Pvalue Approach for Test Conclusion Under the assumption

P-value Approach for Test Conclusion • Under the assumption that H 0 is true, the probability that the test statistic would take a value as extreme or more extreme than that actually observed is called the P-value of the test. • Small P-value gives evidence against H 0. Large P-value gives no evidence against H 0. In general, the smaller the P-value the stronger the evidence against H 0 provided by the data. • The decisive value of the P is the significance level . week 8 1

Example week 8 2

Decision Errors • When we perform a hypothesis test we hope that our decision will be correct, but sometimes it will be wrong. There are two possible errors that can be made in hypothesis test. • The error made by rejecting the null hypothesis H 0 when in fact H 0 is true is called a type I error. The probability of making a type I error is denoted by . • The error made by failing to reject the null hypothesis H 0 when in fact H 0 is false is called a type II error. The probability of making a type II error is denoted by . week 8 3

• Significance level and type I error The significance level of any test is the P(Type I error). week 8 4

Power • The probability of rejecting H 0 when a particular alternative value of the parameter is true is called the power of the test to detect that alternative. • The power of a test against a particular alternative is Power = 1 - β = 1 - P( not rejecting H 0 when H 0 is false) = = P( rejecting H 0 when H 0 is false) week 8 5

Example week 8 6