Statistical Correlations in avant-garde prose writing

The question that this blog post sets itself is: What differences and similarities can be detected in modernist and contemporary authors on the basis of three stylistic variables; hapax, unique and ambiguity, and how are these stylistic variables related to one another?

I: The Data

The data to be analysed in this project were derived from an analysis of twenty-one corpora of avant-garde literary prose through use of the open-source programming language R. The complete works of the authors James Joyce, Virginia Woolf, Gertrude Stein, Sara Baume, Anne Enright, Will Self, F. Scott FitzGerald, Eimear McBride, Ernest Hemingway, Jorge Luis Borges, Joseph Conrad, Ford Madox Ford, Franz Kafka, Katherine Mansfield, Marcel Proust, Elizabeth Bowen, Samuel Beckett, Flann O’Brien, Djuna Barnes, William Faulkner & D.H. Lawrence were used.

Seventeen of these writers were active between the years 1895 and 1968, a period of time associated with a genre of writing referred to as ‘modernist’ within the field of literary criticism. The remaining four remain alive, and have novels published as early as 1991, and as late as 2016. These novelists are known for their identification as latter-day modernists, and perceive their novels as re-engaging with the modernist aesthetic in a significant way.

I.II Uniqueness

The unique variable is a generally accepted measurement used within digital literary criticism to quantify the ‘richness’ of a particular text’s vocabulary. The formula for uniqueness is obtained by dividing the number of distinct word types in a text by the total number of words. For example, if a novel contained 20000 word types, but 100000 total words, the formula for obtaining this text’s uniqueness would be as follows:

20000/100000 = Uniqueness is equal to 0.2

I.III Ambiguity

Ambiguity is a measure used to calculate the approximate obscurity of a text, or the extent to which it is composed of indefinite pronouns. The indefinite pronouns quantified in this study are as follows, ‘another’, ‘anybody’, ‘anyone’, ‘anything’, ‘each’, ‘either’, ‘enough’, ‘everybody’, ‘everyone’, ‘everything’, ‘little’, ‘much’, ‘neither’, ‘nobody’, ‘no one’, ‘nothing’, ‘one’, ‘other’, ‘somebody’, ‘someone’, ‘something’, ‘both’, ‘few’, ‘everywhere’, ‘somewhere’, ‘nowhere’, ‘anywhere’, ‘many’, ‘others’, ‘all’, ‘any’, ‘more’, ‘most’, ‘none’, ‘some’, ‘such’. The formula for ambiguity is:

number of indefinite pronouns / number of total words

I.IV Hapax

Finally, the hapax variable calculates the density of hapax legomena, words which appear only once in a particular author’s oeuvre. The formula for this variable is:

number of hapax legomena / number of total words

a bar chart giving an overview of the data

II: Data Overview

Even before analysing the data in great depth, the fact that these variables are interrelated with one another stands to a logical analysis. Hapax and unique are best understood as an indication of a text’s heterogeneity, as if a text is hapax-rich, the score for uniqueness will be similarly elevated. Ambiguity, as it is a set of pre-defined words, can be considered a measure of a text’s homogeneity, and if the occurrences of these commonplace words are increasing, hapax and uniqueness will be negatively effected. The aim of this study will be to first determine how these measures vary according to the time frame in which the different texts were written, i.e. across modern and contemporary corpora, which correlations between stylistic variables exist, and which of the three is most subject to the fluctuations of another.

more overviews for each variable

IV.I: The Three Groups Hypothesis

A number of things are clear from these representations of the data. The first finding is that the authors fall into approximately three distinct groups. The first is the base- level of early twentieth-century modernist authors, who are all relatively undifferentiated. These are Ernest Hemingway, Virginia Woolf, William Faulkner, Elizabeth Bowen, Marcel Proust, F. Scott Fitzgerald, D.H. Lawrence, Joseph Conrad and Ford Madox Ford. They are all below the mean for the hapax and unique variables.

boxplot of outliers for the unique hapax variable

The second group reach into more extreme values for unique and hapax. These are Djuna Barnes, Jorge Luis Borges, Franz Kafka, Flann O’Brien, James Joyce, Eimear McBride and Sara Baume. Three of these authors are even outliers for the hapax variable, which can be seen in the box plot.

