Appendix 1. List of readability tests used.

Test / Formula
(results yield reading grade level unless noted) / Description
Automated Readability Index (ARI) / 4.71*(AWL) + 0.5*(ASL)
- 21.43 / Originally created for US Air Force materials;
designed for technical documents and manuals.
New ARI / 5.84*(AWL) + 0.37*(ASL)
- 26.01 / Modified version of the ARI created for US Navy materials.
Bormuth Grade Placement
(BGP) / 3.761864 + 1.053153*(AWL)
- 2.138595*(AFW)3
+ 0.152832*(ASL)
- 0.002077*(ASL)2 / Often recommended for student documents.
Considered highly accurate because it incorporates word length, sentence length, and word familiarity.
(based on New Dale-Chall list of familiar words)
Coleman-
Liau Index†
(CLI) / -27.4004*(C/100) + 23.06395 / Meant for secondary age (4th grade to college level) readers. Usually yields the lowest grade when applied to technical documents.
Converts the predicted Cloze score (C) into a grade level.
Powers, Sumner, Kearl (PSK)-
Dale-Chall / 3.2672 + 0.0596*(ASL)
+ 0.1155*(PUFW*100) / Version of the New Dale-Chall which gives a specific grade level rather than a range of grade levels.
Danielson-
Bryan 1
(DB1) / 1.0364*(AWL) + 0.0194*(ACS) - 0.6059 / Originally meant to calculate readability faster because it uses characters instead of syllables as a factor.
New Farr, Jenkins, Paterson
(FJP) / -0.307*(PMW*100)
+ 0.387*(ASL) + 22.05 / A modified version of FJP designed for US Navy technical manuals and forms.
PSK-FJP / 8.4335 + 0.0923*(ASL)
- 0.0648*(PMW*100) / A variation of the FJP based on revised McCall-Crabbs criteria.
Flesch Reading Ease
(FRE)
[INDEX SCORE] / Index score (range 0-100) =
206.835 - 84.6*(ASW)
- 1.015*(ASL) / Meant for secondary and adult-level text;
a standard used by many US government agencies including the Department of Defense.
Index score is convertible to grade level score through published conversion charts.
PSK-Flesch† / 0.0778*(ASL) + 0.0455*(SW100) / Updates the FRE to use revised McCall-Crabbs criteria.
Also calculates grade level rather than index score.
Flesch-Kincaid Grade Level (FKGL) / 11.8*(ASW) + 0.39*(ASL)
- 15.59 / Designed for technical documents;
mostly applicable to manuals and forms.
FORCAST† / 20 - (N/10) / Devised for assessing US Army technical manuals and forms.
The only test not designed for running narrative, thus mostly appropriate for multiple-choice, applications, entrance forms, etc.
Gunning Fog / 0.4*[(ASL)+(PCW)*100] / Generally recommended for business publications and journals.
New Fog Count (NFC) / {[(E + 3*CW)/S]-3}/2 / Modified version of the Gunning Fog index created for the US Navy and designed for technical documents and manuals.
PSK-Gunning Fog / 3.0680 + 0.0877*(ASL)
+ 0.0984*(PCW*100) / Updated Gunning Fog based on the revised McCall-Crabbs criteria.
Harris-Jacobson Wide Range Formula
(HJWRF) / 0.245*[(PCW)*100]
+ 0.160*(ASL) + 0.642 / Based on common words known to 2nd graders.
Gives a "predicted raw score" that is then converted to a grade level readability score.
Simple Measure of Gobbledygook†(SMOG) / 1.0430*√(C30) + 3.1291 / Generally appropriate for secondary age (4th grade to college level) readers.
Tests for 100% comprehension, whereas most formulas test for around 50%-75% comprehension;
thus, usually yields a higher grade level score.
Modified SMOG† / Rounded √(# unique C30);
+1 if rounded value is ≥4 / Designed to create scores closer to other readability formulas (ie, lower grade level scores) than the original SMOG.
Spache, Revised† / 0.121*(ASL) + 0.082*(UFW100) + 0.659 / Based on list of 1041 common words (and their derivatives) known to readers 4th grade and below.
Better for ages Kindergarten to 7th grade.

†Typically these tests use only a sample of text; however, the Readability Studio analyzes the entire passage and standardizes it to the requirements of the respective formula; ACS = average characters per sentence, ie, total number of characters (excluding sentence-ending punctuation) divided by total number of sentences; ASL = average sentence length, ie, total number of words divided by total number of sentences; ASW = average syllables per word, ie, total number of syllables divided by total number of words;AWL = average word length, ie, total number of characters (excluding sentence-ending punctuation) divided by total number of words; C = predicted Cloze score: 141.8401 - 0.214590*R + 1.079812*S; CW = total number of complex words (words with 3 or more syllables); C30 = number of complex words (3 or more syllables) per 30 sentences; E = total number of easy words (words with less than 3 syllables); N = total number of monosyllabic words in 150-word sample; PCW = percentage of complex words, ie, total number of complex words divided by total number of words; For Fog tests, complex words = words >3 syllables, unless proper nouns, words with added suffixes, or compound words composed of simpler words; For HJWRF, complex words = words not on a list of common words known to most 2nd grade students, unless proper nouns or with added suffixes/adverbial forms or hyphenated.PFW = percentage familiar words, ie, number of familiar Dale-Chall words divided by total number of words; PUFW = percentage unfamiliar words, ie, number of unfamiliar Dale-Chall words divided by total number of words; PMW = percentage of monosyllabic words, ie, total number of monosyllabic words divided by total number of words; R = total number of characters; S = total number of sentences; SW100 = number of syllables per 100 words; UFW100 = number of unique unfamiliar words per 100-word sample