What is the default significance level for chisq.test() in R? What is the default significance level for the chisq.test() function in R? I have been trying to figure that one out but couldn't. The documentation seems really poor on these specifications.
 A: Your question makes little sense in a world where computers can easily compute the "exact" p-value of your test for you. There is no default level of significance, hence why it is not documented. In days of yore, one had to look up critical values of the distribution of the test statistic for a given level of significance $\alpha$. The user chooses the level of $\alpha$, the Type I error rate, they are willing to accept. If your observed statistic was equal to or larger than the critical value from the tables for your chosen $\alpha$ then one would conclude it (the test) was significant at that $\alpha$ level.
chisq.test(), in common with most of the hypothesis test functions in R, will compute the exact p-value for the observed test statistic. You, the user, need to decide how to interpret it. If your own default significance level is $\alpha$ of 0.05, then if the observed p-value is less than or equal to this value you can conclude the result of the test is significant. What your "default" level of significance is will be informed by your domain of work/study and the false positive rate you are willing to accept; in ecology for example, the "default" significance is often 0.05.
The p-value also represents evidence against the Null hypothesis. The smaller the value the less likely that the data or test statistic would have been observed if the Null hypothesis was true.
A: chisq.test returns an htest object.  htest objects include many things, but they do not include significance levels.  They do have p-values (accessed with $p.value) which you can compare to a significance level of your choosing, but that's left up to you.
