POL242 LAB MANUAL: EXERCISE 3A

Crosstabulation with Nominal Variables

PURPOSE

MAIN POINTS

Crosstabulation

 

INDEPENDENT VARIABLE

Category I Category II Category III

DEPENDENT VARIABLE

Category I A B C
Category II D E F
Category III G H I

Measures of Association:Nominal data--Phi and Cramer's V

LEVEL OF ASSOCIATION Verbal Description COMMENTS
0.00 No Relationship Knowing the independent variable does not help in predicting the dependent variable.
.00 to .15 Very Weak Not generally acceptable
.15 to .20  Weak  Minimally acceptable
.20 to .25 Moderate  Acceptable
.25 to .30 Moderately Strong  Desirable
.30 to .35 Strong  Very Desirable
.35 to .40 Very Strong Extremely Desirable
.40 to .50 Worrisomely Strong Either an extremely good relationship or the two variables are measuring the same concept
.50 to .99 Redundant The two variables are probably measuring the same concept.
1.00 Perfect Relationship.  If we the know the independent variable, we can perfectly predict the dependent variable. 

INSTRUCTIONS

:

Crosstabulating Nominal Data

  1. Select a Dataset for this exercise, possibly Leger 2013 or Forum Research 2013.
  2. Enter the Questionnaire for the chosen dataset from the Codebooks link on the POL242Y website.
  3. Hypothesize a relationship between two nominal variables in the dataset.
  4. Enter Webstats to select your chosen dataset.
  5. Perform separate trial-runs of the Frequency distribution for each of the variables. Based on the Frequency output, decide how to recode each variable and identify the missing values.
  6. Set the Analysis in Webstats to Bivariate Crosstabs and hit Proceed.
  7. In 'Step 1,' enter the dependent variable first, followed by the independent variable. Be sure to put the dependent or independent variable in the correct entry box. If the variables are placed appropriately, the dependent variable will appear on the left of the crosstab and the independent variable will appear across the top (See diagram above).
  8. Select "Phi and Cramer's V (PHI)" in the 'Step 2' entry box.  This section lists other measures of association that you can choose but since we are working with nominal data select "Phi and Cramer's V (PHI)".
  9. Enter any recodes (if necessary) in 'Step 4' and hit Run.
  10. When evaluating the measures of association, you should look at only Phi for 2 by 2 tables and Cramer's V for other nominal tables.
  11. Determine whether there is a relationship between the variables based on the column-percentages in the crosstab. Then, looking at the value of the measure of association, use the above guidelines to interpret the strength of the relationship.
  12. Repeat the analysis until you find a set of variables with a relationship that has a moderate degree of association ( >.2).

EXAMPLES

Example #1: Using phi with two dichotomous variables

Example #2: Cramer's V

QUESTIONS FOR REFLECTION

  1. Did you discover a relevant relationship in your crosstab based on the column-percentages? If so, was it evident in only one row of the table or in all rows?
  2. Can you compare the magnitude of a Phi-value from one relationship to the magnitude of a Cramer's V value for another relationship?
  3. Would the strength of the relationship be affected if you looked only at the results for only the major parties?
  4. Would the strength of the relationship be affected if you considered 'don't know' responses to be a middle position? What if it those who say don't know are excluded from the analysis?

DISCUSSION

  1. When you find a cell that has a substantially different column-percentage from the other cells in that row, there are usually other rows in the table that also have a difference. For example, if you find a difference in the column-percentage for cells A-B-C, then there is probably also a difference between D-E-F, or G-H-I. This happens because the column-percentage in any given cell influences the column-percentage of the other cells in that column.
  2.  

    INDEPENDENT VARIABLE

    Category I Category II Category III

    DEPENDENT VARIABLE

    Category I A B C
    Category II D E F
    Category III G H I

  3. We can compare two values of the same measures readily.  But be cautious about comparing different measures of association to each other. Eg., you should compare two measures of Phi to one other, but be cautious about comparing a Phi-value to a Cramer's V value.
  4. Find out by declaring scores of 0 and 5 missing on party identification (pid).
  5. Find out by making the appropriate recodes or declaring the appropriate missing values.