Scales are a form of composite measure.  In contrast to indexes, which are basically additive, scales take advantage of any intensity structure that exists among the items being combined into the composite measure.

Whenever there are two or more indicators of a given variable, it is likely that they will indicate differing degrees of that variable.  The Bogardus Social Distance Scale offers an excellent example of this phenomenon.  Consider the following questionnaire items:

Would you will willing to have an ex-convict:

1. Live in your country?
2. Live in your city?
3. Live in your neighborhood?
4. Live next door to you.?

An intensity structure like this one has an interesting implication for data analysis.  Let's say we asked 1,000 people to answer these questions in a survey.  With four responses from each of the respondents, we have a total of 4,000 pieces of data.  And if we wanted to analyze people's prejudice against ex-convicts, we'd have four indicators for each respondent.  The analysis would be a lot simpler if we could give each respondent a single number representing their degree of prejudice against ex-convicts.  We can.

Reflect on the matter for a moment and you'll see that if I tell you how many 'no' answers a person gave, you will be able to tell me which ones they said 'no' to.  Suppose a person said 'no' to two of the relationships with ex-convicts.  Clearly, they would have said 'yes' to 1 and 2, and they would have said 'no' to 3 and 4.  Nothing else would make sense.

If someone only objected to one of the relationships with ex-convicts, you will know right away that they said 'yes' to 1, 2, and 3, only objecting to have one living next door.

In the case of the Bogardus Social Distance Scale, the intensity structure is guaranteed by the logical inclusiveness of the four items: 'next door' is included within 'neighborhood' which is included within 'city' which is included within 'country.'  While there are sixteen possible response patterns, there are only five (indicated in blue) that make sense, as indicated in the table below.
 
 

A similar example of logical structures would be seen in these two questions regarding the permissibility of abortion:  (1) Should a woman be able to get a legal abortion if her pregnancy resulted from rape? and (2) Should a woman be able to get an abortion just because she wants to--for any reason?  While there are four possible response patterns--Yes/Yes, Yes/No, No/Yes, No/No--only three make sense.  To begin, it would make sense for someone to approve of both or disapprove of both.  Also, we can imagine someone saying they would approve of abortion in the case of rape, but not as a matter of free choice.  On the other hand, it would make no sense for someone to approve of abortion for any and all reasons and then balk at the case of rape.  Rape would be included within 'any reason.'

Even when there is no clear, logical structure among the items, an empirical structure may exist anyway.  The clue to such a structure lies in the relative frequencies of the indicators.  Any indicator of a variable that appears in the large majority of cases is probably a weak indicator.  Take the statement, "Women are weaker than men" as an indicator of anti-female prejudice.

Probably a lot of people would agree with that, many insisting that the average man is, in fact, physically stronger than the average woman.  Nonetheless, we might consider the statement some indication of anti-female prejudice because of its generality.  After all, there are many kinds of strength other than the physical, and women are at least as strong as men is many of those.  Thus, if someone agreed with that statement in a questionnaire, we might decide to consider them somewhat prejudiced.  But we'd have to regard it as a relatively weak indicator of prejudice.

By contrast, consider the statement, "Women should not be allowed to vote."  Agreement with that statement clearly indicates a greater intensity of prejudice against women than agreeing with the first statement.  Many fewer people would agree with it.  (In case, you think this statement is an unrealistic example of anti-female prejudice, realize that women were not allowed to vote during the first 144 years after Independence, finally getting the vote in 1920.)

Given the difference in intensity between these two indicators, there is a good chance that everyone wanting to deny women the vote would also say they are weaker than men--even though there's no logical link between the two sentiments.  We could imagine someone believing woman are as strong as men but still not wanting them to vote.  It is unlikely that would happen, however, given the different intensities of the two items.

Whether the several indicators available for measuring a variable form a scale is an empirical question.  If we had several indicators of prejudice against women, each representing a different degree of support in the population, the question is whether knowing the number of indicators present in a given case would let us predict which indicators were present.  If I tell you a person appeared prejudiced on 5 or the 7 indicators, would you be able to reproduce accurately which 5 they were?

The textbook explains how to calculate the coefficient of reproducibility, which is the measure of how well we can reproduce the original set of data by knowing the scale scores assigned on the basis of an intensity structure.