Activity 8.1

Measurement Difficulties and Indexes

10 points

Due at the beginning of class, Friday, March 20, 2009

In Topic 8, you read about several indexes that are used to measure complex quantities that are not defined and measured easily.  In this activity, you will work with one of those indexes, the Fog Index, which measures reading difficuly.  You will analyze different reading passages to get a better sense of how the different components affect the result, and why this index gives a measurement of a text’s reading difficulty.

1.  Some properties are easier to understand and measure than others.  For example, we all understand how to measure the height of a person or the time it takes a particular person to complete an exam.  It is not as clear how to measure a person’s intelligence or a customer's satisfaction with services delivered to him or her.

1. a.  List three additional properties of a person that are defined and measured fairly easily.

1. b. List three additional properties of a person that are more difficult to define and measure.

2.  Now, consider another property, the property of “reading difficulty of a passage of text.”  For the most part, we can probably agree that such a property exists: some passages of text are certainly easier to read than others.  But how might you measure this property?

2. a.  List three factors that might go into measuring a passage’s reading difficulty.

2. b.  Consider the following three passages of text:

Passage 1:
To engage in a serious discussion of race in America, we must begin not with the problems of black people, but with the flaws of American society, flaws rooted in historic inequalities and longstanding cultural stereotypes.  How we set up the terms for discussing racial issues shapes our perception and response to these issues.  As long as black people are viewed as a “them,” the burden falls on blacks to do all the “cultural” and “moral” work necessary for healthy race relations.  The implication is that only certain Americans can define what it means to be American, and the rest must simply “fit in.”

The emergence of strong black-nationalist sentiments among blacks, especially among your people, is a revolt against this sense of having to “fit in.”

Passage 2:
Everyone agreed to this and off they went walking briskly and stamping their feet. Lucy proved a good leader. At first she wondered whether she would be able to find the way, but she recognized an odd-looking tree on one place and a stump in another and brought them on to where the ground became uneven and into the little valley and at last to the very door of Mr Tumnus's cave. But there a terrible surprise awaited them.

The door had been wrenched off its hinges and broken to bits. Inside, the cave was dark and cold and had the damp feel and smell of a place that had not been lived in for several days. Snow had drifted in from the doorway and was heaped on the floor, mixed with something black, which turned out to be the charred sticks and ashes from the fire. Someone had apparently flung it about the room and then stamped it out. The crockery lay smashed on the floor and the picture of the Faun's father had been slashed into shreds with a knife.

Passage 3:
The truck drove to a part of town that George had never seen before.  At last it stopped in front of a large building.  It was the Museum.  George did not know what a Museum was.  He was curious.  While the guard was busy reading his paper, George slipped inside.

He walked up the steps and into a room full of all sorts of animals.  At first George was scared, but then he noticed that they did not move.  They were not alive, they were stuffed animals, put into the Museum so that everybody could get a look at them.

2. c. Based on your impression from reading these passages once, rank the three from least difficult to most difficult to read.
Least difficult:         Next in difficulty:                Most difficult:

3.  Because longer sentences tend to be more difficult to read than shorter ones, the number of words per sentence in a passage of text would seem to be a reasonable measure of reading difficulty.

In Word, it is fairly easy to find the word count on a selection of text.  The status bar displays the number of words in the selection. For example, 100/1440 means that the selection accounts for 100 words of the total number of words in the document, 1,440.

Once you have determined the word count for each passage, set up a table in an Excel spreadsheet, like the one shown here, and record the number of words and the number of sentences for each of the three passages.  Then use the appropriate formula in Excel use to compute the number of words per sentence.  Copy and paste your table into your Word document when you are done.

4.  Based on “words per sentence,” rank the three passages from least difficult to most difficult.
Least difficult:                     Next in difficulty:                            Most difficult:

5.  Another measure of reading difficulty might be the number of “big” words in a passage of text.  Count the number of “big” words, using the definition of “big” we discussed in class:

words with three or more syllables, except proper names, and compound words formed from easy words (like "everything"), formed from a suffix (such as "ed" or "ing"), or connected with a hyphen.

How many “big” words (as defined above) did each passage have?  Give a list of the “big” words in each.  If a word occurs more than once, you need to count it each time, but just list it once.

6.  Here you will add two columns (to the right of your “Words per Sentence” column) to your spreadsheet.  The first new column will be “Number of Big Words,” and you can fill this by entering the number of “big” words you found for each passage in #5.  The second new column will be labeled “Percentage of Big Words,” and calculate the percentage of big words per passage, which is:
Number of big words / Total number of words .
Copy and paste your updated table into your Word document.

7.  Based on the “Percentage of Big Words” you just calculated, rank the three passages from least difficult to most difficult.
Least difficult:                    Next in difficulty:                            Most difficult: 

8.  The Fog Index is a measure of reading difficulty used by newspaper and magazine editors.  This measure takes into account both sentence length and word size.  Set up another column on your spreadsheet to calculate the Fog Index, where you can use the following formula:

Fog Index = 0.4 * ( words_per_sentence  +  percent_of_Big_Words )

Copy and paste your updated table into your Word document.

9.  A Fog Index value of 9 purportedly indicates a ninth-grade reading level, a value of 12 indicates a 12^th grade reading level, and a value of 14 indicates a college-sophomore reading level.  Based on your calculations, does this seem reasonable?  Why or why not?

10.  Use the spreadsheet you set up to help answer the following questions, and give numeric answers:
10. a.  How would the Fog Index for each of the passages change if everything else stays the same but the number of “big” words is doubled?

10. b.  How would the Fog Index for each of the passages change if the number of words and the number of “big” words are what they were originally (you should undo the change you made in #10.a. above), but the number of sentences is doubled?

11.  There are several web-sites that offer automated versions of the Fog Index.  For example,  http://simbon.madpage.com/Fog/ .   Input Passage 3 into a Fog Index calculator. (If the above web-site is not available, you may "Google" another one and use it, just remember to share the URL.)  What does it return as the Fog Index?  Did it identify the same “Big” words that you did for Passage 3 above? 

Summary
In this activity, you examined the Fog Index for several passages of text and looked at whether the Fog Index is a reasonable measure of reading difficulty.  You also considered how the Fog Index would change if there were more “big” words or more sentences in the passages.

Passage 1: West, Cornel.  Race Matters.  Boston: Beacon Press, 1993, p. 3.
Passage 2: Lewis, C.S.  The Lion, the Witch and the Wardrobe.  New York: Scholastic Inc., 1981, pp. 53-54.
Passage 3: Rey, H. A.  Curious George Gets a Medal.  Boston: Houghton Mifflin Company, 1957, pp. 30-31.