---------------------------------------------------------------------------------------------------- log: C:\MyDocs\STATISTICS\OBrien84Multivariate\ado\auto.log log type: text opened on: 10 Apr 2008, 11:57:19 . * auto.log . * . * Demonstrate the umbrella program for performing O'Brien's Umbrella test. . * See O'Brien PC. Biometrics 1984;40:1079-1087. . * . sysuse auto (1978 Automobile Data) . by foreign: summarize mpg weight length ---------------------------------------------------------------------------------------------------- -> foreign = Domestic Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 52 19.82692 4.743297 12 34 weight | 52 3317.115 695.3637 1800 4840 length | 52 196.1346 20.04605 147 233 ------------------------------------------------------------------------------------------------- -> foreign = Foreign Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 22 24.77273 6.611187 14 41 weight | 22 2315.909 433.0035 1760 3420 length | 22 168.5455 13.68255 142 193 . umbrella mpg weight length, by(foreign) highlow(L H H) Number of response variables: 3 Variable | Outcome -------------+----------------------------------------------------- mpg | lower values are better weight | higher values are better length | higher values are better ------------------------------------------------------------------------------------------------- -> foreign = Domestic Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 52 19.82692 4.743297 12 34 weight | 52 3317.115 695.3637 1800 4840 length | 52 196.1346 20.04605 147 233 ------------------------------------------------------------------------------------------------- -> foreign = Foreign Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 22 24.77273 6.611187 14 41 weight | 22 2315.909 433.0035 1760 3420 length | 22 168.5455 13.68255 142 193 Missing observations dropped from analysis = 0 O'Brien's Umbrella test is the following Kruskal-Wallis test on the sum of the ranks across the dependent variables. Kruskal-Wallis equality-of-populations rank test +---------------------------+ | foreign | Obs | Rank Sum | |----------+-----+----------| | Domestic | 52 | 2336.00 | | Foreign | 22 | 439.00 | +---------------------------+ chi-squared = 20.839 with 1 d.f. probability = 0.0001 chi-squared with ties = 20.841 with 1 d.f. probability = 0.0001 . umbrella mpg weight length, by(foreign) highlow(L H H) ranktable id(make) Number of response variables: 3 Variable | Outcome -------------+----------------------------------------------------- mpg | lower values are better weight | higher values are better length | higher values are better ------------------------------------------------------------------------------------------------- -> foreign = Domestic Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 52 19.82692 4.743297 12 34 weight | 52 3317.115 695.3637 1800 4840 length | 52 196.1346 20.04605 147 233 ------------------------------------------------------------------------------------------------- -> foreign = Foreign Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 22 24.77273 6.611187 14 41 weight | 22 2315.909 433.0035 1760 3420 length | 22 168.5455 13.68255 142 193 List of ranks ------------------------------------------------------------------------------------------------- -> foreign = Domestic +----------------------------------------------------------------+ | make r_mpg r_weight r_length sum_of_ranks | |----------------------------------------------------------------| 