new lab 9
Index Construction
PURPOSE
 To learn to construct an index.
MAIN POINTS
 The Reliability procedure tests only the suitability of a set of variables for the construction of an index (internal validation).
 To construct an index you use the compute command, e.g., COMPUTE NEWNAME=Q1+Q2+Q3+Q4.
 Recoding your index into fewer categories is often essential to create interpretable crosstabs.
 Using your index in crosstabulation enables you to examine its relations to other variables. This permits not only external validation of your index; it can also enhance your explanatory research..
EXAMPLE
 Dataset:
 PPIC October 2016
 Concept:
 Attitude toward recreational use of Marijuana (Alpha =.78)
 Indicators:
Syntax
*Identifying MJ Index Items*. recode q21 (1=1) (2=0) into MJPropD. value labels MJPropD 1 'yes' 0 'no'. recode q36 (1=1) (2=0) into MJLegalD. value labels MJLegalD 1 'yes' 0 'no'. recode q36a (1=1) (2=.5) (3=.0) into MJTry. value labels MJTry 1 'recent' .5 'not recent' 0 'no'. *Replicating the Reliability Analysis*. reliability /variables=MJPropD MJLegalD MJTry /scale('MJ3') MJPropD MJLegalD MJTry /statistics=descrpitive /summary=total. *Constructing the Index*. compute RawMJ3 = (MJPropD + MJLegalD + MJTry). fre var RawMJ3 /statistics = mean median mode stddev var skew kurtosis. *Recoding the Index*. recode RawMJ3 (0, .5=0) (1 thru 2= .5) (2.5, 3 =1) into MJ3. value labels MJ3 0 'low' .5 'med' 1 'hi'. fre var MJ3.
 Syntax Legend
 Comments can be inserted between asterisks *. . .*.
 Most of the above syntax is familiar from the previous lab.
 The compute command is where the index is constructed. However a subsequent frequency command of the raw index is also necessary to see the index and calculate its summary measures.
 Recoding an index is essential to produce effective tables. Here recodes place about 1/3 of the cases in each category, using the cumulative percent column of the frequency analysis of the raw index as a guide.
 Recode the index into a new name as it is will be useful to retain both the complete raw and recoded forms of an index.
 Output for Raw Index
RawMJ3
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
.00
341
20.0
27.7
27.7
.50
143
8.4
11.6
39.3
1.00
74
4.3
6.0
45.3
1.50
30
1.8
2.4
47.7
2.00
223
13.1
18.1
65.8
2.50
257
15.1
20.9
86.7
3.00
164
9.6
13.3
100.0
Total
1232
72.3
100.0
Missing
System
472
27.7
Total
1704
100.0
Summary Statistics
Mean= 1.44
Median= 2
Mode= 0
StdDev= 1.14
variance= 1.30
Skew= .09
Kurtosis= – 1.62
The newly computed index variable has many categories, making a crosstab unwieldy. Therefore recode into fewer categories.
*Recoding the Index*.
recode RawMJ3 (0, .5=0) (1 thru 2= .5) (2.5, 3 =1) into MJ3. value labels MJ3 0 'low' .5 'med' 1 'hi'. fre var MJ3.
Frequency Distribution for Recoded Index
MJ3 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
low 
484 
28.4 
39.3 
39.3 
med 
327 
19.2 
26.5 
65.8 

