I'm performing a study and I have the following table, where each binary column means a given attempt of communication in a given time:
Device 1: 1 1 1 0 0 0 0
Device 2: 0 1 0 1 1 0 1
Device 3: 1 0 1 1 1 0 0
Device n: 1 1 1 1 0 1 0
Typically, I have a set o devices that perform a given attempt of communication at the same time. When the outcome of this attempt is 1 it means that a link was established and 0 otherwise.
I'd like to perform a statistical analysis that proves that a failure of communication (0) doesn't affect all devices equally. For instance, a given device doesn't establish communication, but this doesn't mean that all devices will fail together in a given attempt.
From my probability classes some years ago, I remember that we can check if some variables are independent using:
(A $\cap$ B $\cap$ C) = P(A).P(B).P(C), where A is the probability of communication failure for Device 1, B for Device 2 and C for device n. Does it make sense this independence checking? What statistical test should I use for this particular study?
Any help is appreciated!
Thanks in advance.