- Text
- Probability,
- Density,
- Variable,
- Variables,
- Interval,
- Variance,
- Population,
- Distributions,
- Hypothesis,
- Theorem,
- Mathematical,
- Statistics,
- Applications,
- Edition,
- Marvin.pcriot.com

www.downloadslide.com 15.8 The Friedman Test for Randomized Block Designs 771 15.36 Assuming no ties, obtain the exact null distribution of the Kruskal–Wallis H statistic for the case k = 3, n 1 = n 2 = n 3 = 2. [Because the sample sizes are all equal, if ranks 1 and 2 are assigned to treatment 1, ranks 3 and 4 are assigned to treatment 2, and ranks 5 and 6 are assigned to treatment 3, the value of H is exactly the same as if ranks 3 and 4 are assigned to treatment 1, ranks 5 and 6 are assigned to treatment 2, and ranks 1 and 2 are assigned to treatment 3. That is, for any particular set of ranks, we may interchange the roles of the k populations and obtain the same values of the H statistic. Thus, the number of cases that we must consider can be reduced by a factor of 1/k!. Consequently, H must be evaluated only for (6!/[2! · 2! · 2!])/3! = 15 distinct arrangements of ranks.] 15.8 The Friedman Test for Randomized Block Designs In Section 12.4, we discussed the merits of a randomized block design for an experiment to compare the performance of several treatments. We assume that b blocks are used in the experiment, which is designed to compare the locations of the distributions of the responses corresponding to each of k treatments. The ANOVA, discussed in Section 13.9, was based on the assumptions that the observations in each blocktreatment combination were normally distributed **with** equal variances. As in the case of the one-way layout, SST was the key quantity in the analysis. The Friedman test, developed by Nobel Prize–winning economist Milton Friedman (1937), is designed to test the null hypothesis that the probability distributions of the k treatments are identical versus the alternative that at least two of the distributions differ in location. The test is based on a statistic that is a rank analogue of SST for the randomized block design (see Section 13.9) and is computed in the following manner. After the data from a randomized block design are obtained, **with**in each block the observed values of the responses to each of the k treatments are ranked from 1 (the smallest in the block) to k (the largest in the block). If two or more observations in the same block are tied for the same rank, then the average of the ranks that would have been assigned to these observations is assigned to each member of the tied group. However, ties need to be dealt **with** in this manner only if they occur **with**in the same block. Let R i denote the sum of the ranks of the observations corresponding to treatment i and let R i = R i /b denote the corresponding average of the ranks (recall that in a randomized block design, each treatment is applied exactly once in each block, resulting in a total of b observations per treatment and hence in a total of bk total observations). Because ranks of 1 to k are assigned **with**in each block, the sum of the ranks assigned in each block is 1 + 2 +···+k = k(k + 1)/2. Thus, the sum of all the ranks assigned in the analysis is bk(k + 1)/2. If R denotes the overall average of the ranks of all the bk observations, it follows that R = (k + 1)/2. Consider the rank analog of SST for a randomized block design given by k∑ W = b (R i − R) 2 . i=1 If the null hypothesis is true and the probability distributions of the treatment responses do not differ in location, we expect the R i -values to be approximately equal and the resulting value for W to be small. If the alternative hypothesis were true, we would

