Chapter 13Non Parametric Methods (distribution free, no assumption of normality) 6) Run the SAS code below, and interpret your output by answering the following questions: A) Interpret the results of the ANOVA (Proc GLM). What is the betweengroup estimate of the variance? What is the withingroups variance? What did you conclude about the test of the null hypothesis at pvalue < 0.05 that the mean age for men in all 3 centers are identical? B) Interpret the results of the Wilcoxon Rank Sum Test (Proc NPAR1WAY) and ttest. What did you conclude from the results of the Wilcoxon Rank Sum Test about the test of the null hypothesis at pvalue <0.05 that the median of FEV1 for the Hopkins center is equal to the median of FEV1 of the Rancho patients? What did you conclude from the ttest? When would the Wilcoxon Rank Sum test be the more appropriate test? How would you decide? data treadmill; input air_1 air_2 co2_1 co2_2 co4_1 co4_2 center fev1 age; datalines; 983 957 1005 790 1020 885 1 3.23 60 260 290 256 239 255 265 1 3.47 66 709 489 593 400 630 419 1 1.86 65 655 490 710 520 645 415 1 2.47 55 240 200 245 225 330 255 1 3.01 62 295 298 315 293 310 305 1 1.69 70 238 239 320 250 327 230 1 2.1 51 475 495 510 430 525 440 1 2.81 72 520 588 380 400 378 465 1 3.28 58 902 665 660 405 610 645 1 3.36 61 294 350 330 240 345 298 1 2.61 71 715 635 960 795 630 605 1 . 41 675 600 690 610 705 707 1 2.91 70 765 655 700 470 725 505 1 1.98 57 540 525 515 495 590 645 1 2.57 55 530 502 515 500 534 508 1 2.08 63 300 300 280 280 362 300 1 2.47 64 562 485 465 465 610 525 1 2.47 76 285 240 330 315 250 250 1 2.74 74 1245 1190 1140 1050 1170 1170 1 2.88 54 760 750 705 770 855 675 1 2.63 58 420 410 425 430 450 375 1 2.53 73 605 727 590 635 365 380 2 3.22 56 660 442 448 380 453 251 2 2.88 65 495 445 485 493 375 410 2 1.71 65 547 463 718 482 652 489 2 2.89 63 549 701 452 499 693 757 2 3.77 57 924 1001 883 830 1073 1005 2 3.29 47 252 388 280 255 296 375 2 3.39 72 554 537 515 503 568 428 2 . 56 713 785 893 838 786 800 2 3.86 52 535 556 548 541 555 516 2 2.64 75 871 767 752 724 621 670 2 2.71 66 440 456 400 429 407 480 2 2.71 62 657 632 728 592 676 547 2 3.41 68 544 466 478 429 478 380 2 2.87 75 300 315 475 450 410 320 2 . 60 320 420 530 490 360 300 2 2.61 73 367 419 465 415 190 260 2 3.39 63 414 491 366 379 454 450 2 3.17 64 420 361 393 344 520 356 3 2.79 67 801 705 772 628 770 562 3 3.22 56 480 480 390 465 470 445 3 2.25 65 420 604 820 622 780 615 3 2.98 61 205 280 315 408 240 225 3 2.47 63 315 315 351 316 360 352 3 2.77 59 640 515 498 614 343 470 3 2.95 42 450 472 455 455 574 480 3 3.56 53 450 480 501 497 480 490 3 2.88 63 590 580 650 590 560 500 3 2.63 65 278 275 280 315 240 230 3 3.38 60 527 408 450 450 495 380 3 3.07 57 505 490 . . 442 435 3 2.81 62 720 580 719 557 706 486 3 3.17 70 210 222 200 260 190 204 3 2.23 73 506 506 644 632 600 532 3 2.19 63 522 502 580 616 497 500 3 4.06 55 524 604 447 401 440 420 3 1.98 52 398 244 428 375 333 386 3 2.81 58 380 317 350 350 400 390 3 2.85 68 304 305 306 319 362 290 3 2.43 70 256 257 245 255 203 194 3 3.2 72 680 735 714 705 769 671 3 3.53 45 ;