2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Spring 2015 Room 150 Harvill Building 8:00 - 8:50 Mondays, Wednesdays & Fridays.

4. Schedule of readings Before next exam (April 10 th ) Please read chapters 7 – 11 in Ha & Ha Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

5. By the end of lecture today 4/8/15 Use this as your study guide Logic of hypothesis testing Steps for hypothesis testing Hypothesis testing with Analysis of Variance (ANOVA) Constructing brief, complete summary statements Review for Exam 3

6. No homework Just study for Exam 3

7. Labs continue this week with Exam 3 review

8. Exam 3 – This Friday (4/10/15) Study guide is online now Bring 2 calculators (remember only simple calculators, we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID

9. Homework

12. Type of major in school 4 (accounting, finance, hr, marketing) Grade Point Average 0.05 2.83 3.02 3.24 3.37

13. Homework 0.3937 0.1119 0.3937 / 0.1119 = 3.517 3.517 3.009 3 24 0.03 If observed F is bigger than critical F: Reject null & Significant! If p value is less than 0.05: Reject null & Significant! # groups - 1 # scores - number of groups # scores - 1 4-1=3 28 - 4=24 28 - 1=27

14. Homework Yes F (3, 24) = 3.517;p < 0.05 The GPA for four majors was compared. The average GPA was 2.83 for accounting, 3.02 for finance, 3.24 for HR, and 3.37 for marketing. An ANOVA was conducted and there is a significant difference in GPA for these four groups (F (3,24) = 3.52; p < 0.05).

15. Number of observations in each group Average for each group (We REALLY care about this one)

16. “SS” = “Sum of Squares” - will be given for exams Number of groups minus one (k – 1)  4-1=3 Number of people minus number of groups (n – k)  28-4=24

17. MS between MS within SS between df between SS within df within

20. Type of executive 3 (banking, retail, insurance) Hours spent at computer 0.05 10.8 8 8.4

21. 11.46 2 11.46 / 2 = 5.733 5.733 3.88 2 12 0.0179 If observed F is bigger than critical F: Reject null & Significant! If p value is less than 0.05: Reject null & Significant!

22. Yes F (2, 12)= 5.73; p < 0.05 The number of hours spent at the computer was compared for three types of executives. The average hours spent was 10.8 for banking executives, 8 for retail executives, and 8.4 for insurance executives. An ANOVA was conducted and we found a significant difference in the average number of hours spent at the computer for these three groups, (F (2,12) = 5.73; p < 0.05).

23. Number of observations in each group Just add up all scores Average for each group

24. “SS” = “Sum of Squares” - will be given for exams Number of groups minus one (k – 1)  3-1=2 Number of people minus number of groups (n – k)  15-3=12

25. MS between MS within SS between df between SS within df within

27. 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 = Revisit

28. 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 Revisit

29. 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

30. 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 Between group variability Total variability Within group variability Revisit

31. 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 Between group variability Total variability Within group variability Revisit

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

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. Degrees of freedom between is _____; degrees of freedom within is ____ a. 16; 4 b. 4; 16 c. 12; 3 d. 3; 12. correct

41. 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

42. 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

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, 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

44. 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

45. 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

46. 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

47. Let’s try one An ANOVA was conducted comparing “best racquet” scores for different types of tennis racquets. The results were: F(4, 45) = 9.49; p < 0.05. What should we conclude? a. we rejected the null hypothesis b. we did not reject the null hypothesis F(4, 45) = 9.49; p < 0.01 correct

48. Let’s try one An ANOVA was conducted comparing “best racquet” scores for different types of tennis racquets. The results were: F(4, 45) = 9.49; p < 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 F(4, 45) = 9.49; p < 0.01 correct

49. Let’s try one An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). For each brand of ski we rated 10 skis. Degrees of freedom between is _____; degrees of freedom within is ____ a. 30; 3 b. 3; 30 c. 27; 2 d. 2; 27. correct

50. Let’s try one An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). For each brand of ski we rated 10 skis. Mean Square between is _____; Mean Square within is ____ a. 6.9, 1.5 b. 1.5, 6.9, c. 13.8, 41.5 d. 41.5, 13.8. correct

51. Let’s try one An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). For each brand of ski we rated 10 skis. The F ratio is: a..25 b. 1 c. 4.51 d. 25. correct

52. An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). Alpha = 0.05. Please complete this ANOVA table. 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

53. An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). Alpha = 0.01. Please complete this ANOVA table. We should: a. reject the null hypothesis b. not reject the null hypothesis Let’s try one p NOT <.01 Observed F bigger than Critical F correct

54. An ANOVA was conducted comparing ratings for the best Brand of skis (4FRNT, K2, and Rossignol). The best rated brand of skis was ____ a. 4FRNT b. K2 c. Rossignol Let’s try one correct

55. an alpha of 0.01 Tasi is a small business owner who wanted to know whether her advertising campaign would make a difference in the average amount of money spent by her customers. She has two businesses, one in California and one in Florida. She completed an ad campaign in California, but had no advertising campaign in Florida. She then compared sales and completed a t-test using an alpha of 0.01. The results are presented in this table. Which of the following best describes the results of her experiment: a. There is a significant difference t(98) = 2.25; p <0.01 b. There is not a significant difference t(98) = 2.25; p <0.01 c. There is a significant difference t(98) = 2.25; n.s. d. There is not a significant difference t(98) = 2.25; n.s. Let’s try one correct

56. Let’s try one Theodora is researcher who compares how different companies address workers’ quality of life and general productivity. She created a questionnaire that measured these two constructs and gave the test to 140 men and 140 women. Please refer to this table to answer the following question: Which of the following best describe Theodora’s findings on worker productivity? a.A t-test was calculated and there is a significant difference in productivity between the two groups t(278) = 3.64; p < 0.05 b.A t-test was calculated and there is no significant difference in productivity between the two groups t(278) = 3.64; n.s. c.A t-test was calculated and there is a significant difference in productivity between the two groups t(280) = 3.64; p < 0.05 d.A t-test was calculated and there is no significant difference in productivity between the two groups t(280) = 3.64; n.s. correct

57. Let’s try one Refer again to Theodora’s findings presented on the table. Let’s assume for this question that Theodora set her alpha at 0.01, which of the following is true? a. Theodora found a significant difference between men and women’s quality of life, but not between men and women’s productivity. b.Theodora found a significant difference between men and women’s productivity, but not between men and women’s quality of life measures c. Theodora found a significant difference between men and women for both productivity and quality of life measures. d. Theodora found no significant difference between men and women for neither productivity nor quality of life measures. correct

58. .. Which of the following would represent a one-tailed test? a. Please test to see whether men or women are taller b. With an alpha of.05 test whether advertising increases sales c. With an alpha of.01 test whether management strategies affect worker productivity d. Does a stock trader’s education affect the amount of money they make in a year? correct

59. Which of the following represents a significant finding: a. p < 0.05 b. the observed statistic (z score) is not bigger than critical value c. the observed z statistic is nearly zero d. do not reject the null hypothesis Careful with “exceeds” correct

60. A t-test was conducted to see whether “Bankers” or “Retailers” spend more time in front of their computer. Which best summarizes the results from this excel output: a. Bankers spent significantly more time in front of their computer screens than Retailers, t(3.5) = 8; p < 0.05 b. Bankers spent significantly more time in front of their computer screens than Retailers, t(8) = 3.5; p < 0.05 c. Retailers spent significantly more time in front of their computer screens than Bankers, t(3.5) = 8; p < 0.05 d. Retailers spent significantly more time in front of their computer screens than Bankers, t(8) = 3.5; p < 0.05 e. There was no difference between the groups correct

61. A t-test was conducted to see whether “Bankers” or “Retailers” spend more time in front of their computer. Which critical t would be the best to use a. 3.5 b. 1.859 c. 2.306 d..004 e..008 Let’s try one correct

