R，比较两个2x2矩阵/表之间差异的显着性

Question

In my statistical analysis, I'm comparing how likely it is for a sample to have answered (Y/N) to Question 2 given their answer (Y/N) to Question 1.

millenials_q1q2 <- matrix(c(25, 150, 100, 25),ncol=2, byrow=FALSE)
babyboomers_q1q2 <- matrix(c(100,75,60,60),ncol=2, byrow=FALSE)

I've been able to use proptable to chart the row and column percentages:

prop.table(test_data1, 1)
prop.table(test_data1, 2)

prop.table(test_data2, 1)
prop.table(test_data2, 2)

What I'm hoping to do is directly compare the two matrices to assess the significance of the difference between the two patterns.

I hope that this makes sense and gives enough context!

EDIT (for further context):

I've subsettted the dataset by demographic (ie Millenials, Baby Boomers), and I'm interested in exploring if/how these sub-samples answered Q1 and Q2 differently.

The matrices above represent distinct differences in how they answered the questions, and I'm interested in measuring that difference. (compared to, say, the following matrices which are similar)

millenials_same <- matrix(c(55, 45, 55, 45),ncol=2, byrow=FALSE)
babyboomers_same <- matrix(c(57, 44, 53, 46),ncol=2, byrow=FALSE)

Does that help clarify my question? Thanks!

Answer 1

Assuming these matrices to have paired data, you can construct a confidence interval on the difference of each pair.

1. Create a matrix "D" with values test_data1-test_data2 (first item of "D" is test_data1[1]-test_data2[1])
2. Construct a confidence interval on the mean of values in "D"

More details on step 2 can be seen here: http://www.cyclismo.org/tutorial/R/confidence.html

If the confidence interval doesn't include "0", you can say that there is no evidence to say that the difference in the values is insignificant.