2. Stage Screen Row B 13 121110 20191817 14 13 121110 19181716 1514 Gallagher Theater 16 65879 Row R 6 58 7 9 Lecturer’s desk Row A Row B Row C 4 3 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 3 21 3 2 43 21 Row A 17 16 15 Row A Row C 131211 10 1514 6 58 7 9 Row D 13121110 1514 16 6 58 7 9 20191817 Row D Row E 131211 10 1514 6 58 7 9 19181716 Row E Row F 13121110 1514 16 6 58 7 9 20191817 Row F Row G 13121110 1514 6 58 7 9 19181716 Row G Row H 13121110 1514 16 6 58 7 9 20191817 Row H Row I 13121110 1514 6 58 7 9 19181716 Row I Row J 13121110 1514 16 6 58 7 9 20191817 Row J Row K 13121110 1514 6 58 7 9 19181716 Row K Row L 13121110 1514 16 6 58 7 9 20 191817 Row L Row M 13121110 1514 6 58 7 9 19181716 Row M Row N 13121110 1514 16 6 5879 20191817 Row N Row O 13121110 1514 6 58 7 9 19181716 Row O Row P 13121110 1514 16 6 5879 20191817 Row P Row Q 13121110 6 5879 161514 Row Q 4 4 Row R 10 879 Row S Row B Row C Row D Row E Row F Row G Row H Row I Row J Row K Row L Row M Row N Row O Row P Row Q 26Left-Handed Desks A14, B16, B20, C19, D16, D20, E15, E19, F16, F20, G19, H16, H20, I15, J16, J20, K19, L16, L20, M15, M19, N16, P20, Q13, Q16, S4 5 Broken Desks B9, E12, G9, H3, M17 Need Labels B5, E1, I16, J17, K8, M4, O1, P16 Left handed

3. Stage Screen 2213 121110 Row A Row B Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 17 Row C Row D Row E Projection Booth 65 4 table Row C Row D Row E 30 27 26252423 282726 2524 23 3127262524 23 R/L handed broken desk 16 1514 13 12 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 Social Sciences 100 Row N Row O Row P Row Q Row R 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 8 7 9 65 4 8 7 9 3 2 6 5 48793 2 1 6 5 48793 2 1 Row F Row G Row H Row J Row K Row L Row M Row N Row O Row P Row Q Row R 6 5 48793 2 1 6 5 48793 2 1 Row I 2213 121110 2019181716151421 Row I 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 Lecturer’s desk 6 5 48793 2 1 262524 23 302928 Row F Row G Row H Row J Row K Row L Row M Row N Row O Row P Row Q Row R Row I 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 Row B 2928 27

4. MGMT 276: Statistical Inference in Management Fall, 2014 Green sheets

5. Reminder Talking or whispering to your neighbor can be a problem for us – please consider writing short notes. A note on doodling

7. Before our next exam (November 6 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

8. No homework Just study for Exam 3 Homework

9. By the end of lecture today 11/4/14 Use this as your study guide Logic of hypothesis testing Hypothesis testing with t-scores (two independent samples) Constructing brief, complete summary statements Review for Exam 3

10. Exam 3 – Thursday (11/6/14) Study guide online Bring 2 calculators (remember only simple calculators, we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID We have lots of tutoring opportunities Please see website for schedule of TA office hours

11. Independent samples t-test Donald is a consultant and leads training sessions. As part of his training sessions, he provides the students with breakfast. He has noticed that when he provides a full breakfast people seem to learn better than when he provides just a small meal (donuts and muffins). So, he put his hunch to the test. He had two classes, both with three people enrolled. The one group was given a big meal and the other group was given only a small meal. He then compared their test performance at the end of the day. Please test with an alpha =.05 Big Meal 22 25 Small meal 19 23 21 Mean= 24 Mean= 21

12. Mean= 24 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 Mean= 21 Complete a t-test

13. Mean= 24 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 Mean= 21 Complete a t-test

14. Mean= 24 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 Mean= 21 Complete a t-test If checked you’ll want to include the labels in your variable range If checked, you’ll want to include the labels in your variable range

