> Because what the p-value is really telling you is the probability that on repeating the experiment you would see a result as or more extreme than what you observed.
That's incorrect. If you perform the exact same experiment twice, the chances are exactly 50% that the first result is more extreme than the second one (neglecting equal outcomes).
This illustrates nicely how hard it is to properly explain the p-value. Things would be more intuitive if people would report confidence intervals. I prefer "x is with a likelihood of 95% between a and b" a thousand times over "we measured x=c and reject the null hypothesis with 95% probability".
That's incorrect. If you perform the exact same experiment twice, the chances are exactly 50% that the first result is more extreme than the second one (neglecting equal outcomes).
This illustrates nicely how hard it is to properly explain the p-value. Things would be more intuitive if people would report confidence intervals. I prefer "x is with a likelihood of 95% between a and b" a thousand times over "we measured x=c and reject the null hypothesis with 95% probability".