Hypothesis Testing

p-value

The $p$-value is the probability of observing your evidence given that the null hypothesis $H_0$ is true.

Convention

• $p<0.05$ strong support of $H_1$
• $p<0.01$ very strong support of $H_1$
• $p\ge 0.05$ insufficient evidence against $H_0$

Level of significance ($\alpha$): $0.1$, $0.05$, $0.01$, etc. (this is domain specific)

In STAT206, the following are our conventions (very common). These values should be decided before the study is conducted:

• $p<0.05$:
  • reject $H_0$
  • fail to reject $H_1
• $p\ge 0.05$
  • fail to reject $H_0$
  • reject $H_1$

How do you calculate the p-value?