2. Modern Languages 14131211109 87 6 54321 111098765 43 2 Row A Row B Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 212019181716 1514 13 12111098 212019181716 13 12111098 141312 table 7 6 54321 Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 321 21 1413 Projection Booth 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 7 6 5432 1 765 43 2 1 7 6 5432 1 765 43 2 1 7 6 54321 765 43 2 1 7 6 54321 765 43 2 1 7 6 54321 table Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 321 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 282726 2524 23 22 R/L handed broken desk Stage Lecturer’s desk Screen 1

3. MGMT 276: Statistical Inference in Management Spring 2015

6. Before our next exam (April 14 th ) Lind (10 – 12) Chapter 10: One sample Tests of Hypothesis Chapter 11: Two sample Tests of Hypothesis Chapter 12: Analysis of Variance Plous (2, 3, & 4) Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence Schedule of readings

7. Logic of hypothesis testing Steps for hypothesis testing Levels of significance (Levels of alpha) what does p < 0.05 mean? what does p < 0.01 mean? Hypothesis testing with t-scores (two independent samples) Analysis of Variance (ANOVA) Constructing brief, complete summary statements By the end of lecture today 4/7/15

8. On class website: Please print and complete homework worksheet #13 & 14 Hypothesis testing using t-tests Homework due – Today (April 7 th ) Please note: Because this homework was longer than most, it is worth two assignments Please note: Because this homework was longer than most, it is worth two assignments On class website: Please print and complete homework worksheet #15 Hypothesis testing using ANOVAs Homework due – Thursday (April 9 th )

9. A girl scout troop leader wondered whether providing an incentive to whomever sold the most girl scout cookies would have an effect on the number cookies sold. She provided a big incentive to one troop (trip to Hawaii), a lesser incentive to a second troop (bicycle), and no incentive to a third group, and then looked to see who sold more cookies. n = 5 x = 10 n = 5 x = 12 n = 5 x = 14 Troop 1 (nada) 10 8 12 7 13 Troop 2 (bicycle) 12 14 10 11 13 Troop 3 (Hawaii) 14 9 19 13 15 What is Independent Variable? How many groups? What is Dependent Variable? How many levels of the Independent Variable? Review

10. Main effect of incentive: Will offering an incentive result in more girl scout cookies being sold? If we have a “effect” of incentive then the means are significantly different from each other we reject the null we have a significant F p < 0.05 We don’t know which means are different from which …. just that they are not all the same To get an effect we want: Large “F” - big effect and small variability Small “p” - less than 0.05 (whatever our alpha is) Review

11. ? ? ? ANOVA table 128 dfMS F # groups - 1 # scores - number of groups # scores - 1 2 12 14 Source Between Within Total 88 40 SS ? ? ? ? ? ? “SS” = “Sum of Squares” - will be given for exams 3-1=2 15-3=12 15- 1=14

12. ANOVA table 128 df MS F 2 12 14 Source Between Within Total 88 40 SS MS between MS within SS within df within 20 7.33 SS between df between 88 12 =7.33 40 2 =20 20 7.33 =2.73 2.73 40 2 88 12 ? ? ?

13. Make decision whether or not to reject null hypothesis 2.73 is not farther out on the curve than 3.89 so, we do not reject the null hypothesis Observed F = 2.73 Critical F (2,12) = 3.89 Conclusion: There appears to be no effect of type of incentive on number of girl scout cookies sold F (2,12) = 2.73; n.s. The average number of cookies sold for three different incentives were compared. The mean number of cookie boxes sold for the “Hawaii” incentive was 14, the mean number of cookies boxes sold for the “Bicycle” incentive was 12, and the mean number of cookies sold for the “No” incentive was 10. An ANOVA was conducted and there appears to be no significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 12) = 2.73; n.s.

14. Let ’ s do same problem Using MS Excel A girlscout troop leader wondered whether providing an incentive to whomever sold the most girlscout cookies would have an effect on the number cookies sold. She provided a big incentive to one troop (trip to Hawaii), a lesser incentive to a second troop (bicycle), and no incentive to a third group, and then looked to see who sold more cookies. Troop 1 (Nada) 10 8 12 7 13 Troop 2 (bicycle) 12 14 10 11 13 Troop 3 (Hawaii) 14 9 19 13 15 n = 5 x = 10 n = 5 x = 12 n = 5 x = 14

15. Let ’ s do one Replication of study (new data)

16. Let ’ s do same problem Using MS Excel

18. SS within df within SS between df between 88 12 =7.33 40 2 =20 20 7.33 =2.73 40 2 88 12 MS between MS within # groups - 1 # scores - number of groups # scores - 1 3-1=2 15-3=12 15- 1=14

19. F critical (is observed F greater than critical F?) P-value (is it less than.05?) No, so it is not significant Do not reject null No, so it is not significant Do not reject null

20. Make decision whether or not to reject null hypothesis 2.7 is not farther out on the curve than 3.89 so, we do not reject the null hypothesis Observed F = 2.73 Critical F (2,12) = 3.89 Also p-value is not smaller than 0.05 so we do not reject the null hypothesis Step 6: Conclusion: There appears to be no effect of type of incentive on number of girl scout cookies sold

21. Make decision whether or not to reject null hypothesis 2.7 is not farther out on the curve than 3.89 so, we do not reject the null hypothesis Observed F = 2.72727272 Critical F (2,12) = 3.88529 Conclusion: There appears to be no effect of type of incentive on number of girl scout cookies sold F (2,12) = 2.73; n.s. The average number of cookies sold for three different incentives were compared. The mean number of cookie boxes sold for the “Hawaii” incentive was 14, the mean number of cookies boxes sold for the “Bicycle” incentive was 12, and the mean number of cookies sold for the “No” incentive was 10. An ANOVA was conducted and there appears to be no significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 12) = 2.73; n.s.