15. Finding Means

16. This is variance for each sample (Remember, variance is just standard deviation squared) Please note: “Pooled variance” is just like the average of the two sample variances, so notice that the average of 3 and 4 is 3.5

17. This is “n” for each sample (Remember, “n” is just number of observations for each sample) df = “degrees of freedom” Remember, “degrees of freedom” is just (n-1) for each sample. So for sample 1: n-1 =3-1 = 2 And for sample 2: n-1=3-1 = 2 Then, df = 2+2=4 This is “n” for each sample (Remember, “n” is just number of observations for each sample)

18. Finding degrees of freedom

19. Finding Observed t

20. Finding Critical t

22. Finding p value (Is it less than.05?)

24. Hypothesis testing α =.05 Step 4: Make decision whether or not to reject null hypothesis Reject when: observed stat > critical stat 1.96396 is not bigger than 2.776 “p” is less than 0.05 (or whatever alpha is) p = 0.121 is not less than 0.05 Step 5: Conclusion - tie findings back in to research problem There was no significant difference, there is no evidence that size of meal affected test scores

25. We compared test scores for large and small meals. The mean test scores for the big meal was 24, and was 21 for the small meal. A t-test was calculated and there appears to be no significant difference in test scores between the two types of meals, t(4) = 1.964; n.s. Start summary with two means (based on DV) for two levels of the IV Describe type of test (t-test versus anova) with brief overview of results Finish with statistical summary t(4) = 1.96; ns Or if it *were* significant: t(9) = 3.93; p < 0.05 Type of test with degrees of freedom Value of observed statistic n.s. = “not significant” p<0.05 = “significant”

26. Independent samples t-test Donald is a consultant and leads training sessions. As part of his training sessions, he provides the students with breakfast. He has noticed that when he provides a full breakfast people seem to learn better than when he provides just a small meal (donuts and muffins). So, he put his hunch to the test. He had two classes, both with three people enrolled. The one group was given a big meal and the other group was given only a small meal. He then compared their test performance at the end of the day. Please test with an alpha =.05 What if we ran more subjects? Big Meal 22 25 22 25 22 25 Small meal 19 23 21 19 23 21 19 23 21 Mean= 24 Mean= 21

27. Hypothesis testing Step 1: Identify the research problem Step 2: Describe the null and alternative hypotheses H o : The size of the meal has no effect on test scores Did the size of the meal affect the learning / test scores? H 1 : The size of the meal does have an effect on test scores Step 3: Decision rule α =.05 None of this will change with more subjects

28. Let’s run more subjects using our excel!

29. Finding Means Let’s run more subjects using our excel!

30. This is variance for each sample (Remember, variance is just standard deviation squared) Please note: “Pooled variance” is just like the average of the two sample variances, so notice that the average of 2.25 and 3 is 2.625

31. Let’s run more subjects using our excel! This is “n” for each sample (Remember, “n” is just number of observations for each sample) df = “degrees of freedom” Remember, “degrees of freedom” is just (n-1) for each sample. So for sample 1: n-1 =9-1 = 8 And for sample 2: n-1=9-1 = 8 Then, df = 8+8=16 This is “n” for each sample (Remember, “n” is just number of observations for each sample)

32. Finding degrees of freedom Let’s run more subjects using our excel!

33. Finding Observed t Let’s run more subjects using our excel!

34. Finding Critical t Let’s run more subjects using our excel!

35. Remember, if the “t Stat” is bigger than the “t Critical” then we “reject the null”, and conclude we have a significant effect

36. Finding p value (Is it less than.05?) Let’s run more subjects using our excel!

37. In this case, p = 0.0012 which is less than 0.05, so we “do reject the null” Remember, if the “p” is less than 0.05 then we “reject the null”, and conclude we have a significant effect

38. We compared test scores for large and small meals. The mean test score for the big meal was 24, and was 21 for the small meal. A t-test was calculated and there was a significant difference in test scores between the two types of meals t(16) = 3.928; p < 0.05 Let’s run more subjects using our excel!

