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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. Use this as your study guide By the end of lecture today7/31/12 Hypothesis testing with t-scores (one-sample) Hypothesis testing with t-scores (two independent samples) Constructing brief, complete summary statements Interpreting excel output

  5. Type of goggles Failure depth (in meters) 86.625 100.0625 Two-tailed 0.05 180.92 113.53 147.22 147.22 yes -3.13 2.04 30 0.000385 yes The Abyss brand of goggle survived a deeper depth (100 meters) than the Trident brand (86 meters). A t-test showed this to be a significant difference t(30)=-3.13; p < 0.05 We would recommend The Abyss brand of goggle because it leaked less in deep water .

  6. Type of mall Rating from survey 15.65 13.7 Two-tailed 0.05 3.8 4.3 4.05 4.07 yes -3.06 2.02 38 0.004 yes The Springdale Mall scored higher overall (mean score = 15.65), while the Autumndale Mall scored lower (13.7). A t-test showed this to be a significant difference t(38)=-3.06; p < 0.05 Based on the findings of this questionnaire, we would conclude that the Springdale Mall is the superior property

  7. Homework review

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

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

  10. . Homework Is there a difference in mpg between these two cars There is no difference in mpg between these two cars There is a difference in mpg between these two cars 0.05 2-tail 18 2.101 (n1 – 1) s12 + (n2 – 1) s22 S2pooled = n1 + n2 - 2 = .82 (10 – 1) (.80)2 + (10 – 1) (1)2 17 – 18.5 -1.5 S2pooled = t = = .4049691 101+ 102- 2 .82/10 + .82/10 = -3.704

  11. . Homework Yes Yes Yes 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 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 0.05 2-tail 22

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

  13. . Homework Yes Yes Yes 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 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 0.05 2-tail 22 1.717

  14. . Homework = .6201 = .4502 = .2936 = 2.26 Yes Yes Yes (12 – 1) (.6201)2 + (12 – 1) (4502)2 8.208 – 7.708 0.5 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 S2pooled = t = = .2212 121+ 122- 2 .2936/12 + .2936/12

  15. . . A note on z scores, and t score: • Numerator is always distance between means • (how far away the distributions are) • Denominator is always measure of variability • (how wide or much overlap there is between distributions) Difference between means Difference between means Difference between means Variabilityof curve(s) Variabilityof curve(s) Variabilityof curve(s)

  16. Independent samples t-test Are the two means significantly different from each other, or is the difference just due to chance? 24 – 21 t = variability 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 Small meal 19 23 21 Big Meal 22 25 25 Mean= 21 Mean= 24 Got to figure this part out: We want to average from 2 samples - Call it “pooled” x1 – x2 t = variability

  17. . Hypothesis testing = 76.44 76.44 - 74 = = 2.03 1.20 Step 3: Calculations µ = 74 N = 25 s = 6.01 76.44 - 74 6.01 critical t critical t 25

  18. Hypothesis testing Step 4: Make decision whether or not to reject null hypothesis Observed t = 2.03 Critical t = 2.064 2.03 is not farther out on the curve than 2.064, so, we do not reject the null hypothesis Step 6: Conclusion: The extra time did not have a significant effect on the scores

  19. Hypothesis testing using Excel Step 1: Identify the research problem Did the size of the meal affect the learning / test scores? Step 2: Describe the null and alternative hypotheses Ho: The size of the meal has no effect on test scores H1: The size of the meal does have an effect on test scores Step 3: Decision rule α= .05 One tail or two tail test?

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

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

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

  23. Finding Means Finding Means

  24. 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

  25. Finding degrees of freedom

  26. This is “n” for each sample (Remember, “n” is just number of observations for each sample) This is “n” for each sample (Remember, “n” is just number of observations for each sample) 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 df = “degrees of freedom”

  27. Finding Observed t

  28. Finding Critical t

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

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

  31. In this case, p = 0.12 which is NOT less than 0.05, so we “do not reject the null” Remember, if the “p” is less than 0.05 then we “reject the null”, and conclude we have a significant effect

  32. 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. Type of test with degrees of freedom n.s. = “not significant” p<0.05 = “significant” Value of observed statistic Start summary with two means (based on DV) for two levels of the IV Finish with statistical summaryt(4) = 1.96; ns Describe type of test (t-test versus anova) with brief overview of results Or if it *were* significant: t(9) = 3.93; p < 0.05

