1 Single Indicator & Composite Measures UAPP 702: Research Design for Urban & Public Policy Based on notes by Steven W. Peuquet. Ph.D.

2 Single Indicators A single indicator is a device for assigning units of observation to levels of a variable.  Questions are commonly used as single indicator devices.  Questions used for this purpose allow the respondent to categorize him or herself to a specified level of a variable.

3 Single Indicators There are three types of questions that produce single indicator measures. Examples of each follow:

4 Single Indicators Example 1: In the last 30 days, how many nights have you slept at an emergency shelter located in Delaware?

5 Single Indicators Explanation of Example 1: This question asks the respondent to assign him- or herself to a level of this variable (which might be called “recent shelter use”). This variable has the properties of a ratio variable. (A person that has stayed in a shelter 30 nights is twice as much as a person who has stayed 15 nights.)

6 Single Indicators Example 2: For the last emergency shelter you stayed at, how satisfied were you with the services provided by that shelter? 1. Very satisfied 2. Somewhat satisfied 3. Neutral (not satisfied or unsatisfied) 4. Somewhat unsatisfied 5. Very unsatisfied

7 Single Indicators Explanation of Example 2: With this question you are asking respondents to categorize themselves into one of five categories. You are ordering them on the basis of how satisfied or unsatisfied they are. This variable has ordinal properties because we don’t know how much more satisfied a person who answers “very satisfied” is compared to a person who answers “somewhat satisfied.”

8 Single Indicators Example 3: What race do you consider yourself to be? 1. African-American or Black 2. Caucasian or White 3. Asian or Oriental 4. Other

9 Single Indicators Explanation of Example 3: This variable allows the respondent to categorize him- or herself into one of four categories (or levels) of this variable called “race.” This variable has nominal values because the responses cannot be averaged, and one response can’t be considered to have a higher rank than another response.

10 Single Indicators vs. Composite Measures If the phenomenon that you are measuring is more complex (like “prejudice” or “socio- economic status” or “intelligence” or “historic significance”) you may need to use a composite measure. The function of a single indicator is to assign units of analysis to categories or levels of a variable. The purpose of a composite measure is exactly the same, but is used when a single indicator won’t do the job.

11 Composite Measures  Composite measures are based on more than one data item.  There are two different types of composite measures:  Indices  Scales

12 Composite Measures Both indices and scales are ordinal measures of variables. The difference between the two is based on how scores are assigned.

13 Composite Measures – Indices An index is constructed through the simple accumulation of scores assigned to individual attributes. All items are weighted the same.

14 Composite Measures – Indices Examples of an index:  “Prejudice” might be measured by adding up the number of prejudicial statements a person agrees with.  Assessing math skills through use of a multiple choice exam. Asking just one question would not be adequate. Several questions taken together will do a better job of measuring how well the student has acquired knowledge about the subject matter.

15 Composite Measures - Scales A scale on the other hand is constructed through the assignment of scores to patterns of responses, recognizing that some items reflect a relatively weak degree of the variable, while other reflect something stronger. Scales take advantage of any intensity structure that may exist among attributes.

16 Composite Measures – Scales Examples of scales:  Essay or multiple choice exam where different questions are worth different amounts of points.  Hierarchy of political activity (voted, contributed money to a campaign, worked on a political campaign, ran for office)

17 Composite Measures – Scales Scales are generally superior to indices because scales take into consideration the intensity with which different items reflect the variable being measured.

18 Composite Measures – Factors to Consider in their Construction  Face validity  Unidimensionality (e.g., don’t mix religion with political orientation)  Amount of variance in responses

19 Composite Measures – Factors to Consider in their Construction  Bi-variate and multi-variate relationship between items (items should be related to each other, but not perfectly related. If items are not related, they are probably measuring different things. If two items are perfectly related, they are redundant, and are not adding any new information).

20 Composite Measures – Factors to Consider in their Construction  “Index scoring” involves making decisions about the range of the index and the frequencies of responses across the chosen range. Once decided, the index is calculated.

21 Composite Measures – Factors to Consider in their Construction  Once created, a composite measure must be validated. The basic question is: does the index or scale actually measure the phenomenon that is sought to be measured?  “Item analysis” – examination of the extent to which the index is related to (predicts responses to) the individual items it comprises  “External validation” – validating the index using some other measure which is not part of the index being evaluated

22 Major Types of Scales Bogardus Social Distance Scale – Increasing intensity of the questions clearly shows a pattern (e.g., Are you willing to let Albanians live in your country, be your neighbor, marry your son or daughter?). Thurstone Scales – Use of “judges” to determine the strength of each of several indicators being used in a scale (e.g. figure skating competition).

23 Major Types of Scales Likert Scales  3- point, 5-point or 7-point scale is common (example: agree, neutral, disagree)  Odd number in scale is used so mid-point is a whole number. Use of an even number of points on the scale forces people to “take a stand” on one side of an issue or the other.  Make questions as simple as possible  Use words respondents will understand  Don’t use double negatives  Don’t put more than one concept in a question

24 Example of the Use of a Composite Measure The Use of the “Index of Dissimilarity” to Measure Racial Residential Segregation in New Castle County, Delaware See example herehere