772 Chapter 15 Nonparametric **Statistics** www.downloadslide.com expect this to lead to differences among the R i -values and corresponding large values of W . Instead of W , Friedman considered the statistic F r = 12W/[k(k + 1)], which may be rewritten (see Exercise 15.44) as 12 k∑ F r = Ri 2 − 3b(k + 1). bk(k + 1) i=1 As previously noted, the null hypothesis of equal locations is rejected in favor of the alternative that the treatment distributions differ in location if the value of F r is large. That is, the corresponding α-level test rejects the null hypothesis in favor of the alternative if F r > f r (α), where f r (α) is such that, when H 0 is true, P[F r > f r (α)] = α. If there are no ties among the observations **with**in the blocks, the null distribution of F r can (tediously) be found by using the methods of Chapter 2. For any values of b and k, the distribution of F r is found as follows. If the null hypothesis is true, then each of the k! permutations of the ranks 1, 2,...,k **with**in each block is equally likely. Further, because we assume that the observations in different blocks are mutually independent, it follows that each of the (k!) b possible combinations of the b sets of permutations for the **with**in-block ranks are equally likely when H 0 is true. Consequently, we can evaluate the value of F r for each possible case and thereby give the null distribution of F r (see Exercise 15.45). Selected values for f r (α) for various choices of k and b are given in Table A.22 of Hollander and Wolfe (1999). Like the other nonparametric procedures discussed in this chapter, the real advantage of this procedure is that it can be used regardless of the form of the actual distributions of the populations corresponding to the treatments. As **with** the Kruskal–Wallis statistic, the null distribution of the Friedman F r statistic can be approximated by a χ 2 distribution **with** k − 1 df as long as b is “large.” Empirical evidence indicates that the approximation is adequate if either b (the number of blocks) or k (the number of treatments) exceeds 5. Again, our examples and exercises deal **with** situations where this large-sample approximation is adequate. If you need to implement a Friedman analysis for small samples, refer to Hollander and Wolfe (1999) to obtain appropriate critical values. Friedman Test Based on F r for a Randomized Block Design Null hypothesis: H 0 : The probability distributions for the k treatments are identical. Alternative hypothesis: H a : At least two of the distributions differ in location. k∑ Test statistic: F r ={12/[bk(k + 1)]} Ri 2 − 3b(k + 1), where i=1 b = number of blocks, k = number of treatments, R i = sum of the ranks for the ith treatment, where the rank of each measurement is computed relative to its size **with**in its own block. Rejection region: F r >χα 2 **with** (k − 1) df. Assumptions: The treatments are randomly assigned to experimental units **with**in blocks. Either the number of blocks (b) or the number of treatments (k) exceeds 5.

