Course Notes - Department of Mathematics and Statistics

7.5 Interpreting the p-valueINTERPRETING THE p-VALUEThe p-value can be thought of as the strength of evidence for retainingthe null hypothesis H 0 .• If p-value < 0.05 then ‘significant at α = 0.05 (5%) level’ or ‘Thereis some evidence that . . .’.• If p-value < 0.01 then ‘significant at α = 0.01 (1%) level’ or ‘Thereis strong evidence that . . .’.• If p-value > 0.05 then ‘not significant at α = 0.05 (5%) level’ or‘There is no evidence that . . .’.Notes on the p-value• Choosing a smaller level of significance (α) requires the test statisticto be more extreme before H 0 is rejected.• Whether we use a one-sided or two-sided test depends on whetherwe use a data based or study based H A .• If H A is one-sided, the p-value is the area in one tail.• If H A is two-sided, the p-value is the area in two tails.Rejecting H 0If we reject the null hypothesis then either:(a) H 0 is true but random variation gave a rare event, or(b) H 0 is not true and we accept H A . We usually accept this option,but there is possible error (α, or type I error).Statistically significant = small p-value (less than 0.05 or 0.01).But is this clinically important?129