Inference Concepts Hypothesis Testing

Summary (from Before) Make statistical hypotheses from research hypothesis Use H0 to make prediction (Assume H0 is true) this is why H0 must be the “equals” situation Compare predicted statistic to observed statistic calculate p-value Compare p-value to rejection criterion (a) if p-value > a then DNR H0 conclude that H0 could be correct if p-value < a then reject H0 conclude that H0 is probably not correct Critical Inference Concepts

if p-value > a then H0 could be correct Recall that `x = 135.9 for H0: m=137, p-value=0.1357, DNR H0 for H0: m=137.1, p-value=0.1151, DNR H0 for H0: m=137.2, p-value=0.0968, DNR H0 for H0: m=137.3, p-value=0.0808, DNR H0 There are always several other hypotheses that would also not be rejected. distrib(135.9,mean=137,sd=10/sqrt(100)) distrib(135.9,mean=137.1,sd=10/sqrt(100)) distrib(135.9,mean=137.2,sd=10/sqrt(100)) distrib(135.9,mean=137.3,sd=10/sqrt(100)) Inference Concepts

DNR vs Accept The data do not contradict this H0, but it is not fully known if this H0 is true. Inference Concepts

if p-value < a then H0 is probably incorrect Even if H0 is truly correct it is possible to observe a statistic in the tail, resulting in a p-value < a, and a rejection of H0. 137 138 139 140 136 135 134 Inference Concepts

Decision Making Errors Set a priori by the researcher Can’t be known, because truth is not known Type I a Correct power Ha mu<100, sigma-10,n=30,alpha=0.05 True mu=95 Type II b Correct Inference Concepts