- Page 1 and 2:
www.downloadslide.com

- Page 3 and 4:
www.downloadslide.com Discrete Dist

- Page 5 and 6:
www.downloadslide.com This page int

- Page 7 and 8:
www.downloadslide.com Mathematical

- Page 9 and 10:
www.downloadslide.com vi Contents 2

- Page 11 and 12:
www.downloadslide.com viii Contents

- Page 13 and 14:
www.downloadslide.com x Contents 11

- Page 15 and 16:
www.downloadslide.com xii Contents

- Page 17 and 18:
www.downloadslide.com xiv Preface o

- Page 19 and 20:
www.downloadslide.com xvi Preface u

- Page 21 and 22:
www.downloadslide.com xviii Preface

- Page 23 and 24:
www.downloadslide.com xx Preface Un

- Page 25 and 26:
www.downloadslide.com xxii Note to

- Page 27 and 28:
www.downloadslide.com 2 Chapter 1 W

- Page 29 and 30:
www.downloadslide.com 4 Chapter 1 W

- Page 31 and 32:
www.downloadslide.com 6 Chapter 1 W

- Page 33 and 34:
www.downloadslide.com 8 Chapter 1 W

- Page 35 and 36:
www.downloadslide.com 10 Chapter 1

- Page 37 and 38:
www.downloadslide.com 12 Chapter 1

- Page 39 and 40:
www.downloadslide.com 14 Chapter 1

- Page 41 and 42:
www.downloadslide.com 16 Chapter 1

- Page 43 and 44:
www.downloadslide.com 18 Chapter 1

- Page 45 and 46:
www.downloadslide.com CHAPTER 2 Pro

- Page 47 and 48:
www.downloadslide.com 22 Chapter 2

- Page 49 and 50:
www.downloadslide.com 24 Chapter 2

- Page 51 and 52:
www.downloadslide.com 26 Chapter 2

- Page 53 and 54:
www.downloadslide.com 28 Chapter 2

- Page 55 and 56:
www.downloadslide.com 30 Chapter 2

- Page 57 and 58:
www.downloadslide.com 32 Chapter 2

- Page 59 and 60:
www.downloadslide.com 34 Chapter 2

- Page 61 and 62:
www.downloadslide.com 36 Chapter 2

- Page 63 and 64:
www.downloadslide.com 38 Chapter 2

- Page 65 and 66:
www.downloadslide.com 40 Chapter 2

- Page 67 and 68:
www.downloadslide.com 42 Chapter 2

- Page 69 and 70:
www.downloadslide.com 44 Chapter 2

- Page 71 and 72:
www.downloadslide.com 46 Chapter 2

- Page 73 and 74:
www.downloadslide.com 48 Chapter 2

- Page 75 and 76:
www.downloadslide.com 50 Chapter 2

- Page 77 and 78:
www.downloadslide.com 52 Chapter 2

- Page 79 and 80:
www.downloadslide.com 54 Chapter 2

- Page 81 and 82:
www.downloadslide.com 56 Chapter 2

- Page 83 and 84:
www.downloadslide.com 58 Chapter 2

- Page 85 and 86:
www.downloadslide.com 60 Chapter 2

- Page 87 and 88:
www.downloadslide.com 62 Chapter 2

- Page 89 and 90:
www.downloadslide.com 64 Chapter 2

- Page 91 and 92:
www.downloadslide.com 66 Chapter 2

- Page 93 and 94:
www.downloadslide.com 68 Chapter 2

- Page 95 and 96:
www.downloadslide.com 70 Chapter 2

- Page 97 and 98:
www.downloadslide.com 72 Chapter 2

- Page 99 and 100:
www.downloadslide.com 74 Chapter 2

- Page 101 and 102:
www.downloadslide.com 76 Chapter 2

- Page 103 and 104:
www.downloadslide.com 78 Chapter 2

- Page 105 and 106:
www.downloadslide.com 80 Chapter 2

- Page 107 and 108:
www.downloadslide.com 82 Chapter 2

- Page 109 and 110:
www.downloadslide.com 84 Chapter 2

- Page 111 and 112:
www.downloadslide.com CHAPTER 3 Dis

- Page 113 and 114:
www.downloadslide.com 88 Chapter 3

- Page 115 and 116:
www.downloadslide.com 90 Chapter 3

- Page 117 and 118:
www.downloadslide.com 92 Chapter 3

- Page 119 and 120:
www.downloadslide.com 94 Chapter 3

- Page 121 and 122:
www.downloadslide.com 96 Chapter 3

- Page 123 and 124:
www.downloadslide.com 98 Chapter 3

- Page 125 and 126:
www.downloadslide.com 100 Chapter 3

