explain why the null hypothesis for a significance test is rejected when the p value is small rather than when it is large
+23248 The null hypothesis (meaning that there is no difference between the two items being tested) is rejected when the p-value is small because the p-value represents the chance that the probability that you are rejecting the hypothesis because of accidental circumstances is small,
As an example: you are testing a medicine versus a placebo.
The null hypothesis is that there is no difference between the medicine and the placebo. (Obviously, if you developed the medicine, you want the medicine to work better than the placebo: you want a difference between the medicine and the placebo.)
The test indicates that there is a difference between the medicine and the placebo. Sometimes the difference is due to the effectiveness of the medicine but sometimes it's just due to pure luck.
The p-value indicates the probability that the difference between the medicine and the placebo was due to pure luck. If the p-value is high, this means that the difference could easily be due to pure luck; if the p-value is small, this (very likely) means that the difference between the medicine and the placebo was due to the medicine.