62. A t-test was conducted to see whether “Bankers” or “Retailers” spend more time in front of their computer. How many bankers and retailers were measured a. 10 bankers were measured; 8 retailers were measured b. 10 bankers were measured; 10 retailers were measured c. 5 bankers were measured; 5 retailers were measured Let’s try one correct

63. 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 correct

64. Let’s try one An ANOVA was conducted and we found the following results: F(3,12) = 3.73 ____. Which is the best summary a. The critical F is 3.89; we should reject the null b. The critical F is 3.89; we should not reject the null c. The critical F is 3.49; we should reject the null d. The critical F is 3.49; we should not reject the null correct

65. Let’s try one Agnes compared the heights of the women’s gymnastics team and the women’s basketball team. If she doubled the number of players measured (but ended up with the same means) what effect would that have on the results? a. the means are the same, so the t-test would yield the same results. b. the means are the same, but the variability would increase so it would be harder to reject the null hypothesis. c. the means are the same, but the variability would decrease so it would be easier to reject the null hypothesis. correct

66. Let’s try one Albert compared the heights of a small sample of 10 women from the women’s gymnastics team to the mean for the whole team (population). This is an example of a one-sample t-test. He found an observed t(9) =.04, what should he do? a. Reject the null hypothesis b. Do not reject the null hypothesis c. There is not enough information correct

67. A table of t-test results How many of these t-tests reach significance with alpha of 0.05? a. 1b. 2c. 3d. 4 correct

68. An advertising firm wanted to know whether the size of an ad in the margin of a website affected sales. They compared 4 ad sizes (tiny, small, medium and large). They posted the ads and measured sales. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between advertising space and sales correct

69. According to the Central Limit Theorem, which is false? As n ↑ As n ↑ x will approach µ As n ↑ curve will approach normal shape As n ↑ curve variability gets bigger a. b. c. d. correct

70. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is true? a. The IV is gender while the DV is time to finish a race b. The IV is time to finish a race while the DV is gender correct

71. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is true? a. The null hypothesis is that there is no difference in race times between the genders b. The null hypothesis is that there is a difference between the genders correct

72. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. A Type I Error would claim that: a. There is a difference when in fact there is b. There is a difference when in fact there isn’t one c. There is no difference when in fact there isn’t one d. There is no difference when in fact there is a difference Which would be a Type II error? correct

73. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. He concluded p < 0.05 what does this mean? a. There is a significant difference between the means b. There is no significant difference between the means correct

74. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is true? a. This is a one-tailed test b. This is a two-tailed test correct

75. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is true? a. This is a quasi, between participant design b. This is a quasi, within participant design a. This is a true, between participant design b. This is a true, within participant design correct

76. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is best describes this study? a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA correct

77. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is best describes his results? a. t(198) = 2.38; p < 0.05 b. t(198) = 2.38; ns c. t(198) = 1.97; p < 0.05 d. t(198) = 1.97; ns correct

78. Let’s try one Albert compared the race times of 20 male and female jockeys for race horses. He wanted to know who averaged faster rides. Which of the following is best describes his results? a. t(198) = 2.38; p < 0.01 b. t(198) = 2.38; ns c. t(198) = 1.97; p < 0.01 d. t(198) = 1.97; ns correct

79. An ANOVA was conducted comparing which type of horse is the fastest (Arabians, Thoroughbreds, or Quarter Horses). We measured how long it took to finish the race. We measured 11 of each type of horse (33 altogether) Please complete this ANOVA table. Degrees of freedom between is _____; degrees of freedom within is ____ a. 30; 2 b. 2; 30 c. 80; 3 d. 3; 80 correct

80. An ANOVA was conducted comparing which type of horse is the fastest (Arabians, Thoroughbreds, or Quarter Horses). We measured how long it took to finish the race. We measured 11 of each type of horse (33 altogether) Mean Square Between is ____ while Mean Square Within is ______ a. 80; 2 b. 2; 80 c. 30; 40 d. 40; 30 correct