hi 
421 
24.7 
34.2 
100.0 

Total 
1232 
72.3 
100.0 

Missing 
System 
472 
27.7 

Total 
1704 
100.0 
The recoded index can be readily crosstabulated with independent variables.
Mean= .47
Median= .5
Mode= .00
StdDev= .43
Variance= .18
Skew = .098
Kurtosis = – 1.63
*Creating Indicators for Party Identification & Ideology*.
fre var q40c. recode q40c (1=0) (3=.5) (2=1) into Democrat. value labels Democrat 1 'Democ' .5 'Indep' 0 'Repub'. crosstabs tables = MJ3 by Democrat liberal3 / cells = column count /statistics = btau. fre var q37. missing values q37 (8,9). recode q37 (1,2=1) (3=.5) (4,5= 0) into liberal3. value labels liberal3 1 'liberal' .5 'middle' 0 'conserv'. fre var liberal3 *Crosstabulation of MJ3 by Democrat & Liberal.* crosstabs tables = MJ3 by Democrat,liberal3 / cells = column count /statistics = btau.
Support for Recreational Marijuana by Partisanship
Support for Recreational MJ  Partisanship  
Repub  Indep  Democ  
Low  61.4%  31.1%  33.5%  
Medium  19.1%  29.1%  28.5%  
High  19.5%  39.9%  37.9%  
Total  272  409  522 
Taub = .152
Source: PPIC October 2016
Support for Recreational Marijuana by Ideology
Support for Recreational MJ  ldeology  
conserv  middle  liberal  
Low  62.0%  34.4%  21.3%  
Medium  18.1%  31.8%  30.4%  
High  20.0%  33.8%  48.3%  
Total  421  337  451 
Taub = .308
Source: PPIC October 2016
pdf file of tables: Tabs for Lab 9
Interpretation
 The recoded variable is more manageable.
 The frequency analysis for the index shows that scores range from zero through three. This makes sense since the index is composed of three items each of which is scored between zero and one.
 Summary measures of central tendency and variation can be calculated.
 The index is recoded into three categories using the cumulative percentages as a guide in finding cut points roughly approximating 33% and 66%.
 The recoded variable is more manageable.
 The index is crosstabulated with an indicators of political partisanship and ideology.
 Crosstabs permit calculation of measures of association between the recoded index and other variables. This can be useful for both external validation and explanatory research.
 The crosstabs and measures of association provide weak support for a partisan explanation of support for recreational marijuana.
INSTRUCTIONS
 Use the data set and questions you worked with in Lab 8.
 Having found a combination of questions that produce an alpha greater than .60, ensure that the range for each of the questions is similar to one another. This is to ensure that none of the items are over or underrepresented in the index. For example, if the first question has a range from 1 to 3 and the second has a range from 1 to 100, then the second will be disproportionately overrepresented. Recode all the questions such that their ranges are similar, not necessarily identical.
 To create the index, combine all the different questions into a new measure using a compute command in the following form
 Compute rawindex=.
 Run a frequency distribution of the new indexed variable and determine whether it is suitable for further data analysis.
 Recode the index into appropriate categories as necessary.
 The new index can be used in crosstabulation like any other variable. This enables you to investigate both the external validity of your measure as well as use it in explanatory research. For example, use your index with an independent or dependent variable and calculate the appropriate measures of association.
QUESTIONS FOR REFLECTION
 How does the relationship between your index and an independent variable differ from what you would obtain using each element of the index to produce a crosstab?
 How is the relationship produced with the index affected by the choices in recoding the indexed variable?
DISCUSSION
 An index often leads to stronger relationships because the measurement errors in each of the constituent indicators tend to balance out. This isn’t the case here with partisanship as the relationship between partisanship and the DV’s three indicators differs considerably.
 Proper recoding of your index requires careful consideration of the possibilities and attention to the substantive meaning of your categories.
 Depending on your coding choices the strength of the relationship in your table may increase, decrease or stay roughly the same.
Advanced Exercises
 The ANES example from the previous lab can be continued here. An earlier example using the ANES 202 data is available here. LINK
 In this lab only three of the four indicators considered in Lab 8 are used to create an index.
 One can create standardized scores (or zscores) for the indicators used to create an index in this lab using the following SPSS syntax:
 /descriptives variables = /save.
 This will create three new standardized variables in the data set: z z z. Their existence can be confirmed by looking at the dataset of by running a frequency analysis on each of these variables. These new variables can be used to create a standardized index using same procedures employed in this lab. Doing so will ensure that all variables are equally weighted in the index. For our purposes, coding our indicators on a common range of values will suffice.