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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 today7/3/14 Logic of hypothesis testing Steps for hypothesis testing Levels of significance (Levels of alpha) Logic of hypothesis testing with Correlations Interpreting the Correlations and scatterplots Simple and Multiple Regression

  5. Homework Overview Assignment 26- Due: Monday, July 7th ANOVA Project All five parts are due Monday 1. A one page report of your design which includes: Description of your experiment, IV, DV, number of participants, method for recruitment and between or within participant design (why?) 2. Gather the data- Try to get at least 10 people (or data points) per level 3. Input data into Excel (hand in data) 4. Complete a ANOVA using Excel 5. Statement of results and a graph of your means Assignment 27, 28, 29 - Due: Tuesday, July 8th Online Modules Correlation Simple regression Multiple regression

  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 Study guide is available on class website

  7. 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

  8. 2x2 ANOVA Low Exercise Weight HighExercise Low High Calorie Intake Effect of exercise and calorie intake on weight Main effect of calorie intake? Yes, lower calorie intake: lower weight Main effect of exercise? Yes, higher exercise: lower weight Interaction? No, the lines are parallel

  9. Low Exercise Weight HighExercise Low High Calorie Intake Main effect of Calorie Intake? – Comparing “High” to “Low” Average would be about here Main Effectof Calorie Intake: Is there a difference between “High Intake” and “Low Intake”? Low Exercise We have two “High Intake” means Weight High HighExercise Low High Calorie Intake Yes there is a difference in Weight Depending on calorie intake. There is a difference between High and Low levels of calorie intake Average would be about here We have two “Low Intake” means High Low

  10. Low Exercise Weight HighExercise Low High Low Exercise Calorie Intake Weight HighExercise Low High Calorie Intake Main effect of Exercise? – Comparing “High” to “Low” Average would be about here Main Effectof Exercise: Is there a difference between “High Exercise” and “Low Exercise”? We have two “High Exercise” means High Yes there is a difference in Weight depending on amount of exercise. There is a difference between High and Low levels of exercise intake Average would be about here We have two “Low Exercise” means HIGH Low

  11. 2x2 ANOVA Brunette Attractive Rating Blonde/Blond Men Women Gender Effect of gender and hair color on perceived attractiveness of opposite sex persons Main effect of gender? Yes, men tend to rate women higher than women rate men Main effect of hair color? Yes, brunettes rated higher than blondes/blonds Interaction? Yes, the lines are not parallel: Men are not affected by hair color as much as women are

  12. Let’s try one In a two-way ANOVA we have one dependent variable and two independent variables. This graph shows a. A main effect of exercise, but no main effect of caloriesb. A main effect of exercise, and a main effect of caloriesc. No main effect of exercise, and no main effect of caloriesd. No main effect of exercise, a main effect of calories High Exercise Low Exercise Weight Low High Calories

  13. Let’s try one In a two-way ANOVA we have one dependent variable and two independent variables. Which of the following graphs shows no interaction College B A a. Ab. Bc. Cd. D Male Elementary Cookies Sold Activity Female Spray None No Spray Hawaii Another Male Spray Incentives High Exercise D Low Exercise C Control Weight Amount ofActivity ADHD Low High No Yes Calories Adderall

  14. Let’s try one In a two-way ANOVA we have one dependent variable and two independent variables. This graph shows College a. A main effect of incentive, but no main effect of ageb. A main effect of incentive, and a main effect of age c. No main effect of incentive, and no main effect of age d. No main effect of incentive, a main effect of age CookiesSold Elementary None Hawaii Incentives

  15. Writing assignment 2-way ANOVA worksheet – Part 1 • Propose an example of an experiment that would consist of two independent variables (IV) and one dependent variable (DV). • The design should be appropriate for an analysis that uses a two-way ANOVA • What is your question / What is your prediction • What is your first IV • How many levels does it have – what are they • What is your second IV • How many levels does it have – what are they • What is your DV • Sketch a line graph of your predicted results

  16. Writing Assignment – Part 2 Factor BB1B2 DependentVariable A1 A2 Factor A Generate an example of three different hypothetical2 x 2 experiments: Independent Variable 1? Independent Variable 2? ? ? Dependent Variable? Main effect of A ? Main effect of B ? Interaction ?

