So here’s the procedure for ruling out the null hypothesis, in executive bullet-point form: Run an experiment. Suppose the null hypothesis is true, and let p be the probability (under that hypothesis) of getting results as extreme as those observed. The number p is called the p-value. If it is very small, rejoice; you get to say your results are statistically significant. If it is large, concede that the null hypothesis has not been ruled out.
