Correspondence Analysis

Correspondence analysis decomposes the chi-square association in a two-way contingency table into a few dimensions and plots row and column categories as points in a low-dimensional map.

대응분석은 이원 분할표의 카이제곱 연관을 몇 개의 차원으로 분해해 행·열 범주를 저차원 지도 위의 점으로 나타내는 기법입니다.

I have a crosstab of age group by preferred brand; how can I see which categories go together in a single map?

연령대별 선호 브랜드 교차표가 있는데, 어떤 범주끼리 함께 묶이는지 한 장의 지도로 볼 수 있을까요?

Correspondence analysis applies a singular value decomposition to the standardized residuals of a contingency table, splitting its total inertia (chi-square divided by n) into dimensions. Row and column principal coordinates place categories with similar profiles close together, and the share of inertia shows how much of the association each dimension captures.

When to use Correspondence Analysis

• You have a two-way table of counts with several categories in each variable.
• You want a visual summary of which row and column categories are associated.
• A chi-square test is significant and you want to describe the pattern behind it.

When to use something else

• You have three or more categorical variables; use multiple correspondence analysis instead.
• You only need to test independence in a small table; use the chi-square test of independence instead.

Assumptions and requirements

• Counts are non-negative frequencies of independent observations.
• Each row and column category has a non-zero total.
• Expected counts are large enough if the chi-square test is interpreted.

What the analysis reports

• Total inertia and chi-square test
• Principal inertias and percentage of inertia per dimension
• Row and column masses
• Row and column principal coordinates with quality of representation

How to report it

A correspondence analysis of the [r] × [c] table (N = [n]) showed a total inertia of [value], χ²([df]) = [value], p = [value]; the first two dimensions accounted for [value]% and [value]% of the inertia.

Related methods

• Multiple Correspondence Analysis
• Chi Square Test
• Cramér's V and Phi Association

Run Correspondence Analysis on Quorant