¹ This report is based on work done under ARDC Project No. 7730, Task No. 17125, in support of the research and development program of the Air Force Personnel and Training Research Center, Lackland Air Force Base, Texas. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.

² Charles C. Fries, The structure of English (New York, 1952).

³ Function words are generally treated as a unit through most of this article, and sometimes, for convenience' sake, the word ‘class’ is applied to them. It should be noted, however, that while function words as a whole display certain characteristics which distinguish them from the parts of speech (Fries 104 ff.), they are not a class in the same sense as Classes 1 to 4, since there is no environment common to them all.

⁴ Taking a suggestion from Paul Roberts' study, Fries's group D, Lg 31.20–4 (1955), we set up an additional criterion for words with -ly; namely, to be classed as Group D such words had to be able to replace very before rapidly, but unable to occur after he behaved —.

⁵ On the question of the accuracy of the percentages in our sample as estimates of the percentages for the sentence population as a whole, we can make a fair approximation for a given word-class at a given sentence position based upon $\sqrt{\frac{pq}{n}}$, the standard error of a percentage, where p is the sample percentage, q = 1 – p, and n is the sample size. We determine the margin of error in our estimate of P, the population percentage, by the formula $\pm \hspace{0.17em}t\sqrt{\frac{pq}{n}}$, where, assuming that p is normally distributed, t is the normal deviate corresponding to some confidence probability (some predetermined level of risk that a given sample might be highly unrepresentative of the population—here, say, 1 in 20, in which event t would be equal to, roughly, 2). In the case of Class 1 words in the first position of 6-word sentences, for example, p = 48% and P would be estimated to lie in the range p ± 4.5%. It should be noted that with these data this formula will not give reliable results where p is less than 10%.

⁶ These averages are not misleading. The variation in percentage of pronoun occurrence among all sentence positions other than sentence initial was relatively small.

⁷ In the case of equiprobable alternatives, there is a simpler formula, H = log₂ r, where r is the number of alternatives. Thus, we may say here that maximum H = log₂ 5.