Day 26: Correspondence Analysis in SPSS – Visualizing Relationships Between Categorical Variables

Day 26: Correspondence Analysis in SPSS – Visualizing Relationships Between Categorical Variables

Welcome to Day 26 of your 50-day SPSS learning journey! Today, we’ll focus on Correspondence Analysis, a multivariate technique used to visualize and analyze relationships between categorical variables. This method is ideal for creating perceptual maps that help uncover patterns in contingency tables.

What is Correspondence Analysis?

Correspondence Analysis (CA) is a statistical technique that represents relationships between rows and columns of a contingency table as points in a low-dimensional space. It’s particularly useful for visualizing categorical data.

For example:

  • Analyzing survey data to see how customer satisfaction levels relate to different product categories.
  • Exploring voting patterns to see how political parties align with demographic groups.

CA generates a perceptual map where:

  • Rows and columns are displayed as points.
  • Closer points indicate stronger associations.

When to Use Correspondence Analysis?

Use Correspondence Analysis when:

  • You have categorical data summarized in a contingency table.
  • You want to explore associations or patterns between the rows and columns.
  • You need a visual representation of relationships.

How to Perform Correspondence Analysis in SPSS

Step 1: Create or Open Your Dataset

For this example, use the following contingency table summarizing survey responses for product preferences by age group:

Product_A Product_B Product_C Total
18-25 30 20 10 60
26-35 25 30 15 70
36+ 10 25 35 70
Total 65 75 60 200
  • Rows: Age groups (e.g., 18–25, 26–35, 36+).
  • Columns: Products (e.g., Product_A, Product_B, Product_C).

Step 2: Access the Correspondence Analysis Tool

  1. Go to Analyze > Dimension Reduction > Correspondence Analysis.
  2. A dialog box will appear.

Step 3: Select the Rows and Columns

  1. Move the row variable (e.g., Age_Group) to the Rows box.
  2. Move the column variable (e.g., Product) to the Columns box.

Step 4: Customize Display Options

  1. Click Statistics:
    • Check Row Profiles, Column Profiles, and Summary Table to display descriptive statistics.
  2. Click Plots:
    • Check Symmetric Normalization to create a combined plot of rows and columns.
    • Click Labels and ensure that points are labeled for easier interpretation.
  3. Click Continue, then OK to run the analysis.

Interpreting the Output

The SPSS output for Correspondence Analysis includes:

1. Correspondence Table

  • Displays row and column profiles (percentages).
  • Example: The row profile for 18-25 might show that 50% prefer Product_A, 33% prefer Product_B, and 17% prefer Product_C.

2. Inertia and Explained Variance

  • Inertia: Measures the amount of variation explained by each dimension.
    • Higher inertia indicates stronger associations.
  • Cumulative Proportion: Indicates the percentage of variance explained by the first two dimensions.

3. Row and Column Coordinates

  • Lists the coordinates of rows and columns in the reduced dimensional space.
  • These coordinates are used to create the perceptual map.

4. Perceptual Map

  • Visualizes the relationships between rows (e.g., age groups) and columns (e.g., products):
    • Points closer together indicate stronger associations.
    • Example: If 18-25 is near Product_A, this age group has a strong preference for Product_A.

Example Interpretation

Suppose you run the Correspondence Analysis and get the following results:

  1. Inertia and Explained Variance:

    • Dimension 1 explains 70% of the variance.
    • Dimension 2 explains 20% of the variance.
    • Combined, these two dimensions explain 90% of the variance, making them sufficient for interpretation.

  2. Perceptual Map:

    • 18-25 is closer to Product_A.
    • 26-35 is closer to Product_B.
    • 36+ is closer to Product_C.

Interpretation:

  • Younger customers (18-25) prefer Product_A, while older customers (36+) prefer Product_C.
  • Middle-aged customers (26-35) are more inclined toward Product_B.

Practice Example: Perform Correspondence Analysis

Use the following contingency table summarizing voting preferences by age group:

Party_A Party_B Party_C Total
18-25 40 30 10 80
26-35 35 45 20 100
36+ 20 40 40 100
Total 95 115 70 280
  1. Perform a Correspondence Analysis to explore relationships between age groups and political parties.
  2. Generate a perceptual map to visualize preferences.
  3. Interpret the associations based on proximity in the map.

Common Mistakes to Avoid

  1. Overinterpreting Dimensions: Focus only on the first two dimensions if they explain most of the variance.
  2. Using Raw Data Instead of a Contingency Table: Ensure your data is summarized as a contingency table before running Correspondence Analysis.
  3. Ignoring Labels: Always label points in the perceptual map for clear interpretation.

Key Takeaways

  • Correspondence Analysis is a useful tool for visualizing relationships between categorical variables.
  • Perceptual maps reveal patterns and associations, making data easier to interpret.
  • Focus on the dimensions that explain the most variance to draw meaningful conclusions.

What’s Next?

In Day 27 of your 50-day SPSS learning journey, we’ll explore Time Series Analysis in SPSS. You’ll learn how to analyze trends, seasonality, and make forecasts for time-dependent data. Stay tuned for this highly practical technique!


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