POL242 LAB MANUAL:EXERCISE 7

Elaboration

CONTENTS

PURPOSE

To learn how to perform a crosstabulation while controlling for a third variable
To learn how to compare partial relationships against the original and identify them as replication, specification or a spurious relationship

MAIN POINTS

Elaboration allows us to examine the relationship between two variables while controlling for a third variable in order to determine whether the control variable has an effect on the original relationship
When we use a control variable the original relationship is separated into partial relationships, according to the categories of the control variable
- For example, if we crosstabulated support for gay marriage and religiosity controlling for age and age is recoded into the categories 'young' and 'old' then two partial relationships would result
- The first partial would show the relationship between support for gay marriage and religiosity among young people
- The second partial would show the relationship between the two variables among old people
The partial relationships can reveal 1 of 3 results
- Replication: The partial relationships are roughly the same as that of the original. This means that the original relationship holds true even when taking into account the control variable
  - For example, if we found a relationship between gender and income indicating that men have a higher income then women we might control for education. If the partial relationships among each of the education categories is the same as the original then we would conclude that the result is replication
  - This means that men have a higher income then women even when they have received the same level of education as their female counterparts
- Specification: All but one of the partial relationships remain the same or become weaker then the original relationship, one partial relationship is the same or stronger then the original relationship. This means that we have specified the conditions under which the original relationship occurs (Babbie, p.436)
  - For an example let's return to the relationship between gender and income again. If when controlling for education we found that the relationship diminished or stayed about the same for each level of education except post-graduate then we would conclude that the result is specification.
  - This means that especially among post-graduates men have a higher income then women, but among people having received other levels of education the relationship is not as important.
- Spurious Relationship: All of the partial relationships are weaker then the original relationship. This means that we have shown the original relationship to be false with the introduction of the control variable.
  - Again looking at the example of gender and income, we might find after controlling for education that all the partial relationships have fallen far below that of the original.
  - This means that the original relationship between gender and income is actually a manifestation of a relationship between education and income. There is no genuine relationship between gender and income because among women and men who received the same level of education income did not differ in any important way.
In the case of a spurious relationship we must also determine whether the control variable is antecedent to the two variables or intervening between them.
- An antecedent variable occurs prior in time to both of the original variables
  - Take for an example a relationship between conservatism and support for gay marriage that is found to be spurious after controlling for religiosity. Since religiosity occurs before conservatism and support for gay marriage this variable is antecedent to both variables.
  - Because the control variable is antecedent in this case, the spurious relationship is termed explaination
- An intervening variable is a variable that is prior in time to one of the original variables but occurs after the other.
  - In the example above of a spurious relationship between gender and income the control variable education is intervening between the two variables. Education comes after gender but before income.
  - Because the control variable is intervening in this case, the spurious relationship is termed interpretation

INSTRUCTIONS

In Webstats enter the specified dataset and select Multivariate Crosstabs as the type of analysis. Then click proceed
We provide three sets of variables below. From these variable sets, select the specified dependent and independent variables for the analysis and enter in missing values for these two variables.
Select the appropriate measure of association:
- If either the dependent or the independent variable is nominal choose Phi and Cramer V
- If both variables are interval or ordinal choose Kendall's tau-b and Kendall's tau-c by pressing 'shift' while clicking.
- Remember that you must take into account the nature of the variable after the recode. An ordinal variable may become a nominal variable after recoding.
Enter the window to edit syntax by clicking the button at the top of the statistical output.
Add the specified missing values for the control variable.
Perform the specified recodes in the syntax. This is important, because the measures of association will not be accurate if you do not properly record. If desired, add value labels for newly recoded variables.
Perform the simple crosstab by clicking run. Note the strength of the original relationship by looking at the appropriate measure of association, for a full review of measures of association refer to the Selecting the Appropriate Measure of Association section of Lab Exercise 3C.
- If one of the variables is nominal and the crosstab is rectangular, then Cramer's V is the correct measure.
- If one of the variables is nominal and the crosstab is square, then Phi is the correct measure.
- If both variables are not nominal and the crosstab is square then the appropriate measure is Tau-b.
- If both variables are not nominal and the crosstab is rectangular then the appropriate measure is Tau-c.
Reenter the syntax window by clicking the back button. Add the control variable to the crosstabulation by adding "by" and then the variable name to the end of the syntax for the original crosstab, then click Run. The addition of "by" and then the third variable is the only change required to allow for a control variable.
Examine the strength of the new partial relationships. Determine whether the elaborated relationship is an example of replication, specification, or a spurious relationship. Carefully explain what factors led you to make your conclusion.
Repeat for each set of variables

