to a maximum of 2.8547 (which corresponds to Vietnamese). ^[5] Vietnamese is also the language with the lowest syllable/word ratio (equal to 1, since in the Vietnamese version of “The North Wind and the Sun” all the words are monosyllabic), while the language with the highest syllable/word ratio (equal to 3.7460) is Yine (an Arawakan language spoken in Peru), and the overall average number of syllables per word is 2.1869. Finally, the minimum value for the word/clause ratio is 5.7 and corresponds to Chickasaw (Muskogean, spoken in the United States), while the maximum value for that ratio is 18.4286 (Irish), in a context where the average number of words per clause is 10.3313. ^[6]

The description of the variables shown in Table 1 can be complemented with the calculation of product–moment correlation coefficients. Those coefficients appear in Table 2, in which the highest absolute value is the one that corresponds to the correlation between the syllable/word ratio and the word/clause ratio, which is equal to –0.6785. The correlation coefficient between phonemes per syllable and syllables per word, conversely, is much smaller (r=–0.2420), while the correlation coefficient between phonemes per syllable and the words per clause is even smaller (r=–0.0522).

The absolute values of those coefficients are related to their statistical significance. For example, correlation between syllables per word and words per clause is significantly different from zero at a 1 % probability level (p=0.0000), while correlation between phonemes per syllable and syllables per word is only statistically significant at a 10 % probability level (p=0.0905), and correlation between phonemes per syllable and words per clause fails to be significant at a any reasonable probability level (p=0.7187).

4 Theoretical foundation

The existence of negative correlation between linguistic measures such as the phoneme/syllable, syllable/word and word/clause ratios can be related to different processes through which languages trade off complexity in one dimension with simplicity in another one. In this section we provide a theoretical justification for those complexity trade-offs, based on an approach known as “synergetic linguistics”. The idea behind this approach is that language is “a self-organizing and self-regulating system whose properties come from the interaction of several constitutive, forming and control requirements” (Köhler 2005). Among them we can mention the so-called “coding requirement” (i. e., the need to provide expressions for given meanings), the “economy requirement” (i. e., the need to use as few elements as possible to produce the desired expressions), and the “stability requirement” (i. e., the need to modify language as little as possible so that it could be understood).

Synergetic linguistics’ models are sometimes based on the idea that language systems are a solution to an optimization problem whose aim is to maximize or to minimize a particular function or combination of functions. ^[7]Köhler (1987), for example, illustrates this idea through a case in which language is assumed to minimize “production effort”, “memory effort” and “decoding effort”, using word length, phoneme inventory size and degree of similarity as control variables. In the problem under analysis in this paper, we can apply a similar model, using our three linguistic ratios (phonemes per syllable, syllables per word and words per clause) as the corresponding control variables.

Let us assume that the three ratios under analysis contribute to satisfy the coding requirement of a language, since larger units in any of those dimensions (i. e., syllables with more phonemes, or words with more syllables, or clauses with more words) are helpful to provide expressions for the meanings that languages have to convey. Increasing complexity in any of those dimensions, however, is bad in terms of the cost that one has to incur to produce the required expressions (production effort) or to remember those expressions (memory effort). Long syllables, words and clauses are therefore inconvenient to satisfy the economy requirement of a given language, but any language can combine shorter and longer components so as to maximize a function that increases in decoding ease and decreases in production and memory effort.

In Figure 2 we have drawn a diagram in which we illustrate that combination, assuming that our three variables make decoding easier (maxD), but phonemes per syllable (Phon/Syll) and syllables per word (Syll/Word) are costly in terms of production effort (minP), and syllables per word and words per clause (Word/Clause) are costly in terms of memory effort (minM).

Figure 2:

Diagram of a language system.

The value that these three ratios take in any particular language can be determined by a process in which each of them helps to increase decoding ease but has a cost in terms of production or memory effort. When a language uses one of these variables in a more complex level (i. e., it has a larger value for the phoneme/syllable, or the syllable/word, or the word/clause ratios), it should compensate that complexity by having a greater simplicity in another dimension. This is the main theoretical basis for complexity trade-offs, which in the context that we are studying should be reflected in the existence of negative correlation between the linguistic measures under analysis.

