Correspondence Analysis: Visualize Category Associations in a Contingency Table
What is Correspondence Analysis?
Correspondence analysis (CA) maps the row and column categories of a contingency table into a low-dimensional space, usually two dimensions, and displays them on a correspondence plot. Categories that lie close together are strongly associated, while distant categories are weakly related. It decomposes the total inertia of the table, which is proportional to the chi-square statistic, so the analysis is meaningful only when a chi-square test first confirms a significant association.
When to Use It
Use correspondence analysis whenever you need to understand how categories of two categorical variables relate, such as defect type by product model, customer rating by spending tier, or brand preference by age group. It is the natural follow-up to a chi-square test: chi-square tells you whether an association exists, correspondence analysis shows where it is. It is a standard tool for market research and quality data exploration with cross-tabulated counts.
How to Use It (Step by Step)
Paste a contingency table of row and column frequencies, and the tool first runs a chi-square independence test. If the association is significant, it decomposes the total inertia into dimensions and draws the correspondence plot with row and column profiles. Interpret clusters of nearby row and column points as strong associations, and check the profile tables for any point that sits far from the origin. Export the plot and profiles directly into your report.
Key Formulas / Example
Total inertia equals the chi-square statistic divided by the total number of observations (chi-square / N), and it measures the overall strength of the row-column association. Each dimension explains a portion of that inertia; the first dimension captures the most and the second the next most. If the first two dimensions explain less than roughly 70% of total inertia, distances on the two-dimensional plot become unreliable, so check higher dimensions or the profile tables before drawing conclusions.