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P-value Approach for Test Conclusion

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.

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P-value Approach for Test Conclusion

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  1. P-value Approach for Test Conclusion • Under the assumption that H0 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 H0. Large P-value gives no evidence against H0. In general, the smaller the P-value the stronger the evidence against H0 provided by the data. • The decisive value of the P is the significance level . week 8

  2. Example week 8

  3. 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 H0 when in fact H0 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 H0 when in fact H0 is false is called a type II error. The probability of making a type II error is denoted by . week 8

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

  5. Power • The probability of rejecting H0 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 H0 when H0 is false) = = P( rejecting H0 when H0 is false) week 8

  6. Example week 8

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