VARIABLE SETS

Set #1
- Dataset: Euro 2002
- Independent Variable: PARTY_RE Recoded party affiliation
- Dependent Variable: Q26E Restrict immigration
- Control Variable: LEFTRGHT Left-Right ideology
- Missing Values:
  - Q26E (3,4,5)
  - PARTY_RE (0)
  - LEFTRGHT (9,10)
- Recodes:
  - LEFTRGHT recode into 3 categories: Category 1 (1 to 3), category 2 (4) and category 3 (5 to 7)
Set #2
- Dataset: CRIC 2003
- Independent Variable: Q29 Language
- Dependent Variable: Q40 Income
- Control Variable: Q26 Education
- Missing Values:
  - Q26 (8)
  - Q29 (11)
  - Q40 (11)
- Recodes:
  - Q26 recode into 3 categories: Category 1 (1 to 3), category 2 (4 and 5) and category 3 (6 and 7)
  - Q29 recode into dummy variable: English category (1) and other category (2 to 10)
  - Q40 recode into 3 categories: Category 1 (1 to 4), category 2 (5 to 7) and category 3 (8 to 10)
Set #3
- Dataset: IRPP 1999
- Independent Variable: Q38 Ethnicity
- Dependent Variable: Q44 Income
- Control Variable: Q41 Education
- Missing Values:
  - Q44 (98,99).
  - Q38 (98,99).
  - Q41 (98,99).
- Recodes:
  - Q41 recode into 3 categories: Category 1 (1 to 4), category 2 (5 and 6) and category 3 (7 to 11)
  - Q38 recode into a dichotomous "dummy" variable: Canadian category 1(1) and all other categories (2 to 31)

EXAMPLE

Example Variable Set:
- Independent Variable: Q7 Support for gay marriage
- Dependent Variable: Q33 Power to overrule Supreme court on gay marriage
- Control Variable: Q44 Religiosity
- Missing Variables:
  - Q33 (99).
  - Q7 (99).
  - Q44(99)
Preliminary Syntax
set width=80/length=none/header=no/messages=none.
get file="/homes/josephf/webstats/CRIC2002.sav".
missing values Q33 (99).
missing values Q7 (99).
missing values Q44(99)
crosstab tables=Q33 by Q7
/cells=column count /statistics=PHI.
crosstab tables=Q33 by Q7
/cells=column count /statistics=PHI.
*startofoutput.
Finish.

Preliminary Output

   1  0  set width=80/length=none/header=no/messages=none.
   2  get file="/homes/josephf/webstats/cric03.sav".
   3  set width=80/length=none/header=no/messages=none.
   4  get file="/homes/josephf/webstats/CRIC2002.sav".
   5  missing values Q33 (99).
   6  missing values Q7 (99).
   7  missing values Q44(99)
   8  crosstab tables=Q33 by Q7
   9   /cells=column count /statistics=PHI.
  10  *startofoutput.


Q33  33. If SC okays gay and lesbian marriage
by  Q7  7. Do you strongly support, support, opp

                    Q7                             Page 1 of 1
            
	    Count  |
            Col Pct|Strongly Support  Oppose   Strongly
                   | support                    oppose    Row
                   |     1  |     2  |     3  |     4  | Total
Q33        --------+--------+--------+--------+--------+
                1  |    20  |    87  |   106  |   173  |   386
  Should           |   9.7  |  16.4  |  44.4  |  64.8  |  31.0
                   +--------+--------+--------+--------+
                2  |   186  |   445  |   133  |    94  |   858
  Should not       |  90.3  |  83.6  |  55.6  |  35.2  |  69.0
                   +--------+--------+--------+--------+
            Column     206      532      239      267     1244
             Total    16.6     42.8     19.2     21.5    100.0



                                                                    Approximate
     Statistic                    Value        ASE1      Val/ASE0   Significance
--------------------            ---------    --------    --------   ------------

Phi                               .45660                              .00000 *1
Cramer's V                        .45660                              .00000 *1


