Thurstone Scaling

# Thurstone Scaling

Thurstone was one of the first and most productive scaling theorists. He actually invented three different methods for developing a unidimensional scale: the method of equal-appearing intervals; the method of successive intervals; and, the method of paired comparisons. The three methods differed in how the scale values for items were constructed, but in all three cases, the resulting scale was rated the same way by respondents. To illustrate Thurstone’s approach, I’ll show you the easiest method of the three to implement, the method of equal-appearing intervals.

## The Method of Equal-Appearing Intervals

### Developing the Focus

The Method of Equal-Appearing Intervals starts like almost every other scaling method – with a large set of statements. Oops! I did it again! You can’t start with the set of statements – you have to first define the focus for the scale you’re trying to develop. Let this be a warning to all of you: methodologists like me often start our descriptions with the first objective methodological step (in this case, developing a set of statements) and forget to mention critical foundational issues like the development of the focus for a project. So, let’s try this again…

The Method of Equal-Appearing Intervals starts like almost every other scaling method – with the development of the focus for the scaling project. Because this is a unidimensional scaling method, we assume that the concept you are trying to scale is reasonably thought of as one-dimensional. The description of this concept should be as clear as possible so that the person(s) who are going to create the statements have a clear idea of what you are trying to measure. I like to state the focus for a scaling project in the form of a command – the command you will give to the people who will create the statements. For instance, you might start with the focus command:

Generate statements that describe specific attitudes that people might have towards persons with AIDS. You want to be sure that everyone who is generating statements has some idea of what you are after in this focus command. You especially want to be sure that technical language and acronyms are spelled out and understood (e.g., what is AIDS?).

### Generating Potential Scale Items

Now, you’re ready to create statements. You want a large set of candidate statements (e.g., 80 – 100) because you are going to select your final scale items from this pool. You also want to be sure that all of the statements are worded similarly – that they don’t differ in grammar or structure. For instance, you might want them each to be worded as a statement which you cold agree or disagree with. You don’t want some of them to be statements while others are questions.

For our example focus on developing an AIDS attitude scale, we might generate statements like the following (these statements came from a class exercise I did in my Spring 1997 undergrad class):

• people get AIDS by engaging in immoral behavior
• you can get AIDS from toilet seats
• AIDS is the wrath of God
• anybody with AIDS is either gay or a junkie
• AIDS is an epidemic that affects us all
• people with AIDS are bad
• people with AIDS are real people
• AIDS is a cure, not a disease
• you can get AIDS from heterosexual sex
• people with AIDS are like my parents
• you can get AIDS from public toilets
• women don’t get AIDS
• I treat everyone the same, regardless of whether or not they have AIDS
• AIDS costs the public too much
• AIDS is something the other guy gets
• living with AIDS is impossible
• children cannot catch AIDS
• AIDS is a death sentence
• because AIDS is preventable, we should focus our resources on prevention instead of curing
• People who contract AIDS deserve it
• AIDS doesn’t have a preference, anyone can get it.
• AIDS is the worst thing that could happen to you.
• AIDS is good because it will help control the population.
• If you have AIDS, you can still live a normal life.
• People with AIDS do not need or deserve our help
• By the time I would get sick from AIDS, there will be a cure
• AIDS will never happen to me
• you can’t get AIDS from oral sex
• AIDS is spread the same way colds are
• AIDS does not discriminate
• You can get AIDS from kissing
• AIDS is spread through the air
• Condoms will always prevent the spread of AIDS
• People with AIDS deserve what they got
• If you get AIDS you will die within a year
• Bad people get AIDS and since I am a good person I will never get AIDS
• I don’t care if I get AIDS because researchers will soon find a cure for it.
• AIDS distracts from other diseases that deserve our attention more
• bringing AIDS into my family would be the worst thing I could do
• very few people have AIDS, so it’s unlikely that I’ll ever come into contact with a sufferer
• if my brother caught AIDS I’d never talk to him again
• People with AIDS deserve our understanding, but not necessarily special treatment
• AIDS is a omnipresent, ruthless killer that lurks around dark alleys, silently waiting for naive victims to wander passed so that it might pounce.
• I can’t get AIDS if I’m in a monogamous relationship
• the nation’s blood supply is safe
• universal precautions are infallible
• people with AIDS should be quarantined to protect the rest of society
• because I don’t live in a big city, the threat of AIDS is very small
• I know enough about the spread of the disease that I would have no problem working in a health care setting with patients with AIDS
• the AIDS virus will not ever affect me
• Everyone affected with AIDS deserves it due to their lifestyle
• Someone with AIDS could be just like me
• People infected with AIDS did not have safe sex
• Aids affects us all.
• People with AIDS should be treated just like everybody else.
• AIDS is a disease that anyone can get if there are not careful.
• It’s easy to get AIDS.
• The likelihood of contracting AIDS is very low.
• The AIDS quilt is an emotional reminder to remember those who did not deserve to die painfully or in vain
• The number of individuals with AIDS in Hollywood is higher than the general public thinks
• It is not the AIDS virus that kills people, it is complications from other illnesses (because the immune system isn’t functioning) that cause death
• AIDS is becoming more a problem for heterosexual women and their offsprings than IV drug users or homosexuals
• A cure for AIDS is on the horizon
• A cure for AIDS is on the horizon
• Mandatory HIV testing should be established for all pregnant women

