I don't understand why a lower p value is stronger evidence against the null hypothesis. P value is a probability; so, wouldn't a lower p value mean that your statistic was very lucky (rare)?
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confused -
You are on the right track but on the wrong side of the road...
A low p-value is indeed "rare" but you need to look at with respect to the "status quo" or null hypothesis.
The "test statistic" is SO FAR AWAY from the status quo that it is highly unlikely that it simply happened by chance. So the test statistic must indeed be "different" from the status quo so we need to reject it.
The farther away the test statistic is from the mean, the lower the p-value and the greater evidence we have that the test statistic is significantly different from the status quo or null.
Hope that clears it up.
You are on the right track but on the wrong side of the road...
A low p-value is indeed "rare" but you need to look at with respect to the "status quo" or null hypothesis.
The "test statistic" is SO FAR AWAY from the status quo that it is highly unlikely that it simply happened by chance. So the test statistic must indeed be "different" from the status quo so we need to reject it.
The farther away the test statistic is from the mean, the lower the p-value and the greater evidence we have that the test statistic is significantly different from the status quo or null.
Hope that clears it up.