[cetacea]

Even better, p-values should not be used at all. If I have data in hand, I want to use it to find out the probability that my hypothesis is true. But p-value analysis requires me to instead ask a different question that I don't really care about, involving whether my data are consistent with the null hypothesis.

Everything is just so much more sensible if you allow yourself to assign probabilities to hypotheses, rather than assuming a hypothesis from the outset and computing opaque statistics relating to your data.

[healer]

There is in fact a probability attached to p-values. A p-value of 0.05 for instance means your conclusions will be wrong 5 out of 100 times. You can reduce the p-value to e.g. 0.001 or any other value you want.

[cwyers]

No, it means that the probability of seeing an effect of that magnitude on a dataset of that size when the null hypothesis is true will happen due to random chance 5 out of 100 times. It says NOTHING about your hypothesis, it is entirely a statement about the null hypothesis.