1. | Plym. Champ 4 2.5 8 14.5 | 2. | Ford Fiesta 10 2.5 2 14.5 | 3. | Dodge Colt 6.5 13 10.5 30 | 4. | Chev. Chevette 8 12 10.5 30.5 | 5. | Plym. Horizon 17 16.5 14 47.5 | |----------------------------------------------------------------| 6. | Buick Opel 13 18 19.5 50.5 | 7. | Plym. Sapporo 13 23 33 69 | 8. | AMC Spirit 29 25 16 70 | 9. | Merc. Bobcat 29 24 17 70 | 10. | Plym. Arrow 10 42 19.5 71.5 | |----------------------------------------------------------------| 11. | Pont. Sunbird 21.5 29 30 80.5 | 12. | Chev. Monza 21.5 31.5 30 83 | 13. | Olds Starfire 21.5 30 32 83.5 | 14. | Ford Mustang 34 26.5 30 90.5 | 15. | AMC Concord 29 35 35 99 | |----------------------------------------------------------------| 16. | Chev. Malibu 29 37 38.5 104.5 | 17. | Merc. Zephyr 38 33.5 40 111.5 | 18. | Chev. Monte Carlo 29 40 49.5 118.5 | 19. | Buick Century 38 41 41 120 | 20. | Pont. Le Mans 43.5 38 47 128.5 | |----------------------------------------------------------------| 21. | AMC Pacer 58.5 47 24 129.5 | 22. | Buick Regal 38 43 49.5 130.5 | 23. | Olds Cutlass 43.5 44 44.5 132 | 24. | Olds Cutl Supr 43.5 45 44.5 133 | 25. | Pont. Grand Prix 43.5 39 53 135.5 | |----------------------------------------------------------------| 26. | Chev. Nova 43.5 53 42 138.5 | 27. | Olds Omega 43.5 48.5 49.5 141.5 | 28. | Buick Skylark 43.5 50 49.5 143 | 29. | Merc. Monarch 52 48.5 44.5 145 | 30. | Pont. Phoenix 43.5 51.5 55 150 | |----------------------------------------------------------------| 31. | Pont. Firebird 52 54 44.5 150.5 | 32. | Plym. Volare 52 46 53 151 | 33. | Cad. Seville 34 71 56.5 161.5 | 34. | Dodge Diplomat 52 55.5 59 166.5 | 35. | Olds 98 34 67.5 68.5 170 | |----------------------------------------------------------------| 36. | Buick LeSabre 52 57 66.5 175.5 | 37. | Pont. Catalina 52 60 64 176 | 38. | Dodge Magnum 62.5 55.5 59 177 | 39. | Olds Delta 88 52 58.5 66.5 177 | 40. | Chev. Impala 62.5 58.5 62.5 183.5 | |----------------------------------------------------------------| 41. | Linc. Versailles 69.5 63 53 185.5 | 42. | Olds Toronado 62.5 66 59 187.5 | 43. | Buick Riviera 62.5 64 61 187.5 | 44. | Dodge St. Regis 58.5 62 68.5 189 | 45. | Merc. Marquis 65.5 61 62.5 189 | |----------------------------------------------------------------| 46. | Cad. Eldorado 69.5 65 56.5 191 | 47. | Merc. XR-7 69.5 70 65 204.5 | 48. | Buick Electra 65.5 69 72 206.5 | 49. | Merc. Cougar 69.5 67.5 70.5 207.5 | 50. | Cad. Deville 69.5 72 70.5 212 | |----------------------------------------------------------------| 51. | Linc. Mark V 73.5 73 73 219.5 | 52. | Linc. Continental 73.5 74 74 221.5 | +----------------------------------------------------------------+ ------------------------------------------------------------------------------------------------- -> foreign = Foreign +-------------------------------------------------------------+ | make r_mpg r_weight r_length sum_of_ranks | |-------------------------------------------------------------| 1. | Honda Civic 10 1 3 14 | 2. | VW Diesel 1 9 5.5 15.5 | 3. | Mazda GLC 6.5 6 4 16.5 | 4. | Renault Le Car 13 4 1 18 | 5. | Datsun 210 2.5 8 14 24.5 | |-------------------------------------------------------------| 6. | Subaru 2.5 10 12 24.5 | 7. | VW Rabbit 17 5 5.5 27.5 | 8. | VW Scirocco 17 7 7 31 | 9. | Toyota Corolla 5 16.5 14 35.5 | 10. | Fiat Strada 34 14 9 57 | |-------------------------------------------------------------| 11. | Honda Accord 17 19 22.5 58.5 | 12. | Datsun 510 21.5 20 19.5 61 | 13. | Audi