Bormuth's study confirmed the curvilinearity of the formula variables. That means their correlation with text difficulty changes in the upper grades, producing a curve when plotted on a chart. Dale and Chall (1948) included an adjustment for this feature in their formula-correction chart. This adjustment was also included in the SMOG formula (McLaughlin 1968), the Fry Graph (Fry 1969), the FORCAST formula (Caylor et al. 1973), Degrees of Reading Progress (Koslin et al. 1987), and the ATOS formula (Paul 2003).

Some critics of the formulas (Rothkopf 1972, Thorndike 1973-74, Selzer 1981, Redish and Selzer 1985) claim that decoding words and sentences is not a problem for adults. Bormuth's study, however, shows that the correlation between the formula variables and comprehension do not change as a function of reading ability (p. 105). Empirical studies have confirmed that, in adult readers, difficulty in reading is linked to word recognition (Stanovich 1984) and decoding of sentences (Massad 1977). We cannot assume that adults are better learners than children of the same reading level. In fact, they are often worse (Russell 1973, Sticht 1982).

Bormuth's next project (1969) was a study of the readability variables and their relationship to comprehension. His subjects included 2,600 fourth-to-twelfth-grade pupils in a Minneapolis school district.

The method consisted first in rating the reading ability of all the students with the California 1963 Reading Achievement test. It used 330 different passages of about 100 words each to confirm the reliability of 164 different variables, many of them never examined before such as the parts of speech, active and passive voice, verb complements, and compound nouns.

The five cloze tests used for each passage (resulting in 1,650 tests) gave him about 276 responses for each deleted word, resulting in over 2 million responses to analyze.

With this data, Bormuth was able to develop 24 new readability formulas, some of which used 14 to 20 variables. These new variables, he found, added little to the validity of the two classic-formula variables and were eventually dropped. The study divided the students of each reading level into two groups, one that was given a multiple-choice test and the other a cloze test of the same material.

Since Thorndike's (1916) recommendation, educators and textbook publishers had used 75% correct scores on a multiple-choice test as the criterion for optimum difficulty for assisted classroom learning, and 90% for independent reading. These criterion scores, however, were based on convention and use, not on scientific study.

This Bormuth study validated the equivalencies of 35%, 45%, and 55% correct cloze criterion scores with 50%, 75%, and 90% correct multiple-choice scores. It also showed that the cloze score of 35% correct answers indicates the level of difficulty required for maximum information gain.

Finally, this study produced three different formulas, one is for basic use, one for machine use, and one for manual use. All three formulas predict the difficulty of texts for all grade levels using a 35%, 45%, 55%, or a mean-cloze criterion.

The Bormuth Mean Cloze formula This formula uses three variables: number of words on the original Dale-Chall list of 3,000, average sentence length in words, and average word length in letters. This formula was later adapted and used in the Degrees of Reading Power used by the College Entrance Examination Board in 1981 (see below). The original Bormuth Mean Cloze formula is: