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MGMT 276: Statistical Inference in Management McClelland Hall, Room 132 8:30 – 10:45 Monday - Thursday Summer II , 2012. Welcome. Please start portfolios. Please read: Chapters 10 – 12 in Lind book and Chapters 2 – 4 in Plous book : (Before the next exam) Lind

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  1. MGMT 276: Statistical Inference in ManagementMcClelland Hall, Room 1328:30 – 10:45 Monday - ThursdaySummer II, 2012. Welcome

  2. Please start portfolios

  3. Please read: Chapters 10 – 12 in Lind book and Chapters 2 – 4 in Plous book: (Before the next exam) Lind Chapter 10: One sample Tests of Hypothesis Chapter 11: Two sample Tests of Hypothesis Chapter 12: Analysis of Variance Chapter 13: Linear Regression and Correlation Chapter 14: Multiple Regression Chapter 15: Chi-Square Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

  4. Where are we? • We are right on schedule… • Four more days of class before our final exam • Wednesday (8/1/12) ANOVA • Thursday (8/2/12) Correlation and Regression • Monday (8/6/12) Multiple Regression • Tuesday (8/7/12) Chi Square and Review for Exam 4 • Wednesday (8/8/12): Final Exam • Homework Assignments have been posted • Study Guide for the Final Exam has been posted

  5. Use this as your study guide By the end of lecture today8/1/12 Hypothesis testing with analysis of variance (ANOVA) Interpreting excel output of hypothesis tests Constructing brief, complete summary statements

  6. “Between Groups”Differences . Difference between means Difference between means Difference between means Variabilityof curve(s) “Within Groups”Variability Variabilityof curve(s) Variabilityof curve(s)

  7. 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)? Still, difference between means • Critical statistic (e.g. z or t or F or r) value? Step 3: Calculations MSBetween F = MSWithin Still, variabilityof curve(s) 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 Section 1 did this

  8. One-way ANOVA Number of cookies sold Bike None Hawaii trip Incentives • One-way ANOVAs test only one independent variable • - although there may be many levels • “Factor” = one independent variable • “Level” = levels of the independent variable • treatment • condition • groups • “Main Effect” of independent variable = difference between levels • Note: doesn’t tell you which specific levels (means) differ from each other A multi-factor experiment would be a multi-independent variables experiment Section 1 did this

  9. Comparing ANOVAs with t-tests Similarities still include: Using distributions to make decisions about common and rare events Using distributions to make inferences about whether to reject the null hypothesis or not The same 5 steps for testing an hypothesis Tells us generally about number of participants / observations Tells us generally about number of groups / levels of IV • The three primary differences between t-tests and ANOVAS are: • 1. ANOVAs can test more than two means • 2. We are comparing sample means indirectly by • comparing sample variances • 3. We now will have two types of degrees of freedom • t(16) = 3.0; p < 0.05 F(2, 16) = 3.0; p < 0.05 Tells us generally about number of participants / observations

  10. One way analysis of varianceVariance is divided Remember, one-way = one IV Total variability Between group variability (only one factor) Within group variability (error variance) 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

  11. Three different types of variance Between groups Within groups Total Between Groups Variability Total Variability Variability between groups F = Within Groups Variability Variability within groups

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

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

  14. . Effect size is considered relativeto variability of distributions Treatment Effect x Variability between groups Treatment Effect x Variabilitywithin groups

  15. x = 1 x = 6 x = 5 What if we want to compare 3 means? One independent variable with 3 means 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 (Hawaii) 6 5 9 4 6 Troop 2 (bicycle) 6 8 5 4 2 Troop 3 (nada) 0 4 0 1 0 Note: 5 girls in each troop

  16. Main effect of incentive Number of cookies sold Number of cookies sold Hawaii None Bike None Bike Hawaii Incentives Incentives

  17. 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. How many levels of the Independent Variable? What is Independent Variable? Troop 3 (Hawaii) 14 9 19 13 15 Troop 1 (nada) 10 8 12 7 13 Troop 2 (bicycle) 12 14 10 11 13 What is Dependent Variable? How many groups? n = 5 x = 10 n = 5 x = 12 n = 5 x = 14

  18. 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 • To get an effect we want: • Large “F” - big effect and small variability • Small “p” - less than 0.05 (whatever our alpha is) We don’t know which means are different from which …. just that they are not all the same

  19. Hypothesis testing: Step 1: Identify the research problem Is there a significant difference in the number of cookie boxes sold between the girlscout troops that were given the different levels of incentive? Describe the null and alternative hypotheses

  20. Hypothesis testing: = .05 Decision rule Degrees of freedom (between) = number of groups - 1 = 3 - 1 = 2 Degrees of freedom (within) = # of scores - # of groups = (15-3) = 12* Critical F(2,12) = 3.98 *or = (5-1) + (5-1) + (5-1) = 12.