That correlation, moreover, is expected to be stronger for measures that are directly related (e. g., phonemes per syllable versus syllables per word, and syllables per word versus words per clause) and weaker for measures that are less related (i. e., phonemes per syllable versus words per clause). This can also be linked to the fact that syllables are the constituents of words, while words are the constituents of clauses. If a language has longer syllables, then those syllables will be able to convey more information, and it will therefore be possible to have shorter words. Similarly, if a language has longer words, that language will be able to use fewer words per clause (because each word can have multiple morphemes, and those morphemes can play the same roles that, in other languages, are played by individual words).

5 Statistical analysis

5.1 Correlation and regression coefficients

In the last part of Section 3, we included a table that shows the product–moment correlation coefficients between phonemes per syllable, syllables per word and words per clause. Another way to appreciate the relationships between those variables is to plot each observation in a graph that represents two of those measures at the same time. This is what we do in Figures 3–5, which correspond to phonemes per syllable versus syllables per word, syllables per word versus words per clause, and phonemes per syllable versus words per clause.

Figure 3:

Phonemes per syllable versus syllables per word.

Figure 4:

Syllables per word versus words per clause.

Figure 5:

Phonemes per syllable versus words per clause.

In each of those figures, we have also depicted two straight lines. They represent the results of running linear regressions to relate the corresponding variables. The full line corresponds to the regression for which the independent variable is the one that appears on the abscissa axis of the graph, while the dotted line corresponds to the regression for which the independent variable is the one that appears on the ordinate axis.

Graphically speaking, one can think of correlation as the inverse of the average distance between the two lines drawn in each figure. On Figure 4, for example, that distance is relatively small, and therefore the correlation coefficient between the two variables (r = –0.6785) is considerably large in absolute value. On the contrary, on Figure 5 the distance between the two lines is very large, and this is related to the fact that the corresponding correlation coefficient (r = –0.0522) is small.

The product–moment correlation coefficients also have a relationship with the slopes of the lines represented in the figures. As all those coefficients are negative, the depicted lines are negatively sloped. But the most exact relationship between the correlation coefficients calculated in Section 3 and the regression lines represented in Figures 3–5 appears if we take into account the values of the slopes of those regression lines, and their corresponding goodness-of-fit measures.

Let us consider, for example, the results obtained when one regresses Phon/Syll against Syll/Word, and Syll/Word against Phon/Syll. These are the following:

[1];Phon/Syll=2.509973−0.095826.Syll/Word; R2=0.05855

[2].Syll/Word=3.573388−0.604350.Phon/Syll;R2=0.05855

As we can see, both regressions produce the same R² coefficient (R² = 0.05855), and the value of that coefficient is exactly the square of the correlation coefficient between Phon/Syll against Syll/Word (r = –0.2420). Moreover, if we look at the regression coefficients that correspond to the slopes of those regression lines (“β₁ = –0.095826” and “β₂ = –0.604350”) and find the square root of the product of those coefficients, we obtain the same result, which is equal to the correlation coefficient between Phon/Syll against Syll/Word. This implies performing the following calculation:

[3];r(PS,SW)=−β1⋅β2=−(−0.095826)⋅(−0.604350)=−0.2420

where PS stands for “phonemes per syllable” and SW stands for “syllables per word”. Note that in this formula we assume that, as both regression coefficients are negative, the corresponding product–moment correlation coefficient must also be negative.

The same situation occurs when we run regressions between Syll/Word and Word/Clause, Word/Clause and Syll/Word, Phon/Syll and Word/Clause, and Word/Clause and Phon/Syll. Their results are the following:

[4];Syll/Word=3.753594−0.151650⋅Word/Clause;R2=0.46031

[5];Word/Clause=16.96909−3.035319⋅Syll/Word;R2=0.46031

[6];Phon/Syll=2.348172−0.004623⋅Word/Clause;R2=0.00273

[7];Word/Clause=11.68831−0.589895⋅Phon/Syll;R2=0.00273

and the corresponding correlation coefficients can be calculated as:

[8];r(SW,WC)=−β3⋅β4=−(−0.151650)⋅(−3.035319)=−0.6785

[9];r(PS,WC)=−β5⋅β6=−(−0.004623)⋅(−0.589895)=−0.0522

where WC stands for “words per clause”.

