(Redirected from Fog Index)

This is a list of formulas which predict textual difficulty.

## Overview

These are method 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 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 per cent 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:

1. Select several 100-word samples throughout the text.
2. Compute the average sentence length in words (divide the number of words by the number of sentences).
3. Compute the percentage of words NOT on the Dale–Chall word list of 3,000 easy words.
4. 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:

Raw Score Final Score
4.9 and below Grade 4 and below
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

$\mbox{Fog grade} = \frac{ \mbox{words} }{ \mbox{sentences} } + \frac{ \mbox{affixes}-\mbox{Personal Pronouns} }{ \frac{ \mbox{words} }{ \mbox{sentences} } }$

## 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 since it 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 dificulty, sentence length is an index of syntactical difficulty.[3]

### Formula

$\mbox{Gunning Fog grade} = 0.4 \times \left [ \frac{ \mbox{words} }{ \mbox{sentences} } + \left ( 100 \times \frac{ \mbox{hard words} }{\mbox{words}} \right ) \right ]$

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 1st to 7th.

### Formula

$\mbox{Spache grade} = \left ( 0.141 \times \frac{ \mbox{words} }{ \mbox{sentences} }\right )+ \left ( 0.086 \times \frac{ \mbox{unfamiliar words} }{ \mbox{words} } \right ) + 0.839$

In 1974 Spache revised his Formula to:

$\mbox{Spache grade (revised)} = \left ( 0.121 \times \frac{ \mbox{words} }{ \mbox{sentences} }\right )+ \left ( 0.082 \times \frac{ \mbox{unfamiliar words} }{ \mbox{words} } \right ) + 0.659$

## Coleman-Liau Index

### Formula

The calculations are performed in two steps. The first step finds the Estimated Close Percentage. The second stop, calculation the actual grade.

$\begin{array}{lcl} \mbox{ECP} = 141.8401 - \left ( 0.214590 \times \mbox{characters} \right ) + \left ( 1.079812 \times \mbox{sentences} \right )\\ \mbox{CLI} = \left ( -27.4004 \times \frac{\mbox{ECP}}{100} \right ) + 23.06395 \end{array}$

A simple version also exists that is not as accurate:

$\mbox{CLI} = \left ( 5.88 \times \frac{\mbox{characters}}{\mbox{words}} \right ) - \left ( 29.5 \times \frac{ \mbox{sentences} }{ \mbox{words} } \right ) - 15.8$

The Automated Readability Index was designed for real-time computing of readability for the electric typewriter.[4]

### Formula

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

## 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 Gunning-Fog the formula uses words which have 3 or more syllables as an indicator for hardness, these are said to be polysyllabic.

### Formula

The original formula was given for a 30 sentence samples, which 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 has made directions for a version which could be done with just mental math.

1. Count the number of words with 3 or more syllables, excluding names, in a 30 sentences.
2. Take the square root of the nearest perfect square