1 / 61

MGMT 276: Statistical Inference in Management Spring , 2013

MGMT 276: Statistical Inference in Management Spring , 2013. Welcome. Hand in your homework. Statistical Inference in Management. Instructor: Suzanne Delaney, Ph.D. Office: 405 “N” McClelland Hall. Phone: 621-2045. Email: delaney@u.arizona.edu.

kirra
Télécharger la présentation

MGMT 276: Statistical Inference in Management Spring , 2013

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MGMT 276: Statistical Inference in ManagementSpring, 2013 Welcome Hand in yourhomework

  2. Statistical Inference in Management Instructor:Suzanne Delaney, Ph.D. Office:405 “N” McClelland Hall Phone:621-2045 Email:delaney@u.arizona.edu Office hours:2:00 – 3:30Mondays and Fridays and by appointment

  3. It went really well! Exam 3 – This past Tuesday Thanks for your patience and cooperation The grades should be posted by Thursday

  4. Homework due – Thursday (April 18th) Please print and complete homework worksheet #18 Hypothesis testing with ANOVA – Original Research Homework due – Tuesday (April 16th) Please print and complete homework worksheet #19 Hypothesis testing using correlations Please click in My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Please double check – All cell phones other electronic devices are turned off and stowed away

  5. Readings for next exam (Exam 4: April 25th) Lind Chapter 13: Linear Regression and Correlation Chapter 14: Multiple Regression Chapter 15: Chi-Square Plous Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions

  6. Exam 4 – Optional Times for Final • Two options for completing Exam 4 • Thursday (4/25/13) • Tuesday (4/30/13) • Must sign up to take Exam 4 on Tuesday (4/23) • Only need to take one exam – these are two optional times

  7. Use this as your study guide Over next couple of lectures 4/11/13 • Logic of hypothesis testing with Correlations • Interpreting the Correlations and scatterplots • Simple 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

  8. 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

  9. 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

  10. 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”

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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 Remember, Correlation = “r” r = .20

  21. 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

  22. 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

  23. 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

  24. 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 then critical r then reject null Step 5: Conclusion - tie findings back in to research problem

  25. Correlation - How do we calculate the exact r? Computational formula for correlation - abbreviated by r Pearson correlation coefficient (r): A number between -1.00 and =1.00 that describes the linear relationship between pairs of quantitative variables The formula:

  26. Correlation - How do we calculate the exact r? We want to know the relationship between math ability and spelling ability. We gave 5 people a 20-point math test and a 20-point spelling test. . . . Name Math(X) Spelling(Y) XY X2 Y2 KL 13 14 182 169 196 GC 9 18 162 81 324 JB 7 12 84 49 144 MD 5 10 50 25 100 RG 1 6 6 1 36 Σ 35 60 484 325 800

  27. Name Math(X) Spelling(Y) XY X2 Y2 KL 13 14 182 169 196 GC 9 18 162 81 324 JB 7 12 84 49 144 MD 5 10 50 25 100 RG 1 6 6 1 36 Σ 35 60 484 325 800 . First let’s draw a scatter plot

  28. Name Math(X) Spelling(Y) XY X2 Y2 KL 13 14 182 169 196 GC 9 18 162 81 324 JB 7 12 84 49 144 MD 5 10 50 25 100 RG 1 6 6 1 36 Σ 35 60 484 325 800 Correlation - Let’s do one Step 1: Find n n = 5 (5 pairs) Step 2: Find ΣX and ΣY Step 3: Find ΣXY Step 4: Find ΣX2 and ΣY2 Step 5: Plug in the numbers The formula:

  29. Name Math(X) Spelling(Y) XY X2 Y2 KL 13 14 182 169 196 GC 9 18 162 81 324 JB 7 12 84 49 144 MD 5 10 50 25 100 RG 1 6 6 1 36 Σ 35 60 484 325 800 r = r = r = (320) [√[(1625)-(1225)] [√[(4000)-(3600)] [√[(5)(325)-(35)2] [√[(5)(800)-(60)2] 320 = [√400] [√400] 400 Step 5: Plug in the numbers The formula: (5)(484)-(35)(60) (2420)-(2100) r = .80

  30. Make decision whether the correlation is different from zero α= 0.05 df = 3 Observed r(3) = 0.80 Critical r(3) = 0.878 Conclusion: r = 0.80 is not bigger than a r = .878 so not a significant r (not significantly different than zero – nothing going on) r(3) = 0.80; n.s.

  31. Observed r(3) = 0.80 r(3) = 0.80; n.s. Critical r(3) = 0.878 Conclusion: r = 0.80 is not bigger than a r = .878 so not a significant r (not significantly different than zero – nothing going on) These data suggest a strong positive correlation between math ability and spelling ability, however this correlation was not large enough to reach significance, r(3) = 0.80; n.s.

  32. What if we ran more subjects?

  33. Correlation - How do we calculate the exact r? Computational formula for correlation - abbreviated by r Pearson correlation coefficient (r): A number between -1.00 and =1.00 that describes the linear relationship between pairs of quantitative variables The formula:

  34. Correlation - How do we calculate the exact r? We want to know the relationship between math ability and spelling ability. We gave 50 people a 20-point math test and a 20-point spelling test. Name Math(X) Spelling(Y) XY X2 Y2 KL 13 14 182 169 196 GC 9 18 162 81 324 JB 7 12 84 49 144 : : :::: RG 1 6 6 1 36 Σ350600484032508000 The same data were copied 10 times to highlight power of larger samples What if we ran more subjects?

  35. Name Math(X) Spelling(Y) XY X2 Y2 KL 13 14 182 169 196 GC 9 18 162 81 324 JB 7 12 84 49 144 :: : : : : RG 1 6 6 1 36 Σ350600484032508000 Correlation - Let’s do one Step 1: Find n n = 50 (50 pairs) Step 2: Find ΣX and ΣY Step 3: Find ΣXY Step 4: Find ΣX2 and ΣY2 Step 5: Plug in the numbers The formula:

  36. Name Math(X) Spelling(Y) XY X2 Y2 KL 13 14 182 169 196 GC 9 18 162 81 324 JB 7 12 84 49 144 MD ::::: RG 1 6 6 1 36 Σ350600484032508000 r = [√[(50)(3250)-(350)2] [√[(50)(8000)-(600)2] 3200 r = 4000 Step 5: Plug in the numbers The formula: (50)(4840)-(350)(600) r = .80

  37. α= 0.05 df = 48 Observed r(48) = 0.80 Critical r(48)= 0.288 r(48) = 0.80; p < 0.05. What if we had run more participants??

  38. Conclusion: r = 0.80 is bigger than a r = .273 so there is a significant r (yes significantly different than zero – something going on) Observed r(48) = 0.80 Critical r(48)= 0.273 r(48) = 0.80; p < 0.05. These data suggest a strong positive correlation between math ability and spelling ability, and this correlation was large enough to reach significance, r(48) = 0.80; p < 0.05

  39. 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

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

  41. 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

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

  43. Five steps to hypothesis testing Step 3: Calculations

  44. Five steps to hypothesis testing Step 3: Calculations

  45. 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

  46. 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

  47. 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

  48. 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

  49. 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

More Related