Fox 25 11 25.5 61.5 | 14. | VW Dasher 25 15 22.5 62.5 | 15. | Datsun 200 25 21 19.5 65.5 | |-------------------------------------------------------------| 16. | BMW 320i 17 26.5 28 71.5 | 17. | Toyota Celica 52 22 25.5 99.5 | 18. | Datsun 810 34 31.5 34 99.5 | 19. | Toyota Corona 52 28 27 107 | 20. | Audi 5000 58.5 33.5 36 128 | |-------------------------------------------------------------| 21. | Volvo 260 58.5 36 38.5 133 | 22. | Peugeot 604 69.5 51.5 37 158 | +-------------------------------------------------------------+ Missing observations dropped from analysis = 0 O'Brien's Umbrella test is the following Kruskal-Wallis test on the sum of the ranks across the dependent variables. Kruskal-Wallis equality-of-populations rank test +---------------------------+ | foreign | Obs | Rank Sum | |----------+-----+----------| | Domestic | 52 | 2336.00 | | Foreign | 22 | 439.00 | +---------------------------+ chi-squared = 20.839 with 1 d.f. probability = 0.0001 chi-squared with ties = 20.841 with 1 d.f. probability = 0.0001 . umbrella mpg weight length, by(foreign) highlow(H L L) ranktable id(make) Number of response variables: 3 Variable | Outcome -------------+----------------------------------------------------- mpg | higher values are better weight | lower values are better length | lower values are better ------------------------------------------------------------------------------------------------- -> foreign = Domestic Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 52 19.82692 4.743297 12 34 weight | 52 3317.115 695.3637 1800 4840 length | 52 196.1346 20.04605 147 233 ------------------------------------------------------------------------------------------------- -> foreign = Foreign Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 22 24.77273 6.611187 14 41 weight | 22 2315.909 433.0035 1760 3420 length | 22 168.5455 13.68255 142 193 List of ranks ------------------------------------------------------------------------------------------------- -> foreign = Domestic +----------------------------------------------------------------+ | make r_mpg r_weight r_length sum_of_ranks | |----------------------------------------------------------------| 1. | Linc. Continental 1.5 1 1 3.5 | 2. | Linc. Mark V 1.5 2 2 5.5 | 3. | Cad. Deville 5.5 3 4.5 13 | 4. | Merc. Cougar 5.5 7.5 4.5 17.5 | 5. | Buick Electra 9.5 6 3 18.5 | |----------------------------------------------------------------| 6. | Merc. XR-7 5.5 5 10 20.5 | 7. | Cad. Eldorado 5.5 10 18.5 34 | 8. | Merc. Marquis 9.5 14 12.5 36 | 9. | Dodge St. Regis 16.5 13 6.5 36 | 10. | Buick Riviera 12.5 11 14 37.5 | |----------------------------------------------------------------| 11. | Olds Toronado 12.5 9 16 37.5 | 12. | Linc. Versailles 5.5 12 22 39.5 | 13. | Chev. Impala 12.5 16.5 12.5 41.5 | 14. | Olds Delta 88 23 16.5 8.5 48 | 15. | Dodge Magnum 12.5 19.5 16 48 | |----------------------------------------------------------------| 16. | Pont. Catalina 23 15 11 49 | 17. | Buick LeSabre 23 18 8.5 49.5 | 18. | Olds 98 41 7.5 6.5 55 | 19. | Dodge Diplomat 23 19.5 16 58.5 | 20. | Cad. Seville 41 4 18.5 63.5 | |----------------------------------------------------------------| 21. | Plym. Volare 23 29 22 74 | 22. | Pont. Firebird 23 21 30.5 74.5 | 23. | Pont. Phoenix 31.5 23.5 20 75 | 24. | Merc. Monarch 23 26.5 30.5 80 | 25. | Buick Skylark 31.5 25 25.5 82 | |----------------------------------------------------------------| 26. | Olds Omega 31.5 26.5 25.5 83.5 | 27. | Chev. Nova 