*1 Pearson chi-square probability

Number of Missing Observations:  158

  11  Finish.

Preliminary Interpretation
- The top corner of the table indicates what information is shown in each cell. In the example above the top corner indicates that the first number in each cell is the column count and the second number is the column percentage.
- The simple crosstab shows a relationship that is extremely strong according to the Cramer's V measure of association.
- We must compare the partial relationships in the next step to the Cramer's V value of 0.45660 shown here
Syntax
set width=80/length=none/header=no/messages=none.
get file="/homes/josephf/webstats/CRIC2002.sav".
missing values Q33 (99).
missing values Q7 (99).
missing values Q44(99)
crosstab tables=Q33 by Q7 by Q44
/cells=column count /statistics=PHI.
*startofoutput.
Finish.

Output

   1  0  set width=80/length=none/header=no/messages=none.
   2  get file="/homes/josephf/webstats/cric03.sav".
   3  set width=80/length=none/header=no/messages=none.
   4  get file="/homes/josephf/webstats/CRIC2002.sav".
   5  missing values Q33 (99).
   6  missing values Q7 (99).
   7  missing values Q44(99)
   8 crosstab tables=Q33 by Q7 by Q44
   9   /cells=column count /statistics=PHI.
   10  *startofoutput.


Q33  33. If SC okays gay and lesbian marriage
by  Q7  7. Do you strongly support, support, opp
Controlling for..
Q44  44. Other than events like weddings and  Value = 1  About once a week or

                    Q7                             Page 1 of 1
            Count  |
           Col Pct |Strongly Support  Oppose   Strongly
                   | support                    oppose    Row
                   |     1  |     2  |     3  |     4  | Total
Q33        --------+--------+--------+--------+--------+
                1  |     1  |     9  |    22  |    81  |   113
  Should           |   6.7  |  17.3  |  36.1  |  66.4  |  45.2
                   +--------+--------+--------+--------+
                2  |    14  |    43  |    39  |    41  |   137
  Should not       |  93.3  |  82.7  |  63.9  |  33.6  |  54.8
                   +--------+--------+--------+--------+
            Column      15       52       61      122      250
             Total     6.0     20.8     24.4     48.8    100.0



                                                                    Approximate
     Statistic                    Value        ASE1      Val/ASE0   Significance
--------------------            ---------    --------    --------   ------------

Phi                               .44498                              .00000 *1
Cramer's V                        .44498                              .00000 *1


*1 Pearson chi-square probability


Q33  33. If SC okays gay and lesbian marriage
by  Q7  7. Do you strongly support, support, opp
Controlling for..
Q44  44. Other than events like weddings and  Value = 2  About two to three t

                    Q7                             Page 1 of 1
            Count  |
           Col Pct |Strongly Support  Oppose   Strongly
                   | support                    oppose    Row
                   |     1  |     2  |     3  |     4  | Total
Q33        --------+--------+--------+--------+--------+
                1  |     1  |     9  |    12  |    17  |    39
  Should           |  14.3  |  23.7  |  44.4  |  73.9  |  41.1
                   +--------+--------+--------+--------+
                2  |     6  |    29  |    15  |     6  |    56
  Should not       |  85.7  |  76.3  |  55.6  |  26.1  |  58.9
                   +--------+--------+--------+--------+
            Column       7       38       27       23       95
             Total     7.4     40.0     28.4     24.2    100.0



                                                                    Approximate
     Statistic                    Value        ASE1      Val/ASE0   Significance
--------------------            ---------    --------    --------   ------------

Phi                               .42551                              .00064 *1
Cramer's V                        .42551                              .00064 *1


*1 Pearson chi-square probability


Q33  33. If SC okays gay and lesbian marriage
by  Q7  7. Do you strongly support, support, opp
Controlling for..
Q44  44. Other than events like weddings and  Value = 3  About once a month

                    Q7                             Page 1 of 1
            Count  |
           Col Pct |Strongly Support  Oppose   Strongly
                   | support                    oppose    Row
                   |     1  |     2  |     3  |     4  | Total
Q33        --------+--------+--------+--------+--------+
                1  |     3  |    11  |    14  |    17  |    45
  Should           |  13.0  |  22.4  |  53.8  |  63.0  |  36.0
                   +--------+--------+--------+--------+
                2  |    20  |    38  |    12  |    10  |    80
  Should not       |  87.0  |  77.6  |  46.2  |  37.0  |  64.0
                   +--------+--------+--------+--------+
            Column      23       49       26       27      125
             Total    18.4     39.2     20.8     21.6    100.0


