●●● ●●●● ●●●●● ●●●● Find p-value and draw conclusion 3: The mathematician have calculated probability corresponding to every TS, and listed in some tables. This is the probability that the test statistic would weigh against Ho at least as strongly as it does for these data 21/1/29
2021/1/29 16 The mathematician have calculated probability corresponding to every T.S, and listed in some tables. This is the probability that the test statistic would weigh against Ho at least as strongly as it does for these data. Find P-value and draw conclusion
●●● ●●●● ●●●●● ●●●● ●●0●● Find p value and draw conclusion ●●●● ●●●● If Psa, we reject Ho in favor of H, at significant level a, We may think that the two populations are different; If P>a, we don t reject Ho at significant level a. We may think that two populations are same 21/1/29
2021/1/29 17 If P≤α, we reject Ho in favor of H1 at significant level α, We may think that the two populations are different; If P>α, we don`t reject Ho at significant level α. We may think that two populations are same. Find P-value and draw conclusion
●●● ●●●● ●●●●● ●●●● Type I error versus type If error in ●●0●● ●●●● ●●●● hypothesis testing Because the predictions in Ho and H, are written so that they are mutually exclusive and all inclusive, we have a situation where one is true and the other is automatically false when Ho is true then Hi is false If we don't reject Ho, we have done the right thing If we reject Ho, we have made a mistake Type I error: Reject Ho when it is true. The probability of type I error is a 21/1/29
2021/1/29 18 TypeⅠerror versus typeⅡ error in hypothesis testing Because the predictions in H0 and H1 are written so that they are mutually exclusive and all inclusive, we have a situation where one is true and the other is automatically false. when H0 is true ,then H1 is false. ✓ If we don’t reject H0 ,we have done the right thing. ✓ If we reject H0 ,we have made a mistake. Type Ⅰ error: Reject H0 when it is true. The probability of type Ⅰ error is
●●● ●●●● ●●●●● ●●●● Type I error versus type If error in ●●0●● ●●●● ●●●● hypothesis testing When Ho is false then H is true If we don't reject Ho, we have made a mistake If we reject Ho, we have done the right thing ype ll error: Don't reject when it is false. The probability of type I error isβ. B is more difficult to assess because it depends on several factors 1-B is called the power of the test 21/1/29
2021/1/29 19 TypeⅠerror versus typeⅡ error in hypothesis testing when H0 is false ,then H1 is true. ✓ If we don’t reject H0 , we have made a mistake. ✓ If we reject H0 , we have done the right thing. TypeⅡ error : Don’t reject when it is false. The probability of type Ⅱ error is . is more difficult to assess because it depends on several factors. 1- is called the power of the test
●●● ●●●● ●●●●● ●●●● ●●0●● ●●●0 State of nature Decision Ho is real Ho is false Don't reject Correct decision type I error 5 10 Correct decision Reject Ho type I error (a) Test power(1-B) 21/1/29
2021/1/29 20 Decision State of nature H0 is real H0 is false Don’t reject H0 Correct decision 1 - α type Ⅱ error (β) Reject H0 type Ⅰ error (α) Correct decision Test power (1-β)