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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. Where are we? • We are right on schedule… • Three more days of class before our final exam • Thursday (8/2/12) Correlation and Regression • Monday (8/6/12) Multiple Regression • Tuesday (8/7/12) Chi Square and Review for Exam 4 • Wednesday (8/8/12): Final Exam • Homework Assignments have been posted • Study Guide for the Final Exam has been posted

  5. Use this as your study guide By the end of lecture today8/2/12 Hypothesis testing with analysis of variance (ANOVA) Interpreting excel output of hypothesis tests Constructing brief, complete summary statements Logic of hypothesis testing with Correlations Interpreting the Correlations and scatterplots Simple and Multiple Regression Using correlation for predictions Regression uses the predictor variable (independent) to make predictions about the predicted variable (dependent)Coefficient of correlation is name for “r”Coefficient of determination is name for “r2”(remember it is always positive – no direction info)Standard error of the estimate is our measure of the variability of the dots around the regression line(average deviation of each data point from the regression line – like standard deviation) Coefficient of regression will “b” for each variable (like slope)

  6. Homework

  7. Homework

  8. Homework

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

  10. 0.3937 0.1119 If observed F is bigger than critical F:Reject null & Significant! If observed F is bigger than critical F:Reject null & Significant! 0.3937 / 0.1119 = 3.517 Homework 3.517 3.009 If p value is less than 0.05:Reject null & Significant! 3 24 0.03 4-1=3 # groups - 1 # scores - number of groups 28 - 4=24 # scores - 1 28 - 1=27

  11. Yes Homework = 3.517; p < 0.05 F (3, 24) 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).

  12. Average for each group(We REALLY care about this one) Number of observations in each group Just add up all scores (we don’t really care about this one)

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

  14. SS between df between SS within df within MS between MS within

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

  16. 11.46 2 If observed F is bigger than critical F:Reject null & Significant! If observed F is bigger than critical F:Reject null & Significant! 11.46 / 2 = 5.733 5.733 3.88 If p value is less than 0.05:Reject null & Significant! 2 12 0.0179

  17. Yes p < 0.05 F (2, 12) = 5.73; 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).

  18. Average for each group(We REALLY care about this one) Number of observations in each group Just add up all scores (we don’t really care about this one)

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

  20. SS between df between SS within df within MS between MS within

  21. Scatterplot displays relationships between two continuous variables 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

  22. 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

  23. Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Height of Mothers by Height of Daughters Height ofMothers Positive Correlation Height of Daughters

  24. Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Brushing teeth by number cavities BrushingTeeth Negative Correlation NumberCavities

  25. Perfect correlation = +1.00 or -1.00 One variable perfectly predicts the other Height in inches and height in feet Speed (mph) and time to finish race Positive correlation Negative correlation

  26. Correlation The more closely the dots approximate a straight line,(the less spread out they are) 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

  27. Correlation

  28. 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 Number of Birthday Cakes

  29. 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

  30. 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

  31. Correlation - How do numerical values change? http://neyman.stat.uiuc.edu/~stat100/cuwu/Games.html http://argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm Let’s estimate the correlation coefficient for each of the following r = +.80 r = +1.0 r = -1.0 r = -.50 r = 0.0

  32. This shows the strong positive (.8) relationship between the heights of daughters (measured in inches) with heights of their mothers (measured in inches). 48 52 5660 64 68 72 Both axes and values are labeled Both axes and values are labeled Both variables are listed, as are direction and strength Height of Mothers (in) 48 52 56 60 64 68 72 76 Height of Daughters (inches)

  33. Break into groups of 2 or 3 Each person hand in own worksheet. Be sure to list your name and names of all others in your group Use examples that are different from those is lecture 1. Describe one positive correlation Draw a scatterplot (label axes) 2. Describe one negative correlation Draw a scatterplot (label axes) 3. Describe one zero correlation Draw a scatterplot (label axes) 4. Describe one perfect correlation (positive or negative) Draw a scatterplot (label axes) 5. Describe curvilinear relationship Draw a scatterplot (label axes)

  34. Both variables are listed, as are direction and strength Both axes and values are labeled Both axes and values are labeled This shows the strong positive (.8) relationship between the heights of daughters (measured in inches) with heights of their mothers (measured in inches). 48 52 5660 64 68 72 1. Describe one positive correlation Draw a scatterplot (label axes) Height of Mothers (in) 2. Describe one negative correlation Draw a scatterplot (label axes) 48 52 56 60 64 68 72 76 Height of Daughters (inches) 3. Describe one zero correlation Draw a scatterplot (label axes) 4. Describe one perfect correlation (positive or negative) Draw a scatterplot (label axes) 5. Describe curvilinear relationship Draw a scatterplot (label axes)

  35. 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? Step 3: Calculations MSBetween F = MSWithin Step 4: Make decision whether or not to reject null hypothesis If observed r is bigger then critical r then reject null Step 5: Conclusion - tie findings back in to research problem

  36. 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

  37. Correlation Correlation: Measure of how two variables co-occur and also can be used for prediction • Range between -1 and +1

  38. Correlation • The closer to zero the weaker the relationship and the worse the prediction • Positive or negative

  39. 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

  40. 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

  41. 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

  42. http://www.ruf.rice.edu/~lane/stat_sim/reg_by_eye/index.html http://argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm Let’s estimate the correlation coefficient for each of the following r = +.98 r = .20

  43. http://www.ruf.rice.edu/~lane/stat_sim/reg_by_eye/index.html http://argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm Let’s estimate the correlation coefficient for each of the following r = +. 83 r = -. 63

  44. http://www.ruf.rice.edu/~lane/stat_sim/reg_by_eye/index.html http://argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm Let’s estimate the correlation coefficient for each of the following r = +. 04 r = -. 43

  45. 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

  46. These three have same scatter (none) But different slopes These three have same slope These three have same slope http://www.ruf.rice.edu/~lane/stat_sim/reg_by_eye/index.html http://argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm Let’s review the values of the correlation coefficient for each of the following Top Row: Variability differs (aka scatter or noise) These three have same slope These three have same slope But different scatter These three have same slope Middle Row: Slope differs Bottom Row: Non-linear relationships

  47. 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** * p < 0.05 ** p < 0.01

  48. 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

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