  21. Appendix B.4 (pg.518) F (2,12) α= .05 Critical F(2,12) = 3.89

  22. “SS” = “Sum of Squares”- will be given for exams- you can think of this as the numerator in a standard deviation formula ANOVA table F Source df MS SS Between ? ? ? ? Within ? ? ? Total ? ?

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

  24. ANOVA table MSbetween MSwithin 40 88 SSbetween 12 2 ANOVA table dfbetween F Source df MS SS ? Between 40 2 ? 2.73 20 Within 88 12 ? 7.33 Total 128 14 SSwithin dfwithin 88 20 =2.73 =7.33 40 7.33 12 =20 2

  25. Make decision whether or not to reject null hypothesis Observed F = 2.73 Critical F(2,12) = 3.89 2.73 is not farther out on the curve than 3.89 so, we do not reject the null hypothesis F(2,12) = 2.73; n.s. Conclusion: There appears to be no effect of type of incentive on number of girl scout cookies sold 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.

  26. Let’s do same problemUsing 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

  27. Let’s do same problemUsing MS Excel

  28. Let’s do same problemUsing MS Excel

  29. Let’s do oneReplication of study(new data)

  30. Let’s do same problemUsing MS Excel

  31. Let’s do same problemUsing MS Excel

  32. MSbetween MSwithin 40 88 SSbetween 12 2 dfbetween 3-1=2 # groups - 1 SSwithin dfwithin # scores - number of groups 15-3=12 88 20 =2.73 =7.33 40 # scores - 1 7.33 12 =20 2 15- 1=14

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

  34. Make decision whether or not to reject null hypothesis Observed F = 2.73 Critical F(2,12) = 3.89 2.7 is not farther out on the curve than 3.89 so, we do not reject the null hypothesis 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

  35. Make decision whether or not to reject null hypothesis Observed F = 2.72727272 F(2,12) = 2.73; n.s. Critical F(2,12) = 3.88529 2.7 is not farther out on the curve than 3.89 so, we do not reject the null hypothesis Conclusion: There appears to be no effect of type of incentive on number of girl scout cookies sold 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.

  36. Let’s do another oneUsing MS Excel Notice exact same data but twice as many subjects (I just copied the data twice for this example) This is just to highlight the power of more subjects even if size of treatment doesn’t change

  37. Let’s do oneReplication of study(new data)

  38. Let’s do oneReplication of study(new data)

  39. Let’s do oneReplication of study(new data)

  40. Let’s do oneReplication of study(new data) # groups - 1 # scores - number of groups # scores - 1

  41. Let’s do oneReplication of study(new data) SSwithin SSbetween df df

  42. Let’s do oneReplication of study(new data) MSbetween MSwithin

  43. Let’s do oneReplication of study(new data) F critical(is it greater than F?) P-value(is it less than .05?)

  44. Make decision whether or not to reject null hypothesis Observed F = 6.136364 Critical F(2,27) = 3.354131 6.14 is farther out on the curve than 3.35 so, we do reject the null hypothesis Also p-value is smaller than 0.05 so we do reject the null hypothesis

  45. Make decision whether or not to reject null hypothesis Observed F = 6.136364 F(2,27) = 6.14; p < .05 Critical F(2,27) = 3.354131 Notice: F(2,27) = 6.14; p < .01 6.14 is farther out on the curve than 3.35 so, we do reject the null hypothesis Conclusion: There appears to be an effect of type of incentive on number of girl scout cookies sold

  46. Make decision whether or not to reject null hypothesis Observed F = 6.136364 F(2,27) = 6.14; p < .05 Critical F(2,27) = 3.354131 Notice: F(2,27) = 6.14; p < .01 6.14 is farther out on the curve than 3.35 so, we do reject the null hypothesis Conclusion: There appears to be an effect of type of incentive on number of girl scout cookies sold 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 there is a significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 27) = 6.14; p < 0.05

  47. ANOVA - Analysis of VarianceThe larger the ratio (F) the bigger the effect(taking into account the error variance) • When the null hypothesis is true: • the ratio of the between-groups population variance (estimate) to • the within-groups population variance (estimate) should be about 1. • When the research hypothesis is true, • this ratio should be greater than 1 Variability between groups F = Variability within groups MSBetween F = MSWithin

  48. When the null hypothesis is true: • the ratio of the between-groups population variance (estimate) to • the within-groups population variance (estimate) should be about 1. • the three means are equal • When the alternative hypothesis is true, • this ratio should be greater than 1 (F will be large & p will be small) By comparing the within group and between group variance we are able to answer questions about whether the differences between the means of groups are significant

  49. 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.

  50. Variability between groups F = Let’s try one Variability within groups Which figure would depict the largest F ratio a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above 1. 2. 3.

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