Could it helpfully guide our reading of Julius Caesar if we had a precise answer to the question what common words are used relatively more or less often in that play than in Shakespeare's tragedies as a whole? This is a particular version of a more general query where you compare phenomena in Set A, which consists of one or more texts, with Set B, which likewise consists of one or more texts. Set A is called the Analysis Work(s) and Set B the Reference Work(s). The terminology is arbitrary, but you are interested in identifying distinctive features of something by comparing it with a relevant other. You would not expect differences between a play of Shakespeare and a year's run of the Wall Street Journal to yield much insight, unless you were interested in, say, how sixteenth-century syntax differed from contemporary syntax. But striking differences between usage in one Shakespearean tragedy and the corpus of all the tragedies might draw attention to something important.

You do this comparison by following the steps in the procedure called Compare Many Wordforms in the Analysis menu of WordHoard. In this procedure, the computer compares the frequencies of all the words in Julius Caesar (subject to some filtering) with all the words in the tragedies. The comparison rests on a gigantic "as if." It treats the words in the tragedies as if they were so many colored marbles in a jar. It looks at the words in Julius Caesar as another set of colored marbles and seeks to determine the probability that the marbles in the Julius Caesar Jar could have been drawn at random from the Shakespearean Tragedy Jar.

This is a gigantic "as if" because there is not the slightest reason to assume that writing is anything like drawing words at random from some box or jar. But there is nonetheless some utility to the "as if." We are all creatures of habit, and we may expect writers to share some habits and have some personal habits of their own. To the extent that a writer's habits are relatively constant, you may think of them as default random distribution and measure deviations from it. Some of these deviations will have perfectly obvious explanations. For instance, from a statistical perspective, the names 'Brutus', 'Rome', 'Caesar' are astronomically more frequent in Julius Caesar than in Shakespearean tragedy at large. But what else would you expect? Other deviations might be in various ways interesting.

The mathematics involved in this peculiar "as if" are fairly complex, but you need not understand them in detail to make intelligent use of the result. That result is expressed as a log likelihood ratio, which, if you really want to know, corresponds to chi square values for one degree of freedom. But the important thing is to have a sense of the odds associated with particular log likelihood ratios. The following table shows that logarithmic progressions are deceptive to the non-mathematical eye: apparently small increases in number stand for huge decreases in probability. The asterisk column refers to the use of asterisks in the log likelihood result sets to mark ranges of increasingly low probability. More is less.

It is equally true that you should not overestimate the significance of vanishingly small probabilities. Language is full of rare events, and of the many rare events that could happen quite a few will.

If you run a log likelihood comparison on parts of speech in Julius Caesar and all tragedies, you notice that names are far more common, nouns and adjectives considerably less common, and interjection somewhat less common. While the fact that Roman names are common in Julius Caesar is without any interest, one can make something of the fact that naming is a disproportionately common event: it is a nice way of drawing attention to a certain feature of Romanness. A lemma-based comparison shows that 'she' is much less common, while 'man', 'to-day', 'do', 'mighty', 'countryman', 'street', 'honourable', 'run', and 'every' are considerably more common than in the tragedies at large.

It turns out that each of these words points to some major concern of the play. Thus you might want to think of the log likelihood ratio as a self-indexing feature that draws a provisional survey to be refined by subsequent interpretation. It is interesting to observe how much of the information in this initial overview is communicated by the relative frequencies of very ordinary words. In the discourse of Italian opera the word 'tintura' is often used to refer to the distinctive colouring of a particular score. Similarly, a text may have a distinctive quality that lives in the peculiar fabric of common words in that play. These are subtle effects, but you can get at them with surprising precision by measuring common words that are disproportionately common or rare.

You should never expect that such measurements will produce entirely new insights. In fact, a statistically based result that contradicts or lies outside the judgment of experienced readers is ipso facto suspect. Good readers have always been subtle, if informal, statisticians, and an effect that has escaped generations of readers is hard to reconcile with the idea of an author who knows what s/he is doing. On the other hand, frequency-based inquiries may be an excellent way of demonstrating in detail how an effect is built. At a minimum, a list of over- and under-used words in a particular text will often mark the terrain of useful inquiry.