Confusion regarding p-values and false discovery rate I get stuck with understanding of the following two statements (from Wikipedia on p-values):


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The p-value is the probability of obtaining at least as extreme results given that the null hypothesis is true whereas the significance level $\alpha$ is the probability of rejecting the null hypothesis given that it is true.


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If one defines a false positive rate as the fraction of all “statistically significant” tests in which the null hypothesis is actually true, several arguments suggest that this is at least about 30 percent for p-values that are close to 0.05.

It is more or less explained in the Regina Nuzzo's 2014 Nature editorial. I predefined a level of significance = 0.05, made a single test and got a p-value of 0.049. The second statement tells me that the chances that I will be able to replicate this result using another sample is not 95%, but much lower. (I think it should be dependent on prior probabilities, but the statement in wikipedia makes more general conclusion).
The questions are:


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*Is the second statement correct? Does it suggest that a priori probabilities of two hypothesis are equal to 0.5?

*How to understand it intuitively? 
 A: I suggest you to read http://rsos.royalsocietypublishing.org/content/1/3/140216 that contains most of the elements you need. 
To answer your first question, for a set of tests providing $p$-values $\in  [0.045,0.05]$ and power=0.8, the FDR (as defined in the second statement of your question) is 26% if there are as many tests with true effect as tests with no true effect (page 9 of the paper). Notice that the restriction to $p$-value $\in  [0.045,0.05]$ is very important and the FDR decreases with letting the $p$-value having smaller values or/and when the proportion of true effect tests increases.
To answer your second question, the two statements are radically different. Indeed, in statement 2 of FDR, the ratio is obtained by averaging over all conclusive tests accounting from both the real effect case and the not-real effect case (with a given proportion). While in the first statement for the type I error, the ratio is computed over the (hypothetical) tests for the all observations that could be generated under the null hypothesis of no real effect only. 