31.5 22 33 86.5 | 28. | Pont. Grand Prix 31.5 36 22 89.5 | 29. | Olds Cutl Supr 31.5 30 30.5 92 | 30. | Olds Cutlass 31.5 31 30.5 93 | |----------------------------------------------------------------| 31. | Buick Regal 37 32 25.5 94.5 | 32. | AMC Pacer 16.5 28 51 95.5 | 33. | Pont. Le Mans 31.5 37 28 96.5 | 34. | Buick Century 37 34 34 105 | 35. | Chev. Monte Carlo 46 35 25.5 106.5 | |----------------------------------------------------------------| 36. | Merc. Zephyr 37 41.5 35 113.5 | 37. | Chev. Malibu 46 38 36.5 120.5 | 38. | AMC Concord 46 40 40 126 | 39. | Ford Mustang 41 48.5 45 134.5 | 40. | Olds Starfire 53.5 45 43 141.5 | |----------------------------------------------------------------| 41. | Chev. Monza 53.5 43.5 45 142 | 42. | Pont. Sunbird 53.5 46 45 144.5 | 43. | Plym. Arrow 65 33 55.5 153.5 | 44. | AMC Spirit 46 50 59 155 | 45. | Merc. Bobcat 46 51 58 155 | |----------------------------------------------------------------| 46. | Plym. Sapporo 62 52 42 156 | 47. | Buick Opel 62 57 55.5 174.5 | 48. | Plym. Horizon 58 58.5 61 177.5 | 49. | Chev. Chevette 67 63 64.5 194.5 | 50. | Dodge Colt 68.5 62 64.5 195 | |----------------------------------------------------------------| 51. | Ford Fiesta 65 72.5 73 210.5 | 52. | Plym. Champ 71 72.5 67 210.5 | +----------------------------------------------------------------+ ------------------------------------------------------------------------------------------------- -> foreign = Foreign +-------------------------------------------------------------+ | make r_mpg r_weight r_length sum_of_ranks | |-------------------------------------------------------------| 1. | Peugeot 604 5.5 23.5 38 67 | 2. | Volvo 260 16.5 39 36.5 92 | 3. | Audi 5000 16.5 41.5 39 97 | 4. | Toyota Corona 23 47 48 118 | 5. | Toyota Celica 23 53 49.5 125.5 | |-------------------------------------------------------------| 6. | Datsun 810 41 43.5 41 125.5 | 7. | BMW 320i 58 48.5 47 153.5 | 8. | Datsun 200 50 54 55.5 159.5 | 9. | VW Dasher 50 60 52.5 162.5 | 10. | Audi Fox 50 64 49.5 163.5 | |-------------------------------------------------------------| 11. | Datsun 510 53.5 55 55.5 164 | 12. | Honda Accord 58 56 52.5 166.5 | 13. | Fiat Strada 41 61 66 168 | 14. | Toyota Corolla 70 58.5 61 189.5 | 15. | VW Scirocco 58 68 68 194 | |-------------------------------------------------------------| 16. | VW Rabbit 58 70 69.5 197.5 | 17. | Subaru 72.5 65 63 200.5 | 18. | Datsun 210 72.5 67 61 200.5 | 19. | Renault Le Car 62 71 74 207 | 20. | Mazda GLC 68.5 69 71 208.5 | |-------------------------------------------------------------| 21. | VW Diesel 74 66 69.5 209.5 | 22. | Honda Civic 65 74 72 211 | +-------------------------------------------------------------+ Missing observations dropped from analysis = 0 O'Brien's Umbrella test is the following Kruskal-Wallis test on the sum of the ranks across the dependent variables. Kruskal-Wallis equality-of-populations rank test +---------------------------+ | foreign | Obs | Rank Sum | |----------+-----+----------| | Domestic | 52 | 1564.00 | | Foreign | 22 | 1211.00 | +---------------------------+ chi-squared = 20.839 with 1 d.f. probability = 0.0001 chi-squared with ties = 20.841 with 1 d.f. probability = 0.0001 . umbrella mpg weight length, by(foreign) highlow(H H H) ranktable id(make) Number of response variables: 3 Variable | Outcome -------------+----------------------------------------------------- mpg | higher values are better weight | higher values are