### Rating the Scale Items

OK, so now you have a set of statements. The next step is to have your participants (i.e., judges) rate each statement on a 1-to-11 scale in terms of how much each statement indicates a favorable attitude towards people with AIDS. Pay close attention here! You DON’T want the participants to tell you what their attitudes towards AIDS are, or whether they would agree with the statements. You want them to rate the “favorableness” of each statement in terms of an attitude towards AIDS, where 1 = “extremely unfavorable attitude towards people with AIDS” and 11 = “extremely favorable attitude towards people with AIDS.”. (Note that I could just as easily had the judges rate how much each statement represents a negative attitude towards AIDS. If I did, the scale I developed would have higher scale values for people with more negative attitudes).

### Computing Scale Score Values for Each Item

The next step is to analyze the rating data. For each statement, you need to compute the Median and the Interquartile Range. The median is the value above and below which 50% of the ratings fall. The first quartile (Q1) is the value below which 25% of the cases fall and above which 75% of the cases fall – in other words, the 25th percentile. The median is the 50th percentile. The third quartile, Q3, is the 75th percentile. The Interquartile Range is the difference between third and first quartile, or Q3 - Q1. The figure above shows a histogram for a single item and indicates the median and Interquartile Range. You can compute these values easily with any introductory statistics program or with most spreadsheet programs. To facilitate the final selection of items for your scale, you might want to sort the table of medians and Interquartile Range in ascending order by Median and, within that, in descending order by Interquartile Range. For the items in this example, we got a table like the following:

 Statement Number Median Q1 Q3 Interquartile Range 23 1 1 2.5 1.5 8 1 1 2 1 12 1 1 2 1 34 1 1 2 1 39 1 1 2 1 54 1 1 2 1 56 1 1 2 1 57 1 1 2 1 18 1 1 1 0 25 1 1 1 0 51 1 1 1 0 27 2 1 5 4 45 2 1 4 3 16 2 1 3.5 2.5 42 2 1 3.5 2.5 24 2 1 3 2 44 2 2 4 2 36 2 1 2.5 1.5 43 2 1 2.5 1.5 33 3 1 5 4 48 3 1 5 4 20 3 1.5 5 3.5 28 3 1.5 5 3.5 31 3 1.5 5 3.5 19 3 1 4 3 22 3 1 4 3 37 3 1 4 3 41 3 2 5 3 6 3 1.5 4 2.5 21 3 1.5 4 2.5 32 3 2 4.5 2.5 9 3 2 3.5 1.5 1 4 3 7 4 26 4 1 5 4 47 4 1 5 4 30 4 1.5 5 3.5 13 4 2 5 3 11 4 2 4.5 2.5 15 4 3 5 2 40 5 4.5 8 3.5 2 5 4 6.5 2.5 14 5 4 6 2 17 5.5 4 8 4 49 6 5 9.75 4.75 50 8 5.5 11 5.5 35 8 6.25 10 3.75 29 9 5.5 11 5.5 38 9 5.5 10.5 5 3 9 6 10 4 55 9 7 11 4 10 10 6 10.5 4.5 7 10 7.5 11 3.5 46 10 8 11 3 5 10 8.5 11 2.5 53 11 9.5 11 1.5 4 11 10 11 1

### Selecting the Final Scale Items

Now, you have to select the final statements for your scale. You should select statements that are at equal intervals across the range of medians. In our example, we might select one statement for each of the eleven median values. Within each value, you should try to select the statement that has the smallest Interquartile Range. This is the statement with the least amount of variability across judges. You don’t want the statistical analysis to be the only deciding factor here. Look over the candidate statements at each level and select the statement that makes the most sense. If you find that the best statistical choice is a confusing statement, select the next best choice.

