Chisq.test not working in R?

Question

I found out that the chi square test in R may not be working. I don't know where I am doing it wrong.

1) test two similar distribution

# create a sequence from 0 to 1000, seperated by 10
x <- seq(0,1000,10)

# create two similar gaussian distribution
r1<- rnorm(x, 1000,100)
r2 <- rnorm(x, 1000,100)

# run the chi square test
chisq.test(r1,r2,simulate.p.value = TRUE)

The result is:

Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)

data:  r1 and r2
X-squared = 10100, df = NA, p-value = 0.0004998

2) Test two different distribution

# create two different gaussian distribution
r1<- rnorm(x, 500,100)
r2 <- rnorm(x, 1000,100)

# run the chi square test
chisq.test(r1,r2,simulate.p.value = TRUE)

Result:

Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)

data:  r1 and r2
X-squared = 10100, df = NA, p-value = 0.0004998

This suggests that whether the distributions I tested are different or not, the chi sq test will say that they are not the same.

The result is the same whether of not simulate.p.value is TRUE.

Answer 1

Chances are, that you are using chisq.test wrong.

chisq.test(x = r1, y = r2, simulate.p.value = TRUE)

Is not a test, if r1 and r2 stem from the same distribution. Instead, the manual says

Otherwise, x and y must be vectors or factors of the same length; [...] the objects are coerced to factors, and the contingency table is computed from these. Then Pearson's chi-squared test is performed of the null hypothesis that the joint distribution of the cell counts in a 2-dimensional contingency table is the product of the row and column marginals.

You are basically producing a 100x100 contingency table consisting of mostly zeros and some ones.

So if I understand you right, you try to do a chisquare distribution test but asked R to do a chisquare test of independence.