can you guys help me visualize the relationship between p-value and alternative hypothesis… the way i am imagining it is that a larger p-value implies that the null hypothesis can be ignored with larger type-1 error, so the smaller the p-value the smaller the probability of type-1 error which implies stronger evidence for alternative hypothesis cuz there is less error in rejecting the null. right or wrong…
I have a background in statistics, and here is the official definition for P value and hypothesis testing.
P value: the probability of obtaining a coefficient as extreme or more extreme distribution than the one we observed right now if the null hypothesis were true.
#1 a small P value means the probability of obtaining such an extreme distribution is really small, so the null hypothesis is unlikely to be true. We reject null hypothesis and accept the alternative hypothesis.
#2 a big P value means the probability is big, and the null hypothesis could be true and we fail to reject the null hypothesis.
A p-value is like an α: a level of significance.
The best explanation I’ve heard is that α is the chosen level of significance, while the p-value is the observed level of significance.
If p < α, reject H0.
If p > α, don’t reject H0.