better length | higher values are better ------------------------------------------------------------------------------------------------- -> foreign = Domestic Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 52 19.82692 4.743297 12 34 weight | 52 3317.115 695.3637 1800 4840 length | 52 196.1346 20.04605 147 233 ------------------------------------------------------------------------------------------------- -> foreign = Foreign Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 22 24.77273 6.611187 14 41 weight | 22 2315.909 433.0035 1760 3420 length | 22 168.5455 13.68255 142 193 List of ranks ------------------------------------------------------------------------------------------------- -> foreign = Domestic +----------------------------------------------------------------+ | make r_mpg r_weight r_length sum_of_ranks | |----------------------------------------------------------------| 1. | Ford Fiesta 65 2.5 2 69.5 | 2. | Plym. Champ 71 2.5 8 81.5 | 3. | Merc. Bobcat 46 24 17 87 | 4. | AMC Spirit 46 25 16 87 | 5. | AMC Pacer 16.5 47 24 87.5 | |----------------------------------------------------------------| 6. | Plym. Horizon 58 16.5 14 88.5 | 7. | Chev. Chevette 67 12 10.5 89.5 | 8. | Dodge Colt 68.5 13 10.5 92 | 9. | Ford Mustang 41 26.5 30 97.5 | 10. | Buick Opel 62 18 19.5 99.5 | |----------------------------------------------------------------| 11. | Merc. Zephyr 37 33.5 40 110.5 | 12. | Pont. Sunbird 53.5 29 30 112.5 | 13. | Chev. Monza 53.5 31.5 30 115 | 14. | Olds Starfire 53.5 30 32 115.5 | 15. | Merc. Monarch 23 48.5 44.5 116 | |----------------------------------------------------------------| 16. | AMC Concord 46 35 35 116 | 17. | Pont. Le Mans 31.5 38 47 116.5 | 18. | Plym. Sapporo 62 23 33 118 | 19. | Buick Century 37 41 41 119 | 20. | Olds Cutlass 31.5 44 44.5 120 | |----------------------------------------------------------------| 21. | Olds Cutl Supr 31.5 45 44.5 121 | 22. | Pont. Firebird 23 54 44.5 121.5 | 23. | Chev. Malibu 46 37 38.5 121.5 | 24. | Linc. Versailles 5.5 63 53 121.5 | 25. | Plym. Volare 23 46 53 122 | |----------------------------------------------------------------| 26. | Pont. Grand Prix 31.5 39 53 123.5 | 27. | Chev. Nova 31.5 53 42 126.5 | 28. | Plym. Arrow 65 42 19.5 126.5 | 29. | Cad. Eldorado 5.5 65 56.5 127 | 30. | Dodge Magnum 12.5 55.5 59 127 | |----------------------------------------------------------------| 31. | Buick Regal 37 43 49.5 129.5 | 32. | Olds Omega 31.5 48.5 49.5 129.5 | 33. | Buick Skylark 31.5 50 49.5 131 | 34. | Merc. Marquis 9.5 61 62.5 133 | 35. | Chev. Impala 12.5 58.5 62.5 133.5 | |----------------------------------------------------------------| 36. | Chev. Monte Carlo 46 40 49.5 135.5 | 37. | Dodge Diplomat 23 55.5 59 137.5 | 38. | Buick Riviera 12.5 64 61 137.5 | 39. | Olds Toronado 12.5 66 59 137.5 | 40. | Pont. Phoenix 31.5 51.5 55 138 | |----------------------------------------------------------------| 41. | Merc. XR-7 5.5 70 65 140.5 | 42. | Merc. Cougar 5.5 67.5 70.5 143.5 | 43. | Buick LeSabre 23 57 66.5 146.5 | 44. | Pont. Catalina 23 60 64 147 | 45. | Dodge St. Regis 16.5 62 68.5 147 | |----------------------------------------------------------------| 46. | Linc. Mark V 1.5 73 73 147.5 | 47. | Olds Delta 88 23 58.5 66.5 148 | 48. | Cad. Deville 5.5 72 70.5 148 | 49. | Linc. Continental 1.5 74 74 149.5 | 50. | Buick Electra 9.5 69 72 150.5 | |----------------------------------------------------------------| 51. | Cad. Seville 41 71 56.5 168.5 | 