- Page 127 and 128:
www.downloadslide.com 102 Chapter 3

- Page 129 and 130:
www.downloadslide.com 104 Chapter 3

- Page 131 and 132:
www.downloadslide.com 106 Chapter 3

- Page 133 and 134:
www.downloadslide.com 108 Chapter 3

- Page 135 and 136:
www.downloadslide.com 110 Chapter 3

- Page 137 and 138:
www.downloadslide.com 112 Chapter 3

- Page 139 and 140:
www.downloadslide.com 114 Chapter 3

- Page 141 and 142:
www.downloadslide.com 116 Chapter 3

- Page 143 and 144:
www.downloadslide.com 118 Chapter 3

- Page 145 and 146:
www.downloadslide.com 120 Chapter 3

- Page 147 and 148:
www.downloadslide.com 122 Chapter 3

- Page 149 and 150:
www.downloadslide.com 124 Chapter 3

- Page 151 and 152:
www.downloadslide.com 126 Chapter 3

- Page 153 and 154:
www.downloadslide.com 128 Chapter 3

- Page 155 and 156:
www.downloadslide.com 130 Chapter 3

- Page 157 and 158:
www.downloadslide.com 132 Chapter 3

- Page 159 and 160:
www.downloadslide.com 134 Chapter 3

- Page 161 and 162:
www.downloadslide.com 136 Chapter 3

- Page 163 and 164:
www.downloadslide.com 138 Chapter 3

- Page 165 and 166:
www.downloadslide.com 140 Chapter 3

- Page 167 and 168:
www.downloadslide.com 142 Chapter 3

- Page 169 and 170:
www.downloadslide.com 144 Chapter 3

- Page 171 and 172:
www.downloadslide.com 146 Chapter 3

- Page 173 and 174:
www.downloadslide.com 148 Chapter 3

- Page 175 and 176:
www.downloadslide.com 150 Chapter 3

- Page 177 and 178:
www.downloadslide.com 152 Chapter 3

- Page 179 and 180:
www.downloadslide.com 154 Chapter 3

- Page 181 and 182:
www.downloadslide.com 156 Chapter 3

- Page 183 and 184:
www.downloadslide.com 158 Chapter 4

- Page 185 and 186:
www.downloadslide.com 160 Chapter 4

- Page 187 and 188:
www.downloadslide.com 162 Chapter 4

- Page 189 and 190:
www.downloadslide.com 164 Chapter 4

- Page 191 and 192:
www.downloadslide.com 166 Chapter 4

- Page 193 and 194:
www.downloadslide.com 168 Chapter 4

- Page 195 and 196:
www.downloadslide.com 170 Chapter 4

- Page 197 and 198:
www.downloadslide.com 172 Chapter 4

- Page 199 and 200:
www.downloadslide.com 174 Chapter 4

- Page 201 and 202:
www.downloadslide.com 176 Chapter 4

- Page 203 and 204:
www.downloadslide.com 178 Chapter 4

- Page 205 and 206:
www.downloadslide.com 180 Chapter 4

- Page 207 and 208:
www.downloadslide.com 182 Chapter 4

- Page 209 and 210:
www.downloadslide.com 184 Chapter 4

- Page 211 and 212:
www.downloadslide.com 186 Chapter 4

- Page 213 and 214:
www.downloadslide.com 188 Chapter 4

- Page 215 and 216:
www.downloadslide.com 190 Chapter 4

- Page 217 and 218:
www.downloadslide.com 192 Chapter 4

- Page 219 and 220:
www.downloadslide.com 194 Chapter 4

- Page 221 and 222:
www.downloadslide.com 196 Chapter 4

- Page 223 and 224:
www.downloadslide.com 198 Chapter 4

- Page 225 and 226:
www.downloadslide.com 200 Chapter 4

- Page 227 and 228:
www.downloadslide.com 202 Chapter 4

- Page 229 and 230:
www.downloadslide.com 204 Chapter 4

- Page 231 and 232:
www.downloadslide.com 206 Chapter 4

- Page 233 and 234:
www.downloadslide.com 208 Chapter 4

- Page 235 and 236:
www.downloadslide.com 210 Chapter 4

- Page 237 and 238:
www.downloadslide.com 212 Chapter 4

- Page 239 and 240:
www.downloadslide.com 214 Chapter 4

- Page 241 and 242:
www.downloadslide.com 216 Chapter 4

- Page 243 and 244:
www.downloadslide.com 218 Chapter 4

- Page 245 and 246:
www.downloadslide.com 220 Chapter 4

- Page 247 and 248:
www.downloadslide.com 222 Chapter 4

- Page 249 and 250:
www.downloadslide.com 224 Chapter 5

- Page 251 and 252:
www.downloadslide.com 226 Chapter 5

- Page 253 and 254:
www.downloadslide.com 228 Chapter 5

- Page 255 and 256:
www.downloadslide.com 230 Chapter 5

- Page 257 and 258:
www.downloadslide.com 232 Chapter 5

- Page 259 and 260:
www.downloadslide.com 234 Chapter 5

- Page 261 and 262:
www.downloadslide.com 236 Chapter 5

- Page 263 and 264:
www.downloadslide.com 238 Chapter 5

- Page 265 and 266:
www.downloadslide.com 240 Chapter 5

- Page 267 and 268:
www.downloadslide.com 242 Chapter 5

- Page 269 and 270:
www.downloadslide.com 244 Chapter 5

- Page 271 and 272:
www.downloadslide.com 246 Chapter 5

- Page 273 and 274:
www.downloadslide.com 248 Chapter 5

- Page 275 and 276:
www.downloadslide.com 250 Chapter 5

- Page 277 and 278:
www.downloadslide.com 252 Chapter 5

- Page 279 and 280:
www.downloadslide.com 254 Chapter 5

- Page 281 and 282:
www.downloadslide.com 256 Chapter 5

- Page 283 and 284:
www.downloadslide.com 258 Chapter 5

- Page 285 and 286:
www.downloadslide.com 260 Chapter 5

- Page 287 and 288:
www.downloadslide.com 262 Chapter 5

- Page 289 and 290:
www.downloadslide.com 264 Chapter 5

- Page 291 and 292:
www.downloadslide.com 266 Chapter 5

- Page 293 and 294:
www.downloadslide.com 268 Chapter 5

- Page 295 and 296:
www.downloadslide.com 270 Chapter 5

- Page 297 and 298:
www.downloadslide.com 272 Chapter 5

- Page 299 and 300:
www.downloadslide.com 274 Chapter 5

- Page 301 and 302:
www.downloadslide.com 276 Chapter 5

- Page 303 and 304:
www.downloadslide.com 278 Chapter 5

- Page 305 and 306:
www.downloadslide.com 280 Chapter 5

- Page 307 and 308:
www.downloadslide.com 282 Chapter 5

- Page 309 and 310:
www.downloadslide.com 284 Chapter 5

- Page 311 and 312:
www.downloadslide.com 286 Chapter 5

- Page 313 and 314:
www.downloadslide.com 288 Chapter 5

- Page 315 and 316:
www.downloadslide.com 290 Chapter 5

- Page 317 and 318:
www.downloadslide.com 292 Chapter 5

- Page 319 and 320:
www.downloadslide.com 294 Chapter 5

- Page 321 and 322:
www.downloadslide.com CHAPTER 6 Fun

- Page 323 and 324:
298 Chapter 6 Functions of Random V

- Page 325 and 326:
300 Chapter 6 Functions of Random V

- Page 327 and 328:
302 Chapter 6 Functions of Random V

- Page 329 and 330:
304 Chapter 6 Functions of Random V

- Page 331 and 332:
306 Chapter 6 Functions of Random V

- Page 333 and 334:
308 Chapter 6 Functions of Random V

- Page 335 and 336:
310 Chapter 6 Functions of Random V

- Page 337 and 338:
312 Chapter 6 Functions of Random V

- Page 339 and 340:
314 Chapter 6 Functions of Random V

- Page 341 and 342:
316 Chapter 6 Functions of Random V

- Page 343 and 344:
318 Chapter 6 Functions of Random V

- Page 345 and 346:
320 Chapter 6 Functions of Random V

- Page 347 and 348:
322 Chapter 6 Functions of Random V

- Page 349 and 350:
324 Chapter 6 Functions of Random V

- Page 351 and 352:
326 Chapter 6 Functions of Random V

- Page 353 and 354:
328 Chapter 6 Functions of Random V

- Page 355 and 356:
330 Chapter 6 Functions of Random V

- Page 357 and 358:
332 Chapter 6 Functions of Random V

- Page 359 and 360:
334 Chapter 6 Functions of Random V

- Page 361 and 362:
336 Chapter 6 Functions of Random V

- Page 363 and 364:
338 Chapter 6 Functions of Random V

- Page 365 and 366:
340 Chapter 6 Functions of Random V

- Page 367 and 368:
342 Chapter 6 Functions of Random V

- Page 369 and 370:
344 Chapter 6 Functions of Random V

- Page 371 and 372:
www.downloadslide.com CHAPTER 7 Sam

- Page 373 and 374:
www.downloadslide.com 348 Chapter 7

- Page 375 and 376:
www.downloadslide.com 350 Chapter 7

- Page 377 and 378:
www.downloadslide.com 352 Chapter 7

- Page 379 and 380:
www.downloadslide.com 354 Chapter 7

- Page 381 and 382:
www.downloadslide.com 356 Chapter 7

- Page 383 and 384:
www.downloadslide.com 358 Chapter 7

- Page 385 and 386:
www.downloadslide.com 360 Chapter 7

- Page 387 and 388:
www.downloadslide.com 362 Chapter 7

- Page 389 and 390:
www.downloadslide.com 364 Chapter 7

- Page 391 and 392:
www.downloadslide.com 366 Chapter 7

- Page 393 and 394:
www.downloadslide.com 368 Chapter 7

- Page 395 and 396:
www.downloadslide.com 370 Chapter 7

- Page 397 and 398:
www.downloadslide.com 372 Chapter 7

- Page 399 and 400:
www.downloadslide.com 374 Chapter 7

- Page 401 and 402:
www.downloadslide.com 376 Chapter 7

- Page 403 and 404:
www.downloadslide.com 378 Chapter 7

- Page 405 and 406:
www.downloadslide.com 380 Chapter 7

- Page 407 and 408:
www.downloadslide.com 382 Chapter 7

- Page 409 and 410:
www.downloadslide.com 384 Chapter 7

- Page 411 and 412:
www.downloadslide.com 386 Chapter 7

- Page 413 and 414:
www.downloadslide.com 388 Chapter 7

- Page 415 and 416:
www.downloadslide.com CHAPTER 8 Est

- Page 417 and 418:
www.downloadslide.com 392 Chapter 8

- Page 419 and 420:
www.downloadslide.com 394 Chapter 8

- Page 421 and 422:
www.downloadslide.com 396 Chapter 8

- Page 423 and 424:
www.downloadslide.com 398 Chapter 8

- Page 425 and 426:
www.downloadslide.com 400 Chapter 8

- Page 427 and 428:
www.downloadslide.com 402 Chapter 8

- Page 429 and 430:
www.downloadslide.com 404 Chapter 8

- Page 431 and 432:
www.downloadslide.com 406 Chapter 8

- Page 433 and 434:
www.downloadslide.com 408 Chapter 8

- Page 435 and 436:
www.downloadslide.com 410 Chapter 8

- Page 437 and 438:
www.downloadslide.com 412 Chapter 8

- Page 439 and 440:
www.downloadslide.com 414 Chapter 8

- Page 441 and 442:
www.downloadslide.com 416 Chapter 8

- Page 443 and 444:
www.downloadslide.com 418 Chapter 8

- Page 445 and 446:
www.downloadslide.com 420 Chapter 8

- Page 447 and 448:
www.downloadslide.com 422 Chapter 8

- Page 449 and 450:
www.downloadslide.com 424 Chapter 8

- Page 451 and 452:
www.downloadslide.com 426 Chapter 8

- Page 453 and 454:
www.downloadslide.com 428 Chapter 8

- Page 455 and 456:
www.downloadslide.com 430 Chapter 8

- Page 457 and 458:
www.downloadslide.com 432 Chapter 8

- Page 459 and 460:
www.downloadslide.com 434 Chapter 8

- Page 461 and 462:
www.downloadslide.com 436 Chapter 8

- Page 463 and 464:
www.downloadslide.com 438 Chapter 8

- Page 465 and 466:
www.downloadslide.com 440 Chapter 8

- Page 467 and 468:
www.downloadslide.com 442 Chapter 8

- Page 469 and 470:
www.downloadslide.com CHAPTER 9 Pro

- Page 471 and 472:
www.downloadslide.com 446 Chapter 9

- Page 473 and 474:
www.downloadslide.com 448 Chapter 9

- Page 475 and 476:
www.downloadslide.com 450 Chapter 9

- Page 477 and 478:
www.downloadslide.com 452 Chapter 9

- Page 479 and 480:
www.downloadslide.com 454 Chapter 9

- Page 481 and 482:
www.downloadslide.com 456 Chapter 9

- Page 483 and 484:
www.downloadslide.com 458 Chapter 9

