# How to interpret the results of my correspondence analysis?

Im looking for help interpreting an CA Factor MAP

my df is :

df=structure(list(A = c(33.9166666666667, 5.16666666666667, 29.9166666666667,
0, 1.5), B = c(12.6666666666667, 3.16666666666667, 20.6666666666667,
1, 0), C = c(7.33333333333333, 1.33333333333333, 11.3333333333333,
2, 1), D = c(106.416666666667, 26.1666666666667, 196.416666666667,
9, 9.5), E = c(4, 1, 6.5, 1, 1)), .Names = c("A", "B", "C", "D",
"E"), row.names = c(NA, 5L), class = "data.frame")


EDIT 1 :To give a context about these datas : people will buy two products and for each product on or several reasons. For product 1 (reason=1,2,3,4,5) and product 2 (reason=A,B,C,D,E) and the reasons could be combinated. I obtained this table by ponderate the reasons, gives it weight and make addition finally of all matrix. And Now my aims it to explore if there is association between resaons, so I used CA.

I used the following R code :

#install.packages("FactoMineR")
library(FactoMineR)
CA(df)


I understand that there is a clear association between A and 1, and B and 2 in the other side, etc...

• What is the way to interpret these "cluster" of qualitative variables in each part of the two axis?
• Why isn't the axis centered?
• Finally, what does the value dim1=65.45% represent?

I looked on the factorminer site, but I didn't find explanation for such question, or maybe I misunderstood.

EDIT 2: Since i'm interested on choice 1,2,3 and A,B,D I decided to simplify my contingency table and it gives me the following map :

My interpretations :

1. The first Axis oppose modalities 3 and 1, and the modalities D and A.
2. Customer who buy product 1 for the reason 3 tends to buy product 2 for the reason D.
3. Customer who buy product 2 for the reason 1 tends to buy product 2 for the reason A.

I understood also that the center of the graphic is the gravity center and that the percentage of inertia are associated with the two first dimensions that constitute 99.6% and 0.4%, so the principal plan should allow us to have 100% of informations that contained in the 6 variables.

I want to be sure that my conclusion are ok. I have no conclusion for B and 2 and I don't know how to interpret it .

In addition : Now what is strange is when I execute a chisq.test(df), I'm failing to reject the null hypothesis (Reasons of buying 1,2,3,4,5 are independent from Reasons of buying A,B,D,C,D)

Pearson's Chi-squared test

data: df X-squared = 16.632, df = 16, p-value = 0.4098

While it is clear in the AFC that the reasons are not independant, why I don't have significant result of p-value on chi-square ? What is the problem in my analyses ?

Thanks a lot.

• I might recommend you to read something about correspondence analysis, get to know it. Then, if you get specific problems, post a question. – ttnphns Jun 12 '16 at 7:58
• Please take a look on the EDIT 1 and EDIT 2. Thanks a lot. – ranell Jun 12 '16 at 19:12