I'm probably jumping into shark filled waters considering the point of the article is that defining p-values intelligibly is incredibly difficult even for exper

I'm probably jumping into shark filled waters considering the point of the article is that defining p-values intelligibly is incredibly difficult even for experts, but here goes.... > Is the p-value really not the probability of your results being due to chance? No, it is not. It is the probability that the statistical attributes of the data would be equal or more extreme than observed assuming the Null Hypothesis is true. In your definition, there is no assumption of what model the data should conform to...so what does "by random" mean in that context? Also, by random doesn't mean 'not predictable' or useless. If I roll a 100 sided die an infinite number of times, I'd expect the number of observances of '5' to approach .01 of the total distribution. So, the probability of rolling a 5 by random chance is 1 in 100. However, I would not reject my Null Hypothesis since my model predicts exactly this random behavior. Now, if I rolled a die 1000 times and rolled a 5 every time the mean of that distribution (5) would be very, very far from the expected mean of my model if the Null is assumed to be true. And I may be tempted (very) to reject the Null that I am rolling a 100 sided fair die. I will now sit back and wait for my definition and analogy to be torn to shreds. :)