                                                                    Approximate
     Statistic                    Value        ASE1      Val/ASE0   Significance
--------------------            ---------    --------    --------   ------------

Phi                               .41260                              .00009 *1
Cramer's V                        .41260                              .00009 *1


*1 Pearson chi-square probability


Q33  33. If SC okays gay and lesbian marriage
by  Q7  7. Do you strongly support, support, opp
Controlling for..
Q44  44. Other than events like weddings and  Value = 4  Less than once a mon

                    Q7                             Page 1 of 1
            Count  |
           Col Pct |Strongly Support  Oppose   Strongly
                   | support                    oppose    Row
                   |     1  |     2  |     3  |     4  | Total
Q33        --------+--------+--------+--------+--------+
                1  |     8  |    30  |    31  |    28  |    97
  Should           |  13.3  |  14.9  |  49.2  |  56.0  |  25.9
                   +--------+--------+--------+--------+
                2  |    52  |   172  |    32  |    22  |   278
  Should not       |  86.7  |  85.1  |  50.8  |  44.0  |  74.1
                   +--------+--------+--------+--------+
            Column      60      202       63       50      375
             Total    16.0     53.9     16.8     13.3    100.0



                                                                    Approximate
     Statistic                    Value        ASE1      Val/ASE0   Significance
--------------------            ---------    --------    --------   ------------

Phi                               .39756                              .00000 *1
Cramer's V                        .39756                              .00000 *1


*1 Pearson chi-square probability


Q33  33. If SC okays gay and lesbian marriage
by  Q7  7. Do you strongly support, support, opp
Controlling for..
Q44  44. Other than events like weddings and  Value = 5  Never

                    Q7                             Page 1 of 1
            Count  |
           Col Pct |Strongly Support  Oppose   Strongly
                   | support                    oppose    Row
                   |     1  |     2  |     3  |     4  | Total
Q33        --------+--------+--------+--------+--------+
                1  |     7  |    27  |    24  |    30  |    88
  Should           |   7.0  |  14.4  |  42.1  |  68.2  |  22.7
                   +--------+--------+--------+--------+
                2  |    93  |   160  |    33  |    14  |   300
  Should not       |  93.0  |  85.6  |  57.9  |  31.8  |  77.3
                   +--------+--------+--------+--------+
            Column     100      187       57       44      388
             Total    25.8     48.2     14.7     11.3    100.0



                                                                    Approximate
     Statistic                    Value        ASE1      Val/ASE0   Significance
--------------------            ---------    --------    --------   ------------

Phi                               .46936                              .00000 *1
Cramer's V                        .46936                              .00000 *1


*1 Pearson chi-square probability

Number of Missing Observations:  169

  13  Finish.

Interpretation
- All of the resulting Creamer's V values are weaker than the original relationship of 0.45660 except for one which is slightly stronger.
- In the case of people who never go to religious services the Cramer's V value jumps to 0.46936. This means we have specified the circumstances in which the relationship occurs
- Since this is a case of specification, we can conclude that the original relationship between support for gay rights and whether or not the supreme court should be overruled in its decision allowing gay marriage is genuine. However, it occurs specifically among people who do not attend religious services.
QUESTIONS FOR REFLECTION
1. Try to provide an explaination for each of the kinds of elaboration that occured. Why do you think the result was replication, specification or a spurious relationship?
2. In the case of the spurious relationship, was it explaination or interpretation?
DISCUSSION
1. In the example above, the likely reason that the result is specification of this kind is because among people who never attend religious services religiosity does not intervene upon the relationship between support for gay marriage and power to overrule court decision for gar marriage. Religiosity serves to diminish the relationship between the two variables because it explains some of it away.
2. There is no real right answer to the second question, it depends on how one makes their argument. You could argue that the control variable is antecedent to both the dependent and the independent variable, that is to say that political ideology determines party affiliation. In this case the spurious relationship would be explaination. However you could also make the argument that the control variable intervenes between the two variables, that party affiliation determines political ideology (this seems less likely but you could certainly make the argument). In this case the relationship would be characterized as interpretation