There are two genes I am interested in. They both have many samples in which they have no expression. So I decided to see if there is a relationship between when they are expressed. I was looking for a binary correlation in a sense. If gene $1$ is or isn't expressed, does that tell me something about whether gene $2$ is or is not expressed.
Here is a table showing the count information.
| Gene $1$ is expressed | Gene $1$ is not expressed | |
|---|---|---|
| Gene $2$ is expressed | $81$ | $72$ |
| Gene $2$ is not expressed | $162$ | $400$ |
I got a chi-squared value of $30.1$ and p-value of $4\times 10^{-8}$ and a Jaccard similarity of $25$%.
It appears that the Jaccard similarity shows that samples where Gene $1$ is expressed are usually not the same samples in which Gene $2$ is expressed. However, I am wondering how to interpret the chi-squared statistic. What does that tell me about my data? Something about the variables not being independent. But how are they not independent?
Additionally, are these the correct measurements to use to investigate this correlation?
Thanks in advance.