Say I have two vectors:

Action.Taken = c(0,1,0,0,1,1,0,1,0)
Success = c(0,0,0,1,0,1,0,1,0)

The first tells me whether or not a specific action was taken in a trial and the second tells me whether or not that trial succeeded. How would I go analyzing these two vectors to answer the following question: Does taking action (Action.Taken = 1) affect whether or not success is had (Success = 1)? I'd like some measure of significance as an regression/hypothesis testing.

I'm looking for an answer that I can implement using R. I am also quite new to stats, so it would be nice if someone could give me a relatively simple, straightforward answer/example.


  • 3
    $\begingroup$ Consider the chi-square test for independence. $\endgroup$ Jul 14, 2014 at 21:37
  • $\begingroup$ And the correlation coefficient (phi) that can be computed based on Chi-Square. $\endgroup$
    – rolando2
    Jul 14, 2014 at 21:45
  • $\begingroup$ Yeah, I've actually tried the prop.test function, which returns, among other things, the p-value given the null hypothesis that two (or more) proportions aren't different. I think phi is just as simple as cor(dat), but I don't know what/how much that tells me. $\endgroup$
    – userNaN
    Jul 14, 2014 at 21:51

1 Answer 1


As TrynnaDoStat says, I'd suggest using the chi-square test for independence. Start with:

contingency = table(Action.Taken, Success) 

This gives you a contingency table, which displays the number of times you have action {1, 0} and success {1,0}. That can tell you whether success is more frequent when some action is taken. Then use:


The p-value here tests the null that action taken is independent of success. If the p-value is greater than 0.05 you cannot reject the hypothesis that the two are independent at the 5% significance level. In other words, it doesn't matter what action you take - statistically it seems success is equally likely either way (at the 5% level).


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