I have an issue where I want to see if two events may coincide by more than chance.

For instance given the following data I may hypothesise that "Alice" and "Bob" come into the office together more frequently than chance.

MONDAY      x        x               x 
TUESDAY     x        x      x        
THURSDAY    x               
SATURDAY    x        x      x        x 
SUNDAY      x

I know the chance of Alice being at work on a day:

  • $P(A) = 5/7$

And I know chance of Bob being at work on a day:

  • $P(B) = 3/7$

And I know the "observed" chance of Alice and Bob being both at work on a day:

  • $P(AB) = 3/7$

And I can calculate my null hypothesis "expected" chance that Alice and Bob are at work on a day

  • $E(AB) = P(A) \cdot P(B) = 5/7 \cdot 3/7 = 15/49 \approx 2/7$

And I can see that "observed" is higher than "expected".

I'd assumed that was some sort of $\chi^{2}$ test, but my data is boolean (in office or not in office) rather than discrete, and I get odd results back when I try it.

Is this along the right lines? Is there some way of putting a $p$ value (or similar) on this, to say whether this difference is significant or not? And does the presence of Charlie and Eve affect the results?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.