52. | Olds 98 41 67.5 68.5 177 | +----------------------------------------------------------------+ ------------------------------------------------------------------------------------------------- -> foreign = Foreign +-------------------------------------------------------------+ | make r_mpg r_weight r_length sum_of_ranks | |-------------------------------------------------------------| 1. | Fiat Strada 41 14 9 64 | 2. | Renault Le Car 62 4 1 67 | 3. | VW Rabbit 58 5 5.5 68.5 | 4. | Honda Civic 65 1 3 69 | 5. | Toyota Celica 23 22 25.5 70.5 | |-------------------------------------------------------------| 6. | VW Scirocco 58 7 7 72 | 7. | Toyota Corona 23 28 27 78 | 8. | Mazda GLC 68.5 6 4 78.5 | 9. | Audi 5000 16.5 33.5 36 86 | 10. | Audi Fox 50 11 25.5 86.5 | |-------------------------------------------------------------| 11. | VW Dasher 50 15 22.5 87.5 | 12. | VW Diesel 74 9 5.5 88.5 | 13. | Datsun 200 50 21 19.5 90.5 | 14. | Volvo 260 16.5 36 38.5 91 | 15. | Datsun 510 53.5 20 19.5 93 | |-------------------------------------------------------------| 16. | Peugeot 604 5.5 51.5 37 94 | 17. | Datsun 210 72.5 8 14 94.5 | 18. | Subaru 72.5 10 12 94.5 | 19. | Honda Accord 58 19 22.5 99.5 | 20. | Toyota Corolla 70 16.5 14 100.5 | |-------------------------------------------------------------| 21. | Datsun 810 41 31.5 34 106.5 | 22. | BMW 320i 58 26.5 28 112.5 | +-------------------------------------------------------------+ Missing observations dropped from analysis = 0 O'Brien's Umbrella test is the following Kruskal-Wallis test on the sum of the ranks across the dependent variables. Kruskal-Wallis equality-of-populations rank test +---------------------------+ | foreign | Obs | Rank Sum | |----------+-----+----------| | Domestic | 52 | 2417.00 | | Foreign | 22 | 358.00 | +---------------------------+ chi-squared = 30.502 with 1 d.f. probability = 0.0001 chi-squared with ties = 30.511 with 1 d.f. probability = 0.0001 . umbrella mpg weight length, by(foreign) Number of response variables: 3 Variable | Outcome -------------+----------------------------------------------------- mpg | higher values are better weight | higher values are better length | higher values are better ------------------------------------------------------------------------------------------------- -> foreign = Domestic Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 52 19.82692 4.743297 12 34 weight | 52 3317.115 695.3637 1800 4840 length | 52 196.1346 20.04605 147 233 ------------------------------------------------------------------------------------------------- -> foreign = Foreign Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mpg | 22 24.77273 6.611187 14 41 weight | 22 2315.909 433.0035 1760 3420 length | 22 168.5455 13.68255 142 193 Missing observations dropped from analysis = 0 O'Brien's Umbrella test is the following Kruskal-Wallis test on the sum of the ranks across the dependent variables. Kruskal-Wallis equality-of-populations rank test +---------------------------+ | foreign | Obs | Rank Sum | |----------+-----+----------| | Domestic | 52 | 2417.00 | | Foreign | 22 | 358.00 | +---------------------------+ chi-squared = 30.502 with 1 d.f. probability = 0.0001 chi-squared with ties = 30.511 with 1 d.f. probability = 0.0001 . log close log: C:\MyDocs\STATISTICS\OBrien84Multivariate\ado\auto.log log type: text closed on: 10 Apr 2008, 11:57:24 -------------------------------------------------------------------------------------------------