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MGMT 276: Statistical Inference in Management Summer Session I Harvill, Room 101 8:30 – 10:45 Monday - Thursday June 9 – July 10, 2014. Welcome. Green sheet. Please click in. My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z .

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  1. MGMT 276: Statistical Inference in ManagementSummer Session IHarvill, Room 1018:30 – 10:45 Monday - ThursdayJune 9 – July 10, 2014 Welcome Green sheet

  2. Please click in My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

  3. Please start portfolios

  4. Use this as your study guide By the end of lecture today7/2/14 • Logic of hypothesis testing • Steps for hypothesis testing • Levels of significance (Levels of alpha) • Hypothesis testing with Analysis of Variance (ANOVA) • Constructing brief, complete summary statements • Simple vs 2-way ANOVA

  5. Homework due – Thursday July 3rd Assignment 24 & 25- Due: Thursday, July 3rd Hypothesis Testing using t-tests and ANOVA Complete the online modules 14 & 15

  6. Please read before our next exam (July 9th) - Chapters 11 - 15 in Lind book - Chapters 2, 3, 4, 17 and 18 in Plous book: Lind 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 Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions

  7. Homework review

  8. . Homework 22 – same problem using excel Year of Birth Shoe Size 8.2 7.7 1-tail 0.05 2.26 1.7170 22 .017014309 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

  9. . Homework

  10. . Homework Type of instruction Exam score 50 40 2-tail 0.05 CAUTION This is significant with alpha of 0.05 BUT NOT WITH alpha of 0.01 2.66 2.02 38 p = 0.0113 yes 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

  11. . Homework Type of Staff Travel Expenses 142.5 130.29 2-tail 0.05 1.53679 2.2 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.

  12. . Homework Location of lot Number of cars 86.24 92.04 2-tail 0.05 -0.88 2.01 51 p = 0.38 no Fun fact: If the observed t is less than one it will never be significant 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.

  13. . Please hand in your homework – they must be stapled

  14. 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

  15. Sum of squares (SS): The sum of squared deviations around their mean Mean squares (MS): The sum of squares 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 MSBetween F = Mean square within groups: sum of squares within groups divided by its degrees of freedom MSWithin

  16. 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)

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

  18. 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

  19. 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 .

  20. 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 .

  21. 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. We should: a. reject the null hypothesis b. not reject the null hypothesis Observed F bigger than Critical F p < .05

  22. 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. The most expensive neighborhood was the ____ neighborhood a. Southpark b. Northpark c. Westpark d. Eastpark

  23. 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

  24. Let’s try one 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

  25. 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

  26. Let’s try one 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

  27. 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

  28. 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 Let’s try one

  29. 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

  30. 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.

  31. 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 nullb. 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

  32. 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 19c. n – 2; in this case 8d. n – 2; in this case 18

  33. 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 hypothesisb. Do not reject the null hypothesisc. There is not enough information

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

  35. Relationship between advertising space and sales 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

  36. 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 raceb. The IV is time to finish a race while the DV is gender

  37. 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 < 0.05b. t(198) = 2.38; nsc. t(198) = 1.97; p < 0.05d. t(198) = 1.97; ns

  38. 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 < 0.01b. t(198) = 2.38; nsc. t(198) = 1.97; p < 0.01d. t(198) = 1.97; ns

  39. 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

  40. 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

  41. 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

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

  43. The observed F is 2 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

  44. 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. 2 c. 30 d. 40

  45. Homework 26 - ANOVA Project - There are five parts • 1. A one page report of your design (includes all of the information from the writing assignment) • Describe your experiment: what is your question / what is your prediction? • State your Independent Variable (IV), how many levels there are, and the operational definition • State your Dependent Variable (DV), and operational definition • How many participants did you measure, and how did you recruit (sample) them • Was this a between or within participant design (why?) • 2. Gather the data • Try to get at least 10 people (or data points) per level • If you are working with other students in the class you should have 10 data points per level for each member of your group • 3. Input data into Excel (hand in data) • 4. Complete ANOVA analysis hand in ANOVA table • 5. Statement of results (see next slide for example) and include • a graph of your means (just like we did in the homework)

  46. Writing assignment worksheet • Propose an experiment that would consist of one independent • variable (IV) and one dependent variable (DV). The IV should • have three groups (or more). The design should be appropriate • for an analysis that uses an ANOVA • What is your question / What is your prediction • What is your IV • How many levels does it have • What are the levels • What is your DV • How many subjects do you think you can gather data on? • Sketch a bar graph of your predicted results

  47. Two-way analysis of varianceVariance is divided further College Number of cookies sold Elementary Remember, two-way = two IV None Bike Hawaii trip Total variability Between group variability Within group variability Remember, factor = independent variable Remember, within group variability = error variability= random error Factor A Variability Factor B Variability Interaction Variability

  48. What if we add an independent variable?Does “age” make a difference? Does the age and the type of incentive interact? College Number of cookies sold Number of cookies sold Elementary Two-way gives info “Main effects” &“Interactions” Two-way gives info on “interactions” None Bike Hawaii trip One-way ANOVA gives info on“Main effects” One-way ANOVA gives info on“Main effects” None Bike Hawaii trip Incentives Incentives Hawaii trip No incentive Number of cookies sold Number of cookies sold Bike Elementary College Elementary College Age Age We have two main effects and an interaction

  49. Main effects and interactions Do age and the type of incentive interact? We have two main effects and an interaction Does incentive have an effect? College Number of cookies sold Number of cookies sold Elementary None Bike Hawaii trip None Bike Hawaii trip Incentives Incentives Hawaii trip No incentive Number of cookies sold Number of cookies sold Bike Elementary College Elementary College Age Does agehave an effect? Age Rule for interactions: No interaction: If lines are parallel Yes interaction: If lines are (in any way) NOT parallel

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