What does it mean when people say when the p value is low the null must go but it doesnt always seem to work that way?
Answer:
You should understand that p-value is nothing but a probability of a particular event. When we test a hypothesis, we get a test statistic and the p-value. If the p-value is small or low as you were saying, then it would mean that there is a very low probability of rejecting the null hypothesis when it is correct.
Let us take an example. If we have a hypothesis that having garlic can reduce blood pressure. Then our hypothesis is that Having garlic does not have any effect on the blood pressure. The alternate hypothesis is that having garlic would significantly reduce blood pressure levels. Now if the data analysis gives a p-value of .05 (95% confidence level, which is the general convention), then we have enough evidence to reject our null hypothesis. In conclusion, this would mean that there is evidence to suggest that having garlic can help in reducing the blood pressure levels.
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