39. What happened? We ran more subjects: Increased n So, we decreased variability Easier to find effect significant even though effect size didn’t change Big sampleSmall sample This is the sample size

40. What happened? We ran more subjects: Increased n So, we decreased variability Easier to find effect significant even though effect size didn’t change Big sampleSmall sample This is variance for each sample (Remember, variance is just standard deviation squared) This is variance for each sample (Remember, variance is just standard deviation squared)

41. If this is less than.05 (or whatever alpha is) it is significant, and we the reject null df = (n 1 – 1) + (n 2 – 1) = (165 - 1) + (120 -1) = 283

42. Homework review

43. . Homework Is there a difference in mpg between these two cars 2-tail 18 0.05 There is no difference in mpg between these two cars There is a difference in mpg between these two cars

44. α =.05 (df) = 18 Critical t (18) = 2.101 two tail test

45. . Homework Is there a difference in mpg between these two cars 2-tail 18 0.05 2.101 There is no difference in mpg between these two cars There is a difference in mpg between these two cars S 2 pooled = (n 1 – 1) s 1 2 + (n 2 – 1) s 2 2 n 1 + n 2 - 2 =.82 S 2 pooled = (10 – 1) (.80) 2 + (10 – 1) (1) 2 10 1 + 10 2 - 2 = 3.704 t = 17 – 18.5.82/10 +.82/10 = 1.5.4049691

46. . Homework The average mpg is 18.5 for the Ford Explorer and 17.0 for the Expedition. A t-test was conducted and found this difference to be significantly different, t(18) = 3.70; p < 0.05 Yes Is there an increase in foot size from 1960 to 1980 Is there no difference (or a decrease) in foot size from 1960 to 1980 There is an increase in foot size from 1960 to 1980 2-tail 22 0.05

47. α =.05 (df) = 22 Critical t (22) = 1.717 one tail test

48. . Homework The average mpg is 18.5 for the Ford Explorer and 17.0 for the Expedition. A t-test was conducted and found this difference to be significantly different, t(18) = 3.70; p < 0.05 Yes Is there an increase in foot size from 1960 to 1980 Is there no difference (or a decrease) in foot size from 1960 to 1980 There is an increase in foot size from 1960 to 1980 1-tail 22 0.05 1.717

49. . Homework Yes =.6201 =.4502 =.2936 S 2 pooled = (12 – 1) (.6201) 2 + (12 – 1) (4502) 2 12 1 + 12 2 - 2 = 2.26 t = 8.208 – 7.708.2936/12 +.2936/12 = 0.5.2212 Yes The average foot size for women in 1960 is 7.7, while the average foot size for women in 1980 is 8.2. A t-test was conducted and found that the increase in foot size is statistically significant, t(22) = 2.26; p < 0.05

50. . Homework

51. .

52. . Type of instruction Exam score 50 0.05 2-tail 2.66 2.02 40 38 p = 0.0113 yes CAUTION This is significant with alpha of 0.05 BUT NOT WITH alpha of 0.01 The average exam score for those with instruction was 50, while the average exam score for those with no instruction was 40. A t-test was conducted and found that instruction significantly improved exam scores, t(38) = 2.66; p < 0.05

53. . Homework Type of Staff Travel Expenses 142.5 0.05 2-tail 1.53679 2.2 130.29 11 p = 0.153 no The average expenses for sales staff is 142.5, while the average expenses for the audit staff was 130.29. A t-test was conducted and no significant difference was found, t(11) = 1.54; n.s.

54. . Homework Location of lot Number of cars 86.24 0.05 2-tail -0.88 2.01 92.04 51 p = 0.38 no The average number of cars in the Ocean Drive Lot was 86.24, while the average number of cars in Rio Rancho Lot was 92.04. A t-test was conducted and no significant difference between the number of cars parked in these two lots, t(51) = -.88; n.s. Fun fact: If the observed t is less than one it will never be significant

55. A survey was conducted to see whether men or women superintendents make more money. The independent variable is a. nominal level of measurement b. ordinal level of measurement c. interval level of measurement d. ratio level of measurement Correct