Joyce’s position as an extreme outlier in this context is probably due to his novel Finnegans Wake (1939), which was written in an amalgam of English, French, Irish, Italian and Norwegian. It’s no surprise then, that Joyce’s value for hapax is so high. The following quotation may be sufficient to give an indication of how eccentric the language of the novel is:

La la la lach! Hillary rillarry gibbous grist to our millery! A pushpull, qq: quiescence, pp: with extravent intervulve coupling. The savest lauf in the world. Paradoxmutose caring, but here in a present booth of Ballaclay, Barthalamou, where their dutchuncler mynhosts and serves them dram well right for a boors’ interior (homereek van hohmryk) that salve that selver is to screen its auntey and has ringround as worldwise eve her sins (pip, pip, pip)

Though Borges’ and Barnes’ prose may not be as far removed from modern English as Finnegans Wake, both of these authors are known for their highly idiosyncratic use of language; Borges for his use of obscure terms derived from archaic sources, and Barnes for reversing normative grammatical and syntactic structures in unique ways.

The third and final group may be thought of as an intermediary between these two extremes, and these are Katherine Mansfield, Samuel Beckett, Will Self and Anne Enright. These authors share characteristics of both groups, in that the values for ambiguity remain stable, but their uniqueness and hapax counts are far more pronounced than the first group, but not to the extent that they reach the values of the second group.

boxplot displaying stein as an extreme outlier for ambiguity

Gertrude Stein is the only author who’s stylistic profile doesn’t quite fit into any of the three groups. She is perhaps best thought of as most closely analogous to the first group of early twentieth century modernists, but her extreme value for ambiguity should be sufficient to distinguish her in this regard.

The value for ambiguity remains fairly stable throughout the dataset, the standard deviation is 0.03, but if Stein’s values are removed from the dataset, the standard deviation narrows from 0.03 to 0.01.

Two disclaimers need to be made about this general account from the descriptive statistics and graphs. The first is that there is a fundamental issue with making such a schematic account of these texts. The grouping approach that this project has taken thus far is insufficiently nuanced as it could probably be argued that McBride could just as easily fit into the third group as the second. Therefore, the stylistic variables do not adequately distinguish modern and contemporary corpora from one another.

IV.II Word Count

word count for the most prolific authors

It should not escape our attention that those authors who score lowest for each variable and that the first group of early twentieth-century author are the most prolific. The correlation between word count and the stylistic variables was therefore constructed.

Pearson correlation for word count and stylistic variables

Both the Pearson correlation and Spearman’s rho suggest that word count is highly negatively correlated with hapax and unique (as word count increases, hapax and unique decreases and vice versa), but not with ambiguity.

Spearman’s rho for word count and stylistic variables

The fact that the Spearman’s rho scores significantly higher than the Pearson suggests that the relationship between the two are non-linear. This can be seen in the scatter plot.

scatter plot showing the relationship between word count and uniqueness

In the case of both variables, the correlation is obviously negative, but the data points fall in a non-linear way, suggesting that the Spearman’s rho is the better measure for calculating the relationship. In both cases it would seem that Joyce is the outlier, and most likely to be the author responsible for distorting the correlation.

scatter plot displaying the relationship between word count and hapax density
Pearson correlations for word count and each stylistic variable

SPSS flags the correlation between hapax and unique as being significant, as this is clearly the most noteworthy relationship between the three stylistic variables. The Spearman’s rho exceeded the Spearman correlation by a marginal amount, and it was therefore decided that the relationship was non-linear, which is confirmed by the scatter plot below:

Spearman’s rho correlation for word count and stylistic variables

The stylistic variables of unique and hapax are therefore highlycorrelated.

VI: Conclusion

As was said already, the notion that stylistic variables are correlated stands to reason. However, it was not until the correlation tests were carried out that the extent to which uniqueness and hapax are determined by one another was made clear.

The biggest issue with this study is the issue that is still present within digital comparative analyses in literature generally; our apparent incapacity to compare texts of differing lengths. Attempts have been made elsewhere to account for the huge difference that a text’s length clearly makes to measures of its vocabulary, such as vectorised analyses that take measurements in 1000 word windows, but none have yet been wholly successful in accounting for this difference. This study is therefore one among many which presents its results with some clarifiers, considering how corpora of similar lengths clustered together with one another to the extent that they did. The only author that violated this trend was Joyce, who, despite a lengthy corpus of 265500 words, has the highest values for hapax and uniqueness, which marks his corpus out as idiosyncratic. Joyce’s style is therefore the only of the twenty-one authors that we can say has a writing style that can be meaningfully distinguished from the others on the basis of the stylistic variables, because he so egregiously reverses the trend.

But we hardly needed an analysis of this kind to say Joyce writes differently from most authors, did we.


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