system
Given the following post, respond as if you're commenting on Reddit:
human
Do you reject your hypothesis if the variable is not statistically significant, even though the coefficient had the sign you predicted?

My experience reading most articles has been that if a variable's not statistically significant, you just say that it's not statistically significant, period. I've been trying to read more on how to report/interpret results that aren't statistically significant, but I haven't really found an answer regarding whether you confirm/reject your hypothesis that you set before you do your analysis. 

For example, my first hypothesis is that there is a positive association between exercise (independent variable) and happiness (dependent variable). Let's say that the coefficient for exercise is positive, but the exercise variable is not statistically significant (p-value higher than 0.05). Is this hypothesis of a positive association confirmed because of the positive coefficient, or is it rejected because of the p-value?
gpt
> Is this hypothesis of a positive association confirmed because of the positive coefficient, or is it rejected because of the p-value?

The *null* hypothesis is *not* rejected due to the large p-value. This means that the observed results are reasonably explained by the null hypothesis, so we can't reject it as a possibility. 

The specific observed sign of the coefficient does not change this. If there was no effect (i.e. the null was true), the observed coefficient would still have to take on *some* sign by random chance. It could easily end up with the same sign as your alternative simply by random chance - it's basically a 50/50 chance under the null (assuming a null of 0).