  17. Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses For correlation null is that r = 0 (no relationship) Step 2: Decision rule • Alpha level? (α= .05 or .01)? • Critical statistic (e.g. critical r) value from table? • Degrees of Freedom = (n – 2) df = # pairs - 2 Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed r is bigger than critical r then reject null Step 5: Conclusion - tie findings back in to research problem

  18. Finding a statistically significant correlation • The result is “statistically significant” if: • the observed correlation is larger than the critical correlationwe want our r to be big if we want it to be significantly different from zero!! (either negative or positive but just far away from zero) • the p value is less than 0.05 (which is our alpha) • we want our “p” to be small!! • we reject the null hypothesis • then we have support for our alternative hypothesis

  19. Correlation Correlation: Measure of how two variables co-occur and also can be used for prediction • Range between -1 and +1 • The closer to zero the weaker the relationship and the worse the prediction • Positive or negative Remember, We’ll call the correlations “r”

  20. Correlation Range between -1 and +1 +1.00 perfect relationship = perfect predictor +0.80 strong relationship = good predictor +0.20 weak relationship = poor predictor 0 no relationship = very poor predictor -0.20 weak relationship = poor predictor -0.80 strong relationship = good predictor -1.00 perfect relationship = perfect predictor

  21. Remember, Correlation = “r” Positive correlation • Positive correlation: • as values on one variable go up, so do values for other variable • pairs of observations tend to occupy similar relative positions • higher scores on one variable tend to co-occur with higher scores on the second variable • lower scores on one variable tend to co-occur with lower scores on the second variable • scatterplot shows clusters of point • from lower left to upper right

  22. Remember, Correlation = “r” Negative correlation • Negative correlation: • as values on one variable go up, values for other variable go down • pairs of observations tend to occupy dissimilar relative positions • higher scores on one variable tend to co-occur with lower scores on • the second variable • lower scores on one variable tend to • co-occur with higher scores on the • second variable • scatterplot shows clusters of point • from upper left to lower right

  23. Zero correlation • as values on one variable go up, values for the other variable • go... anywhere • pairs of observations tend to occupy seemingly random • relative positions • scatterplot shows no apparent slope

  24. Correlation The more closely the dots approximate a straight line, the stronger the relationship is. • Perfect correlation = +1.00 or -1.00 • One variable perfectly predicts the other • No variability in the scatterplot • The dots approximate a straight line

  25. Time in house Number Correct Time outside Percent Correct Time in the house by time outside of house Perfect correlation = +1.00 or -1.00 One variable perfectly predicts the other Negative Correlation Percent correct on exam by number correct on exam Speed (mph) and time to finish race Height in inches and height in feet Negative correlation Positive correlation Positive correlation

  26. Correlation does not imply causation Is it possible that they are causally related? Yes, but the correlational analysis does not answer that question What if it’s a perfect correlation – isn’t that causal? No, it feels more compelling, but is neutral about causality Number of Birthdays Remember the birthday cakes! Number of Birthday Cakes

  27. Positive correlation: as values on one variable go up, so do values for other variable Negative correlation: as values on one variable go up, the values for other variable go down Number of bathrooms in a city and number of crimes committed Positive correlation Positive correlation

  28. Linear vs curvilinear relationship Linear relationship is a relationship that can be described best with a straight line Curvilinear relationship is a relationship that can be described best with a curved line

  29. This shows a strong positive relationship (r = 0.97) between the appraised price of the house and its eventual sales price r = +0.97 Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

  30. r = +0.97 r = -0.48 This shows a moderate negative relationship (r = -0.48) between the amount of pectin in orange juice and its sweetness Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

  31. Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) This shows a strong negative relationship (r = -0.91) between the distance that a golf ball is hit and the accuracy of the drive r = -0.91

  32. Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) This shows a moderate positive relationship (r = 0.61) between the length of stay in a hospital and the number of services provided r = 0.61 r = -0.91