- Page 485 and 486:
www.downloadslide.com 460 Chapter 9

- Page 487 and 488:
www.downloadslide.com 462 Chapter 9

- Page 489 and 490:
www.downloadslide.com 464 Chapter 9

- Page 491 and 492:
www.downloadslide.com 466 Chapter 9

- Page 493 and 494:
www.downloadslide.com 468 Chapter 9

- Page 495 and 496:
www.downloadslide.com 470 Chapter 9

- Page 497 and 498:
www.downloadslide.com 472 Chapter 9

- Page 499 and 500:
www.downloadslide.com 474 Chapter 9

- Page 501 and 502:
www.downloadslide.com 476 Chapter 9

- Page 503 and 504:
www.downloadslide.com 478 Chapter 9

- Page 505 and 506:
www.downloadslide.com 480 Chapter 9

- Page 507 and 508:
www.downloadslide.com 482 Chapter 9

- Page 509 and 510:
www.downloadslide.com 484 Chapter 9

- Page 511 and 512:
www.downloadslide.com 486 Chapter 9

- Page 513 and 514:
www.downloadslide.com CHAPTER 10 Hy

- Page 515 and 516:
490 Chapter 10 Hypothesis Testing w

- Page 517 and 518:
492 Chapter 10 Hypothesis Testing w

- Page 519 and 520:
www.downloadslide.com 494 Chapter 1

- Page 521 and 522:
496 Chapter 10 Hypothesis Testing w

- Page 523 and 524:
498 Chapter 10 Hypothesis Testing w

- Page 525 and 526:
500 Chapter 10 Hypothesis Testing w

- Page 527 and 528:
www.downloadslide.com 502 Chapter 1

- Page 529 and 530:
www.downloadslide.com 504 Chapter 1

- Page 531 and 532:
506 Chapter 10 Hypothesis Testing w

- Page 533 and 534:
508 Chapter 10 Hypothesis Testing w

- Page 535 and 536:
510 Chapter 10 Hypothesis Testing w

- Page 537 and 538:
512 Chapter 10 Hypothesis Testing w

- Page 539 and 540:
514 Chapter 10 Hypothesis Testing w

- Page 541 and 542:
www.downloadslide.com 516 Chapter 1

- Page 543 and 544:
518 Chapter 10 Hypothesis Testing w

- Page 545 and 546:
www.downloadslide.com 520 Chapter 1

- Page 547 and 548:
522 Chapter 10 Hypothesis Testing w

- Page 549 and 550:
524 Chapter 10 Hypothesis Testing w

- Page 551 and 552:
www.downloadslide.com 526 Chapter 1

- Page 553 and 554:
www.downloadslide.com 528 Chapter 1

- Page 555 and 556:
www.downloadslide.com 530 Chapter 1

- Page 557 and 558:
532 Chapter 10 Hypothesis Testing w

- Page 559 and 560:
534 Chapter 10 Hypothesis Testing w

- Page 561 and 562:
536 Chapter 10 Hypothesis Testing w

- Page 563 and 564:
538 Chapter 10 Hypothesis Testing w

- Page 565 and 566:
www.downloadslide.com 540 Chapter 1

- Page 567 and 568:
542 Chapter 10 Hypothesis Testing w

- Page 569 and 570:
544 Chapter 10 Hypothesis Testing w

- Page 571 and 572:
546 Chapter 10 Hypothesis Testing w

- Page 573 and 574:
548 Chapter 10 Hypothesis Testing w

- Page 575 and 576:
550 Chapter 10 Hypothesis Testing w

- Page 577 and 578:
552 Chapter 10 Hypothesis Testing w

- Page 579 and 580:
554 Chapter 10 Hypothesis Testing w

- Page 581 and 582:
556 Chapter 10 Hypothesis Testing w

- Page 583 and 584:
www.downloadslide.com 558 Chapter 1

- Page 585 and 586:
560 Chapter 10 Hypothesis Testing w

- Page 587 and 588:
562 Chapter 10 Hypothesis Testing w

- Page 589 and 590:
www.downloadslide.com 564 Chapter 1

- Page 591 and 592:
www.downloadslide.com 566 Chapter 1

- Page 593 and 594:
www.downloadslide.com 568 Chapter 1

- Page 595 and 596:
www.downloadslide.com 570 Chapter 1

- Page 597 and 598:
www.downloadslide.com 572 Chapter 1

- Page 599 and 600:
www.downloadslide.com 574 Chapter 1

- Page 601 and 602:
www.downloadslide.com 576 Chapter 1

- Page 603 and 604:
www.downloadslide.com 578 Chapter 1

