Over four years, however, he and his associates revised this position. He eventually admitted that "these formulas are correlated with the conceptual properties of text" and that vocabulary and sentence length are the strongest predictors of difficulty (Kintsch and Miller 1981, p. 222).

While Kintsch and his colleagues did not come up with any easily used formula, they did contributed to our understanding of readability, including the central role of coherence in a text. Kintsch found out that lack of coherence affects lower-grade readers much more than upper-grade ones. The upper-grade readers, in fact, feel challenged to reorganize the text themselves. They may require more opportunities for solving problems, while lower-grade readers require more carefully organized texts.

The Air Force transformational formula. Perhaps the most ambitious attempt to quantify the variables of the cognitive theorists and put them in a formula was the project of Williams, Siegel, Burkett, and Groff (1977). Working for the Air Force Human Resources Laboratory, they examined new variables, produced a new formula, and presented supporting data. The variables they included were:

• Four psycholinguistic variables such as Yngve word depths, transformational complexity, center embedding, and right branching.
• Four Structure of Intellect variables including cognition of semantic units, memory for semantic units, evaluation of symbolic implications, and divergent production of semantic units.

For a criterion, they used cloze scores on 14 passages of about 600 words each taken from the Air Force career-development course. They deleted each tenth word in the cloze test and used only one version out of a possible ten on 51 Air-Force subjects. The computerized formula produced a correlation of 0.601 with text difficulty.

Susan Kemper and the reader's mental load Following Kintsch, Susan Kemper (1983) sought to explain comprehension in terms of underling cognitive processes. She developed a formula designed to measure the "inference load" based on three kinds of causal links:

• Physical states
• Stated mental states
• Inferred mental states

The Kemper formula measures the density of the propositions and embedded clauses. It takes considerable time and effort in comparison to the readability formulas. It has a correlation of .63 with the McCall-Crabbs tests (the original Dale-Chall formula has a correlation of .64).

Kemper (p. 399) commented: "..sentence length and word familiarity do contribute to the comprehension of these passages.... These two different approaches to measuring the grade level difficulty of texts are equivalent in predictive power."

Kemper admitted that her formula, like all readability formulas, is better at predicting problems than fixing them. For writing, both formulas are best used as a general guide.