This paper describes recent research that we have carried out on the arbitration of disputed authorship attribution. In an earlier study, we lemmatized and disambiguated fully the thirty biographies of the Scriptores Historiae Augustae, and the results of the analysis of that work have provided us with a benchmark and control group for further analysis of two major related questions:

• * Can statistical analysis be based successfully upon the argument that "... stylometric theory posits the existence of homogeneity within a single work by a single author." (Ledger & Merriam, 1994).
• * Does such homogeneity imply that stylometric analysis of a subset can be equivalent to the analysis of the whole?

This paper thus extends the reach of our previous research on the analysis of fully lemmatized and disambiguated texts, and describes general problems that occur when subsets of the main text are to be compared in place of the entire text. It thus attempts to lay out ground rules for application of our techniques to texts of lengths that are too extensive for complete manual disambiguation. The importance of the SHA to historians derives from the simple fact that it is a critically important "source" of historical information for much of the tumultuous period leading up to the reign of Constantine the Great, the first Christian emperor of the Roman Empire. The need for stylometric analyses of the texts is based upon the understanding that the usefulness of this set of imperial biographies would be increased greatly if it could be demonstrated that there was but a single mind, and hence but a single human frame of reference for the historical information included; and therefore that the multitude of fabrications and apparently deliberately false statements that infect this irreplaceable work can be treated and allowed for as the creations of but one individual mind. A demonstration of multiple authorship, on the contrary, would imply a disjointed effort of authorship which would be immeasurably more difficult to integrate into a coherent history of those turbulent times. Extensive historical analysis carried out over the past century has resulted in near complete acceptance of the concept of single authorship of the SHA. Our recent research, however, described in an earlier paper (Gurney & Gurney, 1996), and based entirely on internal stylometric methods, shows, to a rather high degree of statistical confidence, that the attribution in the manuscripts to the six otherwise unknown authors is probably based upon historical fact. The initial lemmatization and disambiguation of the SHA was taken to completion, since we could find no proof that subsets are equivalent to the full texts in stylometric analysis. The concept of homogeneity had usually been stated explicitly or implicitly (Ledger & Merriam, 1994), but has apparently not actually been put to the test (Kenny, 1986), although the size of the subsets has been a matter for discussion (Ellegård, 1962; Burrows & Craig, 1994). Hence we completed this highly labour-intensive task of full disambiguation of the more than 100,000 words of text, using techniques described in an earlier conference on the analysis of frequency of use of vocabulary of different kinds, including function words, conjunctions, the most frequently used vocabulary, and the rate of introduction of new lemmas for each 100 words (Gurney & Gurney, 1994). The importance of the Scriptores Historiae Augustae for an attempted understanding of the critical years leading to the era of Constantine and his successors has justified the expenditure of the time and effort involved in the complete lemmatization and manual disambiguation of the text. Such effort is impracticable, however, in texts that run to many hundreds of thousands of words; and for that reason, we have recently developed a new line of research. In this system, our avenue of approach is to make repeated random and non-random choices of subsets of target texts, and to attempt to determine if the results of statistical analyses based upon these chosen subsets are essentially statistically equivalent to those produced by the entire texts. The question of the alternative use of subsets became much more urgent when we embarked upon the course of TEI-compatible tagging of all parts of speech in the SHA, and upon the disambiguation and tagging of its earlier model, the Lives of the Twelve Caesars of Gaius Suetonius Tranquillus, a work of just under 100,000 words that comprises the biographies of the first twelve emperors of Rome. This work of Suetonius is intended to act as a control work to the SHA in our further study of authorship of imperial biographies. We therefore began analyses of various subsets of the works, in comparison with comparable analyses of the entire text, in an attempt to determine if it is accurate to state that a given text by a given author will be internally homogeneous to the point that subsets of itself can be demonstrated to be congruent to it, in the face of stylometric comparison with other works of the same author, or of other authors, or even with each other, and with the full text. The new analysis required production of a new series of subset texts. First came the reduction of each text to a single sentence per disk record. Each of these files was created in three different forms, each with a different combination of sentence-delimiters to determine sentence-length: full stop, full-stop plus semi-colon, and that pair plus full-colon. In this way, we attempted to circumvent the problems of the differences of definition of sentence-length between classical times and the modern, and also between interpretations of editors from differing modern language groups, such as the difference in usage of the semi-colon between German and English-speaking editors (Janson, 1964). Initial analyses demonstrated that the use of the set of three delimiters gives acceptable results, and hence all further research was conducted on sentences that were determined by those three delimiters. From these files, three new groups of files were created for comparison with the original 30. First, 120 files consisting of the four quarters of each text were compiled, in addition to 60 files containing each half. Second, a set of 30 files containing exactly the first 500 words of text was developed. And finally, two sets of 30 files were created, each file containing one-quarter of all sentences of a specific biography of the SHA, chosen randomly from that text (by the linear congruence method of the ICON language): in one set, the file consists of sentences selected from the entire text; and in the other, with sentences chosen in equal numbers from each individual quarter of the text. These randomly-selected files were generated as controls for several reasons, one obtaining from the fact that it is apparent that sentence-length, in general, decreases slightly in each successive quarter of the biographies. The 270 new subset biographies, in their logical groups of 30, were then passed to an application system that generates a large number of matrices of data in a form suitable for transmission to SAS and SPSS. The original techniques that had given striking results in analysis of the 30 complete biographies were next applied to the various matrices that had been created from the subsets. We also applied the techniques to an analysis of sentence-length distributions in the SHA, as some previous researchers have attempted to do. We found, however, that, even in the entire text, there is so little stylometric information encoded in apparent sentence-length, that scarcely more than random distribution can be found. One new type of analysis was also applied, to good effect: that of treating the 4 one-quarter biographies of each original biography as if they were fragments of different works of the same attributed author. By this device, it appears to be possible to ascertain if certain fractions of a work are functionally equivalent to the whole, and if the whole work is cohesive, coherent, uniform and stylometrically homogeneous.