6 Concluding remarks

After performing the numerical exercises described in Section 5, we can now write a few concluding remarks to summarize our results. The main one is that, using the dataset that we have assembled with 50 different versions of “The North Wind and the Sun”, we have found that the syllable/word ratio is negatively correlated with the word/clause ratio, and that relationship is strong enough to appear as statistically significant in all the analyses that we have used for our data (see Table 6).

The correlation coefficient between phonemes per syllable and syllables per word, conversely, fails to be significant at a 5 % probability level when we compute it using the standard Pearson correlation technique. When calculated as a partial correlation coefficient, however, its absolute value increases, and it becomes statistically significant. This conclusion is maintained when we use simultaneous equations’ methods in which we add binary variables related to geographic and genetic factors.

A similar phenomenon occurs with the relationship between the phoneme/syllable ratio and the word/clause ratio, as we can see on the last column of Table 6. In our dataset, these variables initially generate a small and insignificant product–moment correlation coefficient, but this changes considerably when we calculate partial correlation coefficients. Indeed, allowing for the interplay between the three linguistic ratios is enough to produce a coefficient that is statistically significant at a 5 % probability level, and this significance becomes stronger when we estimate that coefficient using seemingly unrelated regressions.

Note that, if we had only used standard product–moment coefficients to analyze the possible existence of negative correlation between our three linguistic ratios, we would have ended up with the conclusion that the only relevant relationship was the one between syllables per word and words per clause. Introducing a relatively simple method to deal with the interaction between the three ratios, and adding a set of binary geographic and genetic variables, we can see that the other negative correlations are also important, and this is especially true for the correlation between the phoneme/syllable and syllable/word ratios.

Our results can also be interpreted under the logic of a synergetic linguistics’ model like the one that we propose in Section 4. In it, we assume that the three analyzed ratios are signals of different aspects of language complexity, and that their values are determined by an optimization process in which higher complexity is good to satisfy coding requirements but bad to satisfy economy requirements (related to production and memory effort). Therefore, when the external conditions in which a language develops (e. g., geographic and genetic factors) induce a certain linguistic measure to become larger, the postulated optimization process implies that this increase in complexity is somehow compensated by a reduction in the value of the other linguistic measures. These trade-offs become greater between linguistic ratios that are directly related (i. e., phoneme/syllable vs. syllable/word, and syllable/word vs. word/clause ratios), and smaller between ratios that are less related (i. e., phoneme/syllable vs. word/clause).

The conclusions obtained in this paper can be compared with results that appear in previous literature. The most compatible results are the ones gotten by Fenk-Oczlon and Fenk (1993, 2005), who also find negative and significant correlations between several linguistic ratios, and see them as evidences of complexity trade-offs. The likely cause of this coincidence is the fact that those authors use basically the same measures that we use in the present work, although their dataset is completely different from ours and many of the languages selected by them are also different.

The correlation between different cross-linguistic measures, conversely, appears to be insignificant in other studies such as Shosted (2006) and Nichols (2009). In those papers, the authors use theoretical measures of linguistic complexity instead of empirical measures based on text analysis. They also calculate correlations using standard Pearson coefficients only, and therefore do not include partial correlation coefficients. Those factors are probably the main causes for the discrepancies between their results and ours.

When some of the abovementioned factors are included in the analysis, some significant negative correlation is likely to appear between different cross-linguistic measures. That is the case of Wichmann et al. (2011), which finds a negative correlation between total inventory size and number of phonemes per word; Moran and Blasi (2014), which finds a negative correlation between vowel inventory size and number of phonemes per word; and Moscoso (2011), which finds a negative relationship between morphological structure and syntactic structure.