null vs alternative hypothesis issac chung + eric gertner

DEFINE: Null hypothesis (H 0 ) : conservative, status quo statement. H 0 = no change, no effect, usual statement about population parameter Alternative hypothesis (H a ) : research hypothesis. Usually statement about value of a parameter that we hope to demonstrate is true

more uses/ definitions. Null hypothesis is the prediction, while the alternative hypothesis lists all other possible outcomes. Alternative hypothesis is only considered or used if null is rejected

NEGOTIATIONS h 0 : “x = y.” h A : “x is =/= y.” h 0 : “x is at least y.” h a : “x < y.” h 0 : “x is at most y.” h a : “x > y.”

Examples of Null/Alternative Given a headline that says that red meat causes cancer: Null Hypothesis: Red meat causes cancer This is our null because it is what we ‘expect’ the answer to be. In other words, it is the hypothesis that our experiment is attempting to prove is NOT true. Alternative Hypothesis: Red meat does not cause cancer This is our alternative because it is the hypothesis that our experiment is attempting to prove is true. That is, the alternative hypothesis is what we are trying to prove if the null turns out to be false. The alternative hypothesis outlines any other possible outcomes besides the null.

Rejecting/Failing to Reject When proving or disproving our null hypothesis, we always want to use the terminology “reject, or fail to reject.” In other words, we wouldn’t say that we believe the alternative hypothesis over the null, but instead that we reject the null hypothesis, or, if our experiment reinforces the null, that we fail to reject the null hypothesis. For example, in an experiment with a significance level of 5%, if our result is less than 0.05, our result is within the rejection zone, and we would say that we fail to reject the null hypothesis.