When we went through our statements, we came up with the following set of items for our scale:

• People with AIDS are like my parents (6)
• Because AIDS is preventable, we should focus our resources on prevention instead of curing (5)
• People with AIDS deserve what they got. (1)
• Aids affects us all (10)
• People with AIDS should be treated just like everybody else. (11)
• AIDS will never happen to me. (3)
• It’s easy to get AIDS (5)
• AIDS doesn’t have a preference, anyone can get it (9)
• AIDS is a disease that anyone can get if they are not careful (9)
• If you have AIDS, you can still lead a normal life (8)
• AIDS is good because it helps control the population. (2)
• I can’t get AIDS if I’m in a monogamous relationship. (4)

The value in parentheses after each statement is its scale value. Items with higher scale values should, in general, indicate a more favorable attitude towards people with AIDS. Notice that we have randomly scrambled the order of the statements with respect to scale values. Also, notice that we do not have an item with scale value of 7 and that we have two with values of 5 and of 9 (one of these pairs will average out to a 7).

You now have a scale – a yardstick you can use for measuring attitudes towards people with AIDS. You can give it to a participant and ask them to agree or disagree with each statement. To get that person’s total scale score, you average the scale scores of all the items that person agreed with. For instance, let’s say a respondent completed the scale as follows:

 Agree Disagree People with AIDS are like my parents. Agree Disagree Because AIDS is preventable, we should focus our resources on prevention instead of curing. Agree Disagree People with AIDS deserve what they got. Agree Disagree Aids affects us all. Agree Disagree People with AIDS should be treated just like everybody else. Agree Disagree AIDS will never happen to me. Agree Disagree It's easy to get AIDS. Agree Disagree AIDS doesn't have a preference, anyone can get it. Agree Disagree AIDS is a disease that anyone can get if they are not careful. Agree Disagree If you have AIDS, you can still lead a normal life. Agree Disagree AIDS is good because it helps control the population. Agree Disagree I can't get AIDS if I'm in a monogamous relationship.

If you’re following along with the example, you should see that the respondent checked eight items as Agree. When we take the average scale values for these eight items, we get a final value for this respondent of 7.75. This is where this particular respondent would fall on our “yardstick” that measures attitudes towards persons with AIDS. Now, let’s look at the responses for another individual:

 Agree Disagree People with AIDS are like my parents. Agree Disagree Because AIDS is preventable, we should focus our resources on prevention instead of curing. Agree Disagree People with AIDS deserve what they got. Agree Disagree Aids affects us all. Agree Disagree People with AIDS should be treated just like everybody else. Agree Disagree AIDS will never happen to me. Agree Disagree It's easy to get AIDS. Agree Disagree AIDS doesn't have a preference, anyone can get it. Agree Disagree AIDS is a disease that anyone can get if they are not careful. Agree Disagree If you have AIDS, you can still lead a normal life. Agree Disagree AIDS is good because it helps control the population. Agree Disagree I can't get AIDS if I'm in a monogamous relationship.

In this example, the respondent only checked four items, all of which are on the negative end of the scale. When we average the scale items for the statements with which the respondent agreed we get an average score of 2.5, considerably lower or more negative in attitude than the first respondent.

## The Other Thurstone Methods

The other Thurstone scaling methods are similar to the Method of Equal-Appearing Intervals. All of them begin by focusing on a concept that is assumed to be unidimensional and involve generating a large set of potential scale items. All of them result in a scale consisting of relatively few items which the respondent rates on Agree/Disagree basis. The major differences are in how the data from the judges is collected. For instance, the method of paired comparisons requires each judge to make a judgement about each pair of statements. With lots of statements, this can become very time consuming indeed. With 57 statements in the original set, there are 1,596 unique pairs of statements that would have to be compared! Clearly, the paired comparison method would be too time consuming when there are lots of statements initially.

Thurstone methods illustrate well how a simple unidimensional scale might be constructed. There are other approaches, most notably Likert or Summative Scales and Guttman or Cumulative Scales.