22. One way analysis of variance Variance is divided Total variability Within group variability (error variance) Between group variability (only one factor) Remember, 1 factor = 1 independent variable (this will be our numerator – like difference between means) Remember, error variance = random error (this will be our denominator – like within group variability Remember, one-way = one IV

23. Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses Step 2: Decision rule Alpha level? ( α =.05 or.01)? Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed t (or F) is bigger then critical t (or F) then reject null Step 5: Conclusion - tie findings back in to research problem Critical statistic (e.g. z or t or F or r) value? MS Within MS Between F = Still, difference between means Still, variability of curve(s)

24. . Difference between means Variability of curve(s) “Between Groups” Variability “Within Groups” Variability

25. Sum of squares (SS): The sum of squared deviations of some set of scores about their mean Mean squares (MS): The sum of squares divided by its degrees of freedom Mean square within groups: sum of squares within groups divided by its degrees of freedom Mean square between groups: sum of squares between groups divided by its degrees of freedom Mean square total: sum of squares total divided by its degrees of freedom MS Within MS Between F =

26. ANOVA Variability within groups Variability between groups F = Variability Between Groups Variability Within Groups “Between” variability bigger than “within” variability so should get a big (significant) F Variability Between Groups Variability Within Groups “Between” variability getting smaller “within” variability staying same so, should get a smaller F Variability Between Groups “Between” variability getting very small “within” variability staying same so, should get a very small F Variability Within Groups

27. ANOVA Variability within groups Variability between groups F = “Between” variability bigger than “within” variability so should get a big (significant) F “Between” variability getting smaller “within” variability staying same so, should get a smaller F “Between” variability getting very small “within” variability staying same so, should get a very small F (equal to 1) Variability Within Groups Variability Between Groups Variability Within Groups Variability Between Groups

28. Let’s try one In a one-way ANOVA we have three types of variability. Which picture best depicts the random error variability (also known as the within variability)? a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above 1. 2. 3. correct

29. Let’s try one In a one-way ANOVA we have three types of variability. Which picture best depicts the between group variability? a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above 1. 2. 3. correct

30. Let’s try one Which figure would depict the largest F ratio a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above Variability within groups Variability between groups F = 1. 2. 3. “F ratio” is referring to "observed F” correct

31. Let’s try one What if your variability between groups was smaller than your variability within groups a. Reject null b. Do not reject null c. Not enough information Variability within groups Variability between groups F = 10 100.10 100 10 Very small Do not reject null Very big Will reject null correct

32. Let’s try one Winnie found an observed z of.74, what should she conclude? (Hint: notice that.74 is less than 1) a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given small observed z score x x If your observed z is within one standard deviation of the mean, you will never reject the null correct

33. Let’s try one Winnie found an observed t of.04, what should she conclude? (Hint: notice that.04 is less than 1) a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given small observed t score x correct

34. Let’s try one Winnie found an observed F ratio of.9, what should she conclude? a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given 1. 2. 3. correct

35. Let’s try one An ANOVA was conducted comparing different types of solar cells and there appears to be a significant difference in output of each (watts) F(4, 25) = 3.12; p < 0.05. In this study there were __ types of solar cells and __ total observations in the whole study? a. 4; 25 b. 5; 30 c. 4; 30 d. 5; 25 # groups - 1 # scores - # of groups # scores - 1 F(4, 25) = 3.12; p < 0.05 How many observations within each group? correct

36. Let’s try one An ANOVA was conducted comparing different types of solar cells and there appears to be significant difference in output of each (watts) F(4, 25) = 3.12; p < 0.05. In this study ___ a. we rejected the null hypothesis b. we did not reject the null hypothesis p <.05 F(4, 25) = 3.12; p < 0.05 Observed F bigger than Critical F correct

37. Let’s try one An ANOVA was conducted comparing different types of solar cells. The analysis was completed using an alpha of 0.05. But Julia now wants to know if she can reject the null with an alpha of at 0.01. In this study ___ a. we rejected the null hypothesis b. we did not reject the null hypothesis p <.05 F(4, 25) = 3.12; p < 0.05 Comparison of the Observed F and Critical F Is no longer are helpful because the critical F is no longer correct. We must use the p value p >.01 correct

38. Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. Please complete this ANOVA table. Degrees of freedom between is _____; degrees of freedom within is ____ a. 16; 4 b. 4; 16 c. 12; 3 d. 3; 12. correct

39. Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. Please complete this ANOVA table. Mean Square between is _____; Mean Square within is ____ a. 300, 300 b. 100, 100 c. 100, 25 d. 25, 100. correct

40. Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. Please complete this ANOVA table. The F ratio is: a..25 b. 1 c. 4 d. 25. correct

41. An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. Please complete this ANOVA table, alpha = 0.05. We should: a. reject the null hypothesis b. not reject the null hypothesis Let’s try one p <.05 Observed F bigger than Critical F correct

42. An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. The most expensive neighborhood was the ____ neighborhood a. Southpark b. Northpark c. Westpark d. Eastpark Let’s try one correct

43. An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark). For each neighborhood we measured the price of four homes. Please complete this ANOVA table. The best summary statement is: a. F(3, 12) = 4.0; n.s. b. F(3, 12) = 4.0; p < 0.05 c. F(3, 12) = 3.49; n.s. d. F(3, 12) = 3.49; p < 0.05 correct

44. Let’s try one An ANOVA was conducted and there appears to be a significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 27) = ___; p < 0.05. Please fill in the blank a. 3.3541 b..00635 c. 6.1363 d. 27.00