  33. Hypothesis testing Step 4: Make decision whether or not to reject null hypothesis Observed t = 1.964 Critical t = 2.776 1.964 is not farther out on the curve than 2.776 so, we do not reject the null hypothesis t(4) = 1.964; n.s. Step 5: Conclusion: There appears to be no difference in test scores between the two groups

  34. How to report the findingsfor a t-test Mean of small meal was 21 Mean of big meal was 24 One paragraph summary of this study. Describe the IV & DV. Present the two means, which type of test was conducted, and the statistical results. Finish with statistical summaryt(4) = 1.96; ns Observed t = 1.964 Start summary with two means (based on DV) for two levels of the IV df = 4 Or if it *were* significant: t(9) = 3.93; p < 0.05 Describe type of test (t-test versus anova) with brief overview of results 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. n.s. = “not significant” p<0.05 = “significant” n.s. = “not significant” p<0.05 = “significant” Type of test with degrees of freedom Value of observed statistic

  35. Independent samples t-test Are the two means significantly different from each other, or is the difference just due to chance? 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 Small meal 19 23 21 Big Meal 22 25 25 Mean= 21 Mean= 24 Let’s use Excel to solve this problem! Section 1 knows Donald

  36. Independent samples t-test What if we ran more subjects? 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 Small meal 19 23 21 19 23 21 19 23 21 Big Meal 22 25 25 22 25 25 22 25 25 Mean= 21 Mean= 24

  37. Hypothesis testing Notice: Additional participants don’t affect this part of the problem Step 1: Identify the research problem Did the size of the meal affect the test scores? Step 2: Describe the null and alternative hypotheses Ho: The size of the meal has no effect on test scores H1: The size of the meal does have an effect on test scores One tail or two tail test?

  38. Hypothesis testing Step 3: Decision rule α= .05 n1 = 9; n2 = 9 Degrees of freedom total (df total) = (n1 - 1) + (n2 – 1) = (9 - 1) + (9 – 1) = 16 Degrees of freedom total (dftotal) = (n total - 2) = 18 – 2 = 16 two tailed test Notice: Two different ways to think about it Critical t(16) = 2.12

  39. two tail test α= .05 (df) = 16 Critical t(16) = 2.12

  40. Mean= 21 Mean= 24 Big Meal Deviation From mean 2 -1 -1 2 -1 -1 2 -1 -1 Small Meal Deviation From mean 2 -2 0 2 -2 0 2 -2 0 SquaredDeviation 4 4 0 4 4 0 4 4 0 Squared deviation 4 1 1 4 1 1 4 1 1 Big Meal 22 25 25 22 25 25 22 25 25 Small meal 19 23 21 19 23 21 19 23 21 Σ = 18 Σ = 24 = 1.50 18 Notice: s2 = 2.25 1 8 1 Notice: Simple Average = 2.625 = 1.732 24 Notice: s2 = 3.0 2 8 2

  41. Mean= 21 Mean= 24 Big Meal 22 25 25 22 25 25 22 25 25 Small meal 19 23 21 19 23 21 19 23 21 Sp = 2.625 S22 = 3.00 S21 = 2.25 S2 = 1.732 S1 = 1.5 (n1 – 1) s12 + (n2 – 1) s22 S2pooled = n1 + n2 - 2 (9 – 1) (1.50)2 + (9 – 1) (1.732)2 = 2.625 S2pooled = 9 + 9 - 2

  42. 24 – 21 = 0.7638 Mean= 21 Mean= 24 Big Meal 22 25 25 22 25 25 22 25 25 Small meal 19 23 21 19 23 21 19 23 21 Sp = 2.625 S2 = 1.732 S1 = 1.5 24 - 21 = 3.928 2.625 2.625 9 9

  43. Hypothesis testing Step 5: Make decision whether or not to reject null hypothesis Observed t = 3.928 Critical t = 2.120 3.928 is farther out on the curve than 2.120 so, we do reject the null hypothesis t(16) = 3.928; p < 0.05 Step 6: Conclusion: There appears to be a difference in hearing sensitivity between the two groups

  44. How to report the findingsfor a t-test Mean of small meal was 21 Mean of big meal was 24 One paragraph summary of this study. Describe the IV & DV. Present the two means, which type of test was conducted, and the statistical results. Start summary with two means (based on DV) for two levels of the IV Observed t = 3.928 Finish with statistical summaryt(9) = 3.93; p < 0.05 Describe type of test (z-test versus t-test) with brief overview of results df = 16 p < 0.05 n.s. = “not significant” p<0.05 = “significant” Type of test with degrees of freedom Value of observed statistic 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

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

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

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

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

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

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