- Page 605 and 606:
www.downloadslide.com 580 Chapter 1

- Page 607 and 608:
www.downloadslide.com 582 Chapter 1

- Page 609 and 610:
www.downloadslide.com 584 Chapter 1

- Page 611 and 612:
www.downloadslide.com 586 Chapter 1

- Page 613 and 614:
www.downloadslide.com 588 Chapter 1

- Page 615 and 616:
www.downloadslide.com 590 Chapter 1

- Page 617 and 618:
www.downloadslide.com 592 Chapter 1

- Page 619 and 620:
www.downloadslide.com 594 Chapter 1

- Page 621 and 622:
www.downloadslide.com 596 Chapter 1

- Page 623 and 624:
www.downloadslide.com 598 Chapter 1

- Page 625 and 626:
www.downloadslide.com 600 Chapter 1

- Page 627 and 628:
www.downloadslide.com 602 Chapter 1

- Page 629 and 630:
www.downloadslide.com 604 Chapter 1

- Page 631 and 632:
www.downloadslide.com 606 Chapter 1

- Page 633 and 634:
www.downloadslide.com 608 Chapter 1

- Page 635 and 636:
www.downloadslide.com 610 Chapter 1

- Page 637 and 638:
www.downloadslide.com 612 Chapter 1

- Page 639 and 640:
www.downloadslide.com 614 Chapter 1

- Page 641 and 642:
www.downloadslide.com 616 Chapter 1

- Page 643 and 644:
www.downloadslide.com 618 Chapter 1

- Page 645 and 646:
www.downloadslide.com 620 Chapter 1

- Page 647 and 648:
www.downloadslide.com 622 Chapter 1

- Page 649 and 650:
www.downloadslide.com 624 Chapter 1

- Page 651 and 652:
www.downloadslide.com 626 Chapter 1

- Page 653 and 654:
www.downloadslide.com 628 Chapter 1

- Page 655 and 656:
www.downloadslide.com 630 Chapter 1

- Page 657 and 658:
www.downloadslide.com 632 Chapter 1

- Page 659 and 660:
www.downloadslide.com 634 Chapter 1

- Page 661 and 662:
www.downloadslide.com 636 Chapter 1

- Page 663 and 664:
www.downloadslide.com 638 Chapter 1

- Page 665 and 666:
www.downloadslide.com CHAPTER 12 Co

- Page 667 and 668:
www.downloadslide.com 642 Chapter 1

- Page 669 and 670:
www.downloadslide.com 644 Chapter 1

- Page 671 and 672:
www.downloadslide.com 646 Chapter 1

- Page 673 and 674:
www.downloadslide.com 648 Chapter 1

- Page 675 and 676:
www.downloadslide.com 650 Chapter 1

- Page 677 and 678:
www.downloadslide.com 652 Chapter 1

- Page 679 and 680:
www.downloadslide.com 654 Chapter 1

- Page 681 and 682:
www.downloadslide.com 656 Chapter 1

- Page 683 and 684:
www.downloadslide.com 658 Chapter 1

- Page 685 and 686:
www.downloadslide.com 660 Chapter 1

- Page 687 and 688:
662 Chapter 13 The Analysis of Vari

- Page 689 and 690:
664 Chapter 13 The Analysis of Vari

- Page 691 and 692:
666 Chapter 13 The Analysis of Vari

- Page 693 and 694:
668 Chapter 13 The Analysis of Vari

- Page 695 and 696:
670 Chapter 13 The Analysis of Vari

- Page 697 and 698:
672 Chapter 13 The Analysis of Vari

- Page 699 and 700:
www.downloadslide.com 674 Chapter 1

- Page 701 and 702:
www.downloadslide.com 676 Chapter 1

- Page 703 and 704:
678 Chapter 13 The Analysis of Vari

- Page 705 and 706:
680 Chapter 13 The Analysis of Vari

- Page 707 and 708:
682 Chapter 13 The Analysis of Vari

- Page 709 and 710:
www.downloadslide.com 684 Chapter 1

- Page 711 and 712:
686 Chapter 13 The Analysis of Vari

- Page 713 and 714:
688 Chapter 13 The Analysis of Vari

- Page 715 and 716:
690 Chapter 13 The Analysis of Vari

- Page 717 and 718:
692 Chapter 13 The Analysis of Vari

- Page 719 and 720:
www.downloadslide.com 694 Chapter 1

- Page 721 and 722:
696 Chapter 13 The Analysis of Vari

- Page 723 and 724:
www.downