So I keep getting tripped up on the conclusion of a p-value. We just had a vice presidential debate. Since my null hypothesis is my dull hypothesis, I submit the following two: H0: The vice-presidential debate had no effect on voter decision. HA: The vice-presidential debate changed the minds of voters. So under the assumption I do all the surveying and statistical math right looking for a changed poll after the debate..... Case 1: I get a p < 0.05 : or "p is low, so reject H0." I reject my null hypothesis. Does this p-value tell me: The vice-presidential debate changed the minds of voters. Essentially, that the alternative hypothesis is true? I think this is a misinterpretation. The definition of the thing is "the probability of obtaining a result equal to or 'more extreme' than what was actually observed, when the null hypothesis is true." In my example, my low p means that if the debate had no effect, the change in polling results after the debate had a low probability of occurring at random. Why does this not mean the vp debate DID have an effect? Case 2: I get a high p-value. So I do NOT reject the null hypothesis. The high p-value says that if my null hypothesis is true (there is no effect) then my observed change in polling results could have happened at random. In other words, I have learned nothing other than the observed change is not large enough to make a difference. Can I say: The vice-presidential debate had no effect on voter decision. Or can I only say I cannot tell?