Question

What do independent trials in relationship to probability theory mean?

Answer 1

By replicating experiments for independent trials, if the same results are repeated, we can be even more sure of their significance. For example, if the same level of significance was found at P = .01 for 4 studies, the probability that all 4 would have found the same results solely by chance = (.01)^4 = .01 * .01 * .01 * .01 = .000000001 = 1 time in a billion that these results all would occur by chance. At that point, I can be very certain in the significance of rejecting the null hypothesis.