1. MADAM SITI AISYAH ZAKARIA EQT 271 SEM 2 2014/2015 CHAPTER 3 ANOVA (EXTRA NOTE & EXERCISE)

2. REFRESH YOUR MIND

3. Agresti/Franklin Statistics, 3 of 82 The 1998 General Social Survey asked subjects how many friend they have. Is this associated with the respondent’s astrological sign (the 13 symbols of the Zodiac)? The ANOVA table for the data reports F=0.61 State the null hypothesis a.The population means for all 12 Zodiac signs are the same. b.At least two population means are different.

4. Agresti/Franklin Statistics, 4 of 82 The 1998 General Social Survey asked subjects how many friend they have. Is this associated with the respondent’s astrological sign (the 13 symbols of the Zodiac)? The ANOVA table for the data reports F=0.61 State the alternative hypothesis a.The population means for all 12 Zodiac signs are the same. b.At least two population means are different.

5. Agresti/Franklin Statistics, 5 of 82 The 1998 General Social Survey asked subjects how many friend they have. Is this associated with the respondent’s astrological sign (the 13 symbols of the Zodiac)? The ANOVA table for the data reports F=0.61 Based on what you know about the F distribution would you guess that the test value of 0.61 provides strong evidence against the null hypothesis? a.No b.Yes

6. Agresti/Franklin Statistics, 6 of 82 The 1998 General Social Survey asked subjects how many friend they have. Is this associated with the respondent’s astrological sign (the 13 symbols of the Zodiac)? The ANOVA table for the data reports F=0.61 The P-value associated with the F-statistic is 0.82. At a significance level of 0.05, what is the correct decision? a.Reject H o b.Fail to Reject H o c.Reject H a d.Fail to Reject H a

7. CONTINUE FROM PART 3 (FACTORIAL EXPERIMENT) INTERACTION FACTOR

8. Agresti/Franklin Statistics, 8 of 82 Exploring Interaction between Factors in Two-Way ANOVA No interaction between two factors means that the effect of either factor on the response variable is the same at each category of the other factor. [Factor A and Factor B] Do not Reject H 0

9. Graphical No interaction or have interaction

10. Agresti/Franklin Statistics, 10 of 82 Exploring Interaction between Factors in Two-Way ANOVA  The lines in the graph is parallel or approximately parallel.  There is no significant interaction effect between the factor.  The difference in estimated means between the two fertilizer levels is the same for each manure level.  The effect of two factor is same

11. Agresti/Franklin Statistics, 11 of 82 Exploring Interaction between Factors in Two-Way ANOVA A graph showing interaction:  Intersection occur – disordinal interaction (SOME INTERACTION) - Not more effect  No intersection – ordinal interaction (SIGNIFICANT INTERACTION) - have more effect

12. Agresti/Franklin Statistics, 12 of 82 Testing for Interaction In conducting a two-way ANOVA, before testing the main effects, it is customary to test a third null hypothesis stating that their is no interaction between the factors in their effects on the response

13. Agresti/Franklin Statistics, 13 of 82 Testing for Interaction The test statistic providing the sample evidence of interaction is: When H 0 is false (reject H 0 ), the F-statistic tends to be large

14. Agresti/Franklin Statistics, 14 of 82 Example: Testing for Interaction with Corn Yield Data ANOVA table for a model that allows interaction:

15. Agresti/Franklin Statistics, 15 of 82 Example: Testing for Interaction with Corn Yield Data The test statistic for H 0 : no interaction is F = 1.10 with a corresponding P-value of 0.311 There is not much evidence of interaction We would not reject H 0 at the usual significance levels, such as 0.05

16. Agresti/Franklin Statistics, 16 of 82 Check Interaction before Main Effects In practice, in two-way ANOVA, you should first test the hypothesis of no interaction

17. Agresti/Franklin Statistics, 17 of 82 Check Interaction before Main Effects If the evidence of interaction is not strong (that is, if the P-value is not small), then test the main effects (factor A and factor B) hypotheses and/or construct confidence intervals for those effects

18. Agresti/Franklin Statistics, 18 of 82 Check Interaction before Main Effects If important evidence of interaction exists (have interaction in your hypothesis), plot and compare the cell means for a factor separately at each category of the other factor

19. REFRESH YOUR MIND

20. Agresti/Franklin Statistics, 20 of 82 An experiment randomly assigns 100 subjects suffering from high cholesterol to one of four groups: low-dose Lipitor, high-dose Lipitor, low- dose Pravachol and high-dose Pravachol. After three months of treatment, the change in cholesterol level is measured. What is the response variable? a.Cholesterol level b.Drug dosage c.Drug type

21. Agresti/Franklin Statistics, 21 of 82 An experiment randomly assigns 100 subjects suffering from high cholesterol to one of four groups: low-dose Lipitor, high-dose Lipitor, low- dose Pravachol and high-dose Pravachol. After three months of treatment, the change in cholesterol level is measured. What are the factors? a.Cholesterol level and drug type b.Drug dosage and cholesterol level c.Drug type and drug dosage

22. ANOVA ONE-WAY or TWO WAY CONCLUSION  Reject H 0  There is difference (which one is difference???)

23. RELATIONSHIP BETWEEN HYPOTHESIS TESTING AND CONFIDENT INTERVAL

24. Agresti/Franklin Statistics, 24 of 82 For the single mean & proportion Confidence Interval vs Hypothesis Testing At the same level in confidence interval and hypothesis testing, when the null hypothesis is rejected, the confidence interval for the mean and proportion will not contain the hypothesized mean/proportion. Likewise, when we do not reject null hypothesis the confidence interval will contain the hypothesized mean/ proportion. ** Applies only for two-tailed test. Allan Bluman, pg. 458

25. Agresti/Franklin Statistics, 25 of 82 For the difference of means & proportions Confidence Interval vs Hypothesis Testing [-8.5, 8.5] Contains zero = If the CI contains zero, we do not reject H 0 (Means that the there is NO DIFFERENCE in population means or proportions) [5.45, 12.45] No zero = If the CI does not contain zero, we reject H 0 (Mean/proportion for population 1 is GREATER than the mean/proportion for population 2) There is difference in population means [-7.3, -3.3] No zero = If the CI does not contain zero, we reject H 0 (Mean/proportion for population 1 is LESS than the mean/proportion for population 2) There is difference in population means ** Applies only for two-tailed test. Eg. in Allan Bluman, pg. 477-478.

26. EXAMPLE HYPOTHESIS TESTING & CONFIDENT INTERVAL

27. Agresti/Franklin Statistics, 27 of 82 Hog Weights A researcher claims that adult hogs fed a special diet will have an average weight of 200 pounds. A sample of 10 hogs has an average weight of 198.2 pounds and a standard deviation of 3.3 pounds. At a 0.05, can the claim be rejected? Also, find the 95% confidence interval of the true mean. 27

28. Agresti/Franklin Statistics, 28 of 82 28

29. Agresti/Franklin Statistics, 29 of 82 Sugar Production Sugar is packed in 5-pound bags. An inspector suspects the bags may not contain 5 pounds. A sample of 50 bags produces a mean of 4.6 pounds and a standard deviation of 0.7 pound. Is there enough evidence to conclude that the bags do not contain 5 pounds as stated at a 0.05? Also, find the 95% confidence interval of the true mean. Answer: Reject H 0 and 95% confidence interval of μ does not contain the hypothesized value μ = 5. Z = - 4.04 CI =[4.46, 4.79] 29

30. GOOD LUCK… THE END….