  33. r = +0.97 r = -0.48 r = 0.61 r = -0.91

  34. Correlation - How do numerical values change? r = +0.97 r = -0.48 r = 0.61 r = -0.91

  35. Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) Variable name is listed clearly Both axes have real numbers listed Both axes and values are labeled This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). 48 52 5660 64 68 72 Height of Mothers (in) 48 52 56 60 64 68 72 76 Height of Daughters (inches)

  36. The more closely the dots approximate a straight line, the stronger the relationship is. Correlation • Perfect correlation = +1.00 or -1.00 • One variable perfectly predicts the other • No variability in the scatter plot • The dots approximate a straight line

  37. Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses For correlation null is that r = 0 (no relationship) Step 2: Decision rule • Alpha level? (α= .05 or .01)? • Critical statistic (e.g. critical r) value from table? • Degrees of Freedom = (n – 2) df = # pairs - 2 Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed r is bigger than critical r then reject null Step 5: Conclusion - tie findings back in to research problem

  38. Five steps to hypothesis testing Problem 1 • Is there a relationship between the: • Price • Square Feet • We measured 150 homes recently sold

  39. Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Is there a relationship between the cost of a home and the size of the home Describe the null and alternative hypotheses • null is that there is no relationship (r = 0.0) • alternative is that there is a relationship (r ≠ 0.0) Step 2: Decision rule – find critical r (from table) • Alpha level? (α= .05) • Degrees of Freedom = (n – 2) • 150 pairs – 2 = 148 pairs df = # pairs - 2

  40. Critical r value from table α= .05 df = 148 pairs Critical valuer(148) = 0.195 df = # pairs - 2

  41. Five steps to hypothesis testing Step 3: Calculations

  42. Five steps to hypothesis testing Step 3: Calculations

  43. Five steps to hypothesis testing Step 3: Calculations r = 0.726965 Critical valuer(148) = 0.195 Observed correlation r(148) = 0.726965 Step 4: Make decision whether or not to reject null hypothesis If observed r is bigger than critical r then reject null Yes we reject the null 0.727 > 0.195

  44. Conclusion: Yes we reject the null. The observed r is bigger than critical r (0.727 > 0.195) Yes, this is significantly different than zero – something going on These data suggest a strong positive correlation between home prices and home size. This correlation was large enough to reach significance, r(148) = 0.73; p < 0.05

  45. Finding a statistically significant correlation • The result is “statistically significant” if: • the observed correlation is larger than the critical correlationwe want our r to be big if we want it to be significantly different from zero!! (either negative or positive but just far away from zero) • the p value is less than 0.05 (which is our alpha) • we want our “p” to be small!! • we reject the null hypothesis • then we have support for our alternative hypothesis

  46. Education Age IQ Income 0.38* Education -0.02 0.52* Age 0.38* -0.02 0.27* IQ 0.52* Income 0.27* Correlation matrices Correlation matrix: Table showing correlations for all possible pairs of variables 1.0** 0.41* 0.65** 0.41* 1.0** 1.0** 0.65** 1.0** Remember, Correlation = “r” * p < 0.05 ** p < 0.01

  47. Education Age IQ Income Correlation matrices Correlation matrix: Table showing correlations for all possible pairs of variables Education Age IQ Income 0.41* 0.38* 0.65** -0.02 0.52* 0.27* * p < 0.05 ** p < 0.01

  48. Finding a statistically significant correlation • The result is “statistically significant” if: • the observed correlation is larger than the critical correlationwe want our r to be big if we want it to be significantly different from zero!! (either negative or positive but just far away from zero) • the p value is less than 0.05 (which is our alpha) • we want our “p” to be small!! • we reject the null hypothesis • then we have support for our alternative hypothesis

  49. Correlation matrices • Variable names • Make up any name that • means something to you • VARX = “Variable X” • VARY = “Variable Y” • VARZ = “Variable Z” Correlation of X with X Correlation of Y with Y Correlation of Z with Z

  50. Correlation matrices Does this correlation reach statistical significance? • Variable names • Make up any name that • means something to you • VARX = “Variable X” • VARY = “Variable Y” • VARZ = “Variable Z” Correlation of X with Y Correlation of X with Y p value for correlation of X with Y p value for correlation of X with Y

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