List of readability tests

This is a list of formulas which predict textual difficulty.

## Overview 
These are ways of predicting how hard a piece of writing will be to understand (its textual difficulty). Research has shown that two main factors affect the ease with which texts are read.p113 There have been many dozens of experimental tests, summarised by Klare.p121–156 Correlations between readability measures and comprehension scores on passages are usual, as are correlations between readability scores are grade levels as chosen by experienced teachers. Quite an important result was got by Murphy, who increased the readability of a farm journal and found the readership much increased.

## One-variable formulae 
### SMOG 
The **SMOG** formula uses one variable to predict the difficulty of a passage of prose.  It was developed G. Harry McLaughlin in 1969 to make calculations as simple as possible. Like Gunning-Fog the formula uses words which have 3 or more syllables as an indicator for hardness; these words are said to be polysyllabic.

The original formula was given for samples of 30 sentences. It is:
:
\mbox{SMOG grade} = 1.0430 \sqrt{ \mbox{hard words in 30 sentences} } \ + 3.1291

This can be adjusted to work with any number of sentences:

:
\mbox{SMOG grade} = 1.0430 \sqrt{ \mbox{hard words} \times \frac{30}{ \mbox{sentences} } } \ + 3.1291

McLaughlin also created directions for an approximate version which can be done with just mental calculation. 
# Count the number of words with 3 or more syllables, excluding names, in a set of 30 sentences
# Take the square root of the nearest perfect square
# Add 3 to get the estimated SMOG grade

## Two-variable formulae 
### The Dale–Chall formula 
**Edgar Dale**, a professor of education at Ohio State University, was one of the first critics of Thorndike's vocabulary-frequency lists. He claimed that they did not distinguish between the different meanings that many words have. He created two new lists of his own. One, his "short list" of 769 easy words, was used by **Irving Lorge** in his formula. The other was his "long list" of 3,000 easy words, which were understood by 80 percent of fourth-grade students. In 1948, he incorporated this list in a formula which he developed with **Jeanne S. Chall**, who was to become the founder of the Harvard Reading Laboratory. 

To apply the formula:
# Select several 100-word samples throughout the text.
# Compute the average sentence length in words (divide the number of words by the number of sentences).
# Compute the percentage of words NOT on the Dale–Chall word list of 3,000 easy words.
# Compute this equation

Raw Score = 0.1579PDW + 0.0496ASL + 3.6365

Where: 
: Raw Score = uncorrected reading grade of a student who can answer one-half of the test questions on a passage.
: PDW = Percentage of Difficult Words not on the Dale–Chall word list.
: ASL = Average Sentence Length

Finally, to compensate for the "grade-equivalent curve," apply the following chart for the Final Score:

In 1995, Dale and Chall published a new version of their formula with an upgraded word list.

### Flesch reading ease score 
The formula for the Flesch reading-ease score is

:
206.835 - 1.015 \left( \frac{\text{total words}}{\text{total sentences}} \right) - 84.6 \left( \frac{\text{total syllables}}{\text{total words}} \right).

Scores can be interpreted as shown in the table below.

The US Department of Defense uses the reading ease test as the standard test of readability for its documents and forms. Florida requires that life insurance policies have a Flesch reading ease score of 45 or greater.

Use of this scale is so ubiquitous that it is bundled with popular word processing programs and services such as KWord, IBM Lotus Symphony, Microsoft Office Word, WordPerfect, and WordPro.

### Gunning Fog 
The **Gunning Fog**, sometimes called the Fog index, is a formula developed by Robert Gunning.  It was first published in his book *The Technique of Clear Writing* in 1952.  It became popular because the score is easy to calculate. 

The formula has been criticized as it mainly uses sentence length. The critics argue that texts created with the formula will use shorter sentences without using simpler words. However, this criticism confuses *prediction of difficulty* with production of prose (writing). The role of readability tests is to predict difficulty; writing better prose is quite another matter. As discussed in prose difficulty, sentence length is an index of syntactical difficulty.

:
\mbox{ARI} = 4.71 \times \frac{ \mbox{letters} }{ \mbox{words} } + 0.50 \times \frac{ \mbox{words} }{ \mbox{sentences} } - 21.43

## References 
## Further reading 
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