56. A survey was conducted to see whether men or women superintendents make more money. The dependent variable is a. nominal level of measurement b. ordinal level of measurement c. interval level of measurement d. ratio level of measurement Correct

57. A survey was conducted to see whether men or women superintendents make more money. The independent variable is a. continuous and qualitative b. continuous and quantitative c. discrete and qualitative d. discrete and quantitative Correct

58. A survey was conducted to see whether men or women superintendents make more money. The dependent variable is a. continuous and qualitative b. continuous and quantitative c. discrete and qualitative d. discrete and quantitative Correct

59. A survey was conducted to see whether men or women superintendents make more money. This is a a. quasi, between subject design b. quasi, within subject design c. true, between subject design d. true, within subject design Correct

60. A survey was conducted to see whether men or women superintendents make more money. This is a a. one-tailed test b. two-tailed test c. three-tailed test d. not enough information Correct

61. A survey was conducted to see whether men or women superintendents make more money. The null hypothesis is a. men make more money b. women make more money c. no difference between amount of money made d. there is a difference between the amount of money made Correct

62. A survey was conducted to see whether men or women superintendents make more money. If the null hypothesis was rejected we will conclude that a. men make more money b. women make more money c.no difference between amount of money made d. there is a difference between the amount of money made Correct

63. A survey was conducted to see whether men or women superintendents make more money. A Type I error would be a. claiming men make more money, when they don’t b. claiming women make more money, when they don’t c.claiming no difference between amount of money made, when there is a difference d. claiming there is a difference between the amount of money made, when there is no difference Correct

64. A survey was conducted to see whether men or women superintendents make more money. A Type II error would be a. claiming men make more money, when they don’t b. claiming women make more money, when they don’t c.claiming no difference between amount of money made, when there is a difference d. claiming there is a difference between the amount of money made, when there is no difference Correct

65. An t-test was conducted, there were ___ men in the study and ___ women. a. 18; 21 b. 21; 18 c. 19; 19 d. 38; 38 Let’s try one Correct

66. A t-test was conducted, which of the following best describes the results: a. t(21) = 2.02; p < 0.05 b. t(21) = 2.02; n.s. c. t(37) = 5.0; p < 0.05 d. t(37) = 5.0; n.s Let’s try one Correct

67. A t-test was conducted, with a two tail test was there a significant difference? a. No, because 5.0 is not bigger than 6.89 b. Yes, because 5.0 is bigger than 1.68. c. Yes, because 5.0 is bigger than 1.37 d. Yes, because 5.0 is bigger than 2.02 Let’s try one Correct

68. Which is true a. p < 0.05 b. p < 0.01 c. p < 0.001 d. All of the above Let’s try one Correct

69. A survey was conducted to see whether women superintendents make more money than men. This is a a. one-tailed test b. two-tailed test c. three-tailed test d. not enough information Note the change in the problem Correct

70. A survey was conducted to see whether women superintendents make more money than men. A t-test was conducted, which of the following best describes the results: Note the results were in the unpredicted direction a. reject the null b. do not reject the null c. not enough information Let’s try one Correct

71. A survey was conducted to see whether women superintendents make more money than men. A t-test was conducted, which of the following best describes the results: Note the results were in the unpredicted direction a. t(21) = 2.02; p < 0.05 b. t(21) = 2.02; n.s. c. t(37) = 5.0; p < 0.05 d. t(37) = 5.0; n.s Let’s try one Correct

72. 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

73. 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

74. 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

75. 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. as the sample size got larger the variability would increase b. as the sample size got larger the variability would decrease c. as the sample size got larger the variability would stay the same Correct

76. 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

77. 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. as the sample size got larger, it would be easier to reject the null b. as the sample size got larger, it would be harder to reject the null c. as the sample size got larger, it would made no difference on whether you reject the null Correct

78. 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, the degrees of freedom should be: a. n – 1; in this case 9 b. n – 1; in this case 19 c. n – 2; in this case 8 d. n – 2; in this case 18 Correct

79. 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

80. A table of t-test results How many of these t-tests reach significance? a. 1b. 2c. 3d. 4 Correct

81. 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

82. 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

83. 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

84. 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