They found that the combination of three variables gives the best account of text difficulty: words per sentence (r² = .897), the average grade-level of words (r² = .891), and characters per word (r² = .839). The formula produces grade-level scores, as they are easier for teachers to understand and use.

The formula developers paid special attention to the Zone of Proximal Development (ZPD) proposed by Vygotsky (1978), the level of optimal difficulty that produces the most learning gain. They found that, for independent reading below the 4^th grade, maximum learning gain requires at least 85% comprehension. Advanced readers need a 92% score on reading quizzes. Those who exceed that percentage should be given material that is more challenging.

Other results of the studies indicate that:

• Maximum learning gain requires careful matching of book readability and reading skill.
• The amount of time spent reading correlates highly with gains in reading skill.
• Book length can be a good indication of readability.
• Feedback and teacher interaction are the most important factors in accelerated reading growth.

Formula applications

Many researchers outside the field of reading have recognized the value of the formulas. Edward Fry (1986) points out that articles on the readability formulas are among the most frequently cited articles of all types of educational research. The applications give researchers an objective means of controlling the difficulty of passages in their experiments.

The following is a sample of readability studies that used formulas: political literature (Zingman 1977), corporate annual reports (Courtis 1987), customer service manuals (Squires and Ross 1990) drivers' manuals (Stahl and Henk 1995), dental health information (Alexander 2000), palliative-care information (Payne et al. 2000), research consent forms (Hochhauser 2002; Mathew 2002; Paasche-Orlow et al. 2003), informed consent forms (Williams et al. 2003) online health information (Oermann and Wilson 2000), lead-poison brochures (Endres et al. 2002) online privacy notices (Graber et al. 2002) medical journals (Weeks and Wallace 2002), environmental health information (Harvey and Fleming 2003) and mental-health information (King et al. 2003).

Court actions and legislation Fry (1989a) points out that the validity of the formulas has been challenged in court and found suitable for legal purposes. The courts increasingly rely on readability formulas to show the readability of texts in protecting the rights of citizens to clear information. Court cases and legislation involving government documents and correspondence, criminal rights, product labeling, private contracts, insurance policies, ballot measures, warranties, and warnings are some of the legal applications of the formulas.

In 1984, Joseph David of New York was upset by his inability to understand a letter of denial he received in response to his appeal for Medicare benefits. Legal Services went to court in behalf of David and other elderly recipients of Medicare in New York. They pointed out that 48% of the population over 65 had less than a 9^th-grade education. Edward Fry testified in court that the denial letter was written at the 16^th-grade level. As a result, the judge ordered the Secretary Heckler of the U.S. Department of Health and Social Services to take "prompt action" to improve the readability of Medicare communications (David vs. Heckler 1984).