Results

The first results demonstrated that the structure of a work, something which a reader recognizes subjectively, appears to be reflected in the stylometric analysis: for the various subsets of a work are not necessarily homogeneous; and the various quarters appear to be incompatible, to various degrees, one with another. For example, the seven works by Spartianus, studied as quarter-works, became twenty-eight works, which can be analyzed in the same manner as the original thirty. The only measure, however, which gives results even remotely comparable to those of the original text, is the analysis of the usage of conjunctions, in which the set of final quarters of the seven texts stands off very clearly from the others. This demonstrates a major drawback to the use of the subsets, however, since it is clear that the only means by which the results of the final quarter can be seen to be relevant and important, is by use of the fully-disambiguated original text as control: the subsets cannot be used as controls for themselves. In the half-text analyses, one test, that of the 15 most frequently used lemmas which appear in each of the 30 segments, gave almost complete differentiation; but most of the other tests gave very indifferent results. In the analysis of function words in the 500-word segments, there was good differentiation of only three authors: Capitolinus, Spartianus, and Lampridius. The various quarter-texts provided mixed results: on one test, quarter #1 provided some differentiation of specific authors; whereas on a different test, and different quarter, other authors were separated. Hence, it is clear that no one test on subsets can provide clear discrimination of authorship, although many do appear to demonstrate a degree of multiple authorship.

Discussion of Results

As the various analyses were carried out, several points became clear:

• * The larger the size of the subset in relation to the full text, the better the result;
• * Any increases above the minimum possible number of key words used to generate full differentiation of authorship in the full texts produced only slight increases in the degree of differentiation. Such increases, when applied to the subsets, however, generated large increases in differentiating power, but without reaching anything near the degree of resolution of the full texts; and in no case was the discrimination clear-cut.

It is very clear from the analysis that, had only small segments of the texts been chosen for analysis, then a hypothesis of multiple authorship could not have been confirmed; it is only the full lemmatization and disambiguation of the entire text which has permitted such a conclusion. It is further evident from this study that the two questions raised for study have both been answered in the negative, namely:

• * There appears to be no homogeneity within any specific work of an individual author; rather, each work is suffused with sufficient variety internally as to maintain the interest of the reader. This variety may be the fundamental cause for analysis of small subsets not to be equivalent to analysis of the whole.

A fundamental conclusion of this experiment is, therefore, that, although it is not permitted to extrapolate, in general, from one experiment on one set of texts, to the stylometrics of other authors and languages, it nevertheless appears clearly necessary, for any research project that intends to use subsets of a text, to ensure that those subsets are stylometrically homogeneous with the full text - a probability, given the results of this experiment, which does not appear to be high.