Summary
Most readability formulas provide only rough estimates of a passage's complexity level.

The goal of most sciences is to reduce phenomena to a formula. Writing, though clearly not a science, is no exception. In the last 60 or so years, various academics have tried to devise formulas identifying the "level" at which a passage or book was written. For example, textbook manufacturers would love a formula telling them whether a given book is appropriate for fifth graders.

To determine level, researchers have devised many readability formulas:

Parameters for formulas include:

• Avg. number of words per sentence.
• Avg. length of words (either characters per words or syllables per word)
• Number of long words per 100, where long word might be words of greater than 3 syllables.
• Number of difficult words per 100, where "difficult" might be words not belonging to a list of common words.

In addition to the relatively easy-to-program parameters shown in the preceding list, researchers have also played with "closure tests." In a closure test, researchers black out every nth word of a passage. Then, test subjects are asked to guess the missing words. When test subjects can guess most of the missing words, the experimenters assume that the passage is on level. When test subjects cannot guess most of the missing words, the experimenters assume that the passage is too complex. Closure tests are pretty good predictors of reading level, but they are much more expensive to run then other readability formulas.

## The Gunning-Fogg Index

```
average number of words per sentence
+ percentage of "long words" (three or more syllables).
-------------------------------------------------------------
Multiplying this sum by 0.4 gives you the grade level
```

The Fry readability index is based on average sentence length and average number of syllables per word. Edward Fry devised it. You can find the index at:

```

http://school.discovery.com/schrockguide/fry/fry2.html

```

The graph is taken from Fry, Edward. Elementary Reading Instruction. NY: McGraw Hill, 1977, pg 217

## Are readability tests good predictors?

Readability tests are decent broad predictors of complexity level. Readability formulas will correctly mark a college history textbook at a higher level than an elementary school history textbook. However, the true complexity of a passage is very, very hard to pin down through mathematical means. For example, Hemmingway's prose might score at a fifth grade level by objective readability formulas. After all, he wrote short sentences filled with commonly-used short words. It is unlikely, though, that educators would feel Hemmingway's tales would be appropriate for a fifth grade classroom. Dr. Seuss' writing presents another problem. Readability formulas based on sentence length would probably score the good doctor's prose as appropriate for K-2. However, readability formulas based on the percentage of common words would flag words like Lorax and Gricle and weight Dr. Seuss at a much higher level.