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List of readability tests
This is a list of formulas which predict textual difficulty.
Contents
Overview
These are ways of finding out how hard a piece of writing is to understand (its textual difficulty).
The Dale–Chall formula
Edgar Dale, a professor of education at Ohio State University, was one of the first critics of Thorndike's vocabularyfrequency 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 fourthgrade 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 100word 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 onehalf 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 "gradeequivalent curve," apply the following chart for the Final Score:
Raw Score  Final Score 

4.9 and below  Grade 4 and below 
5.0 to 5.9  Grades 5–6 
6.0 to 6.9  Grades 7–8 
7.0 to 7.9  Grades 9–10 
8.0 to 8.9  Grades 11–12 
9.0 to 9.9  Grades 13–15 (college) 
10 and above  Grades 16 and above^{[1]} 
Correlating 0.93 with comprehension as measured by reading tests, the Dale–Chall formula is the most reliable formula and is widely used in scientific research. Go to the Okapi Web site for a computerized version of this formula: Okapi
In 1995, Dale and Chall published a new version of their formula with an upgraded word list.^{[2]}
Fog
Uses affixes and personal pronouns.
Formula
 [math] \mbox{Fog grade} = \frac{ \mbox{words} }{ \mbox{sentences} } + \frac{ \mbox{affixes}\mbox{Personal Pronouns} }{ \frac{ \mbox{words} }{ \mbox{sentences} } } [/math]
Gunning Fog
The Gunning Fog, sometimes 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 due to the easy which the score is calculated without a calculator.
The formula has been criticized as it uses only 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.^{[3]}
Formula
 [math] \mbox{Gunning Fog grade} = 0.4 \times \left [ \frac{ \mbox{words} }{ \mbox{sentences} } + \left ( 100 \times \frac{ \mbox{hard words} }{\mbox{words}} \right ) \right ] [/math]
Where:
 words is number of words
 sentences is number of sentences
 hard words is the number of word with 3 or more syllables (excluding endings) which are not names or compound words
Spache
The Spache method compares words in a text to a list of words which are familiar in everyday writing. The words that are not on the list are called unfamiliar. The number of words per sentence are counted. This number and the percentage of unfamiliar words is put into a formula. The result is a reading age. Someone of this age should be able to read the text. It is designed to work on texts for children in primary education or grades from 1^{st} to 7^{th}.
Formula
 [math] \mbox{Spache grade} = \left ( 0.141 \times \frac{ \mbox{words} }{ \mbox{sentences} }\right )+ \left ( 0.086 \times \frac{ \mbox{unfamiliar words} }{ \mbox{words} } \right ) + 0.839 [/math]
In 1974 Spache revised his Formula to:
 [math] \mbox{Spache grade (revised)} = \left ( 0.121 \times \frac{ \mbox{words} }{ \mbox{sentences} }\right )+ \left ( 0.082 \times \frac{ \mbox{unfamiliar words} }{ \mbox{words} } \right ) + 0.659 [/math]
ColemanLiau Index
Formula
The calculations are performed in two steps. The first step finds the Estimated Close Percentage. The second step calculates the actual grade.
 [math] \begin{array}{lcl} \mbox{ECP} = 141.8401  \left ( 0.214590 \times \mbox{characters} \right ) + \left ( 1.079812 \times \mbox{sentences} \right )\\ \mbox{CLI} = \left ( 27.4004 \times \frac{\mbox{ECP}}{100} \right ) + 23.06395 \end{array} [/math]
A simple version also exists that is not as accurate:
 [math] \mbox{CLI} = \left ( 5.88 \times \frac{\mbox{characters}}{\mbox{words}} \right )  \left ( 29.5 \times \frac{ \mbox{sentences} }{ \mbox{words} } \right )  15.8 [/math]
Automated Readability Index
The Automated Readability Index was designed for realtime computing of readability for the electric typewriter.^{[4]}
Formula
 [math] \mbox{ARI} = 4.71 \times \frac{ \mbox{letters} }{ \mbox{words} } + 0.50 \times \frac{ \mbox{words} }{ \mbox{sentences} }  21.43 [/math]
SMOG
The SMOG formula is a way of estimating the difficulty of writing. It was developed G. Harry McLaughlin in 1969 to make calculations as simple as possible. It has a high correlation 0.985 or 0.97% accuracy of the score to the actual grade at which students where able to fully understand the piece of writing.
Like GunningFog the formula uses words which have 3 or more syllables as an indicator for hardness; these words are said to be polysyllabic.
Formula
The original formula was given for a 30 sentence samples, which is:
 [math] \mbox{SMOG grade} = 1.0430 \sqrt{ \mbox{hard words in 30 sentences} } \ + 3.1291 [/math]
This can be adjusted to work with any number of sentences:
 [math] \mbox{SMOG grade} = 1.0430 \sqrt{ \mbox{hard words} \times \frac{30}{ \mbox{sentences} } } \ + 3.1291 [/math]
McLaughlin also created directions for an approximate version which can be done with just mental math.
 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
References
 ↑ Dale, E. and J. S. Chall. 1948. '"A formula for predicting readability". Educational research bulletin Jan.21 and Feb 17, 27:1–20, 37–54.
 ↑ Chall, J. S. and E. Dale. 1995. Readability revisited: The new Dale–Chall readability formula. Cambridge, MA: Brookline Books.
 ↑ Klare G.R. 1963. The measurement of readability. Iowa State University Press, Ames IA
 ↑ Senter R.J.; Smith E.A. (November, 1967). Automated Readability Index.. WrightPatterson Air Force Base. p. iii. AMRLTR6620. http://www.dtic.mil/cgibin/GetTRDoc?AD=AD0667273. Retrieved 20120318.
 Dubay W.H. (2004). "The principles of readability". Costa Mesa, CA: Impact Information. http://eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/1b/bf/46.pdf. Retrieved 20080110.
 Spache G. (1953). "A new readability formula for primarygrade reading materials". The Elementary School Journal 53 (7): 410413. http://links.jstor.org/sici?sici=00135984(195303)53%3A7%3C410%3AANRFFP%3E2.0.CO%3B2D. Retrieved 20080110.
 Coleman M.; Liau T.L. (1975). "A computer readability formula designed for machine scoring". Journal of Applied Psychology 60 (2): 283284.