81. An ANOVA was conducted comparing which type of horse is the fastest (Arabians, Thoroughbreds, or Quarter Horses). We measured how long it took to finish the race. We measured 11 of each type of horse (33 altogether) Please complete this ANOVA table. The F ratio is a..75 b. 1.3 c. 1.5 d. 1.75 correct

82. The critical F ratio a. 2.84 b. 2.92 c. 3.23 d. 3.32 correct

83. The observed F is 1.3 and the critical F ratio is 3.32. What should we conclude? a. reject the null hypothesis b. do not reject the null hypothesis c. p < 0.5 d. both a and c are true correct

84. An ANOVA was conducted comparing which type of horse is the fastest (Arabians, Thoroughbreds, or Quarter Horses). We measured how long it took to finish the race. We measured 11 of each type of horse (33 altogether) Please complete this ANOVA table. The observed F is 2 and the critical F ratio is 3.32. F(2, 30) = ___; n.s. Please fill in the blank a. 3.32 b. 1.3 c. 30 d. 40 correct

85. An advertising firm wanted to know whether the size of an ad in the margin of a website affected sales. They compared 4 ad sizes (tiny, small, medium and large). They posted the ads and measured sales. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between advertising space and sales correct

86. Victoria was also interested in the effect of vacation time on productivity of the workers in her department. In her department some workers took vacations and some did not. She measured the productivity of those workers who did not take vacations and the productivity of those workers who did (after they returned from their vacations). This is an example of a _____. a. quasi-experiment b. true experiment c. correlational study Let’s try one correct

87. Ian was interested in the effect of incentives for girl scouts on the number of cookies sold. He randomly assigned girl scouts into one of three groups. The three groups were given one of three incentives and he looked to see who sold more cookies. The 3 incentives were: 1) Trip to Hawaii, 2) New Bike or 3) Nothing. This is an example of a ___. a. quasi-experiment b. true experiment c. correlational study Let’s try one correct

88. Ian was interested in the effect of incentives and age for girl scouts on the number of cookies sold. He randomly assigned girl scouts into one of three groups. The three groups were given one of three incentives and he looked to see who sold more cookies. The 3 incentives were: 1) Trip to Hawaii, 2) New Bike or 3) Nothing. He also measured their age. This is an example of a ___. a. quasi-experiment b. true experiment c. correlational study d. mixed design Let’s try one correct

89. Marietta is a manager of a movie theater. She wanted to know whether there is a difference in concession sales for afternoon (matinee) movies vs. evening movies. She took a random sample of 25 purchases from the matinee movie (mean of $7.50) and 25 purchases from the evening show (mean of $10.50). She compared these two means. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between movie times and amount of concession purchases. Let’s try one correct

90. Marietta is a manager of a movie theater. She wanted to know whether there is a difference in concession sales for afternoon (matinee) movies and evening movies. She took a random sample of 25 purchases from the matinee movie (mean of $7.50) and 25 purchases from the evening show (mean of $10.50). Which of the following would be the appropriate graph for these data Relationship between movie times and amount of concession purchases. Let’s try one Matinee Evening Concession purchase a. Movie Time Concession b. Movie Times Concession purchase d. c. Concession purchase Movie Times correct

91. Pharmaceutical firm tested whether fish-oil capsules taken daily decrease cholesterol. They measured cholesterol levels for 30 male subjects and then had them take the fish-oil daily for 2 months and tested their cholesterol levels again. Then they compared the mean cholesterol before and after taking the capsules. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between daily fish-oil capsules and cholesterol levels in men. correct

92. Elaina was interested in the relationship between the grade point average and starting salary. She recorded for GPA. and starting salary for 100 students and looked to see if there was a relationship. This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA Relationship between GPA and starting salary Let’s try one Relationship between GPA and Starting salary GPA Starting Salary correct

93. -1.64 or +1.64 Critical z values One-tailedTwo-tailed α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58 5% 2.5% 1%.5% Match each level of significance to each situation. Which situation would be associated with a critical z of 1.96? a. A b. B c. C d. D A B CD Hint: Possible values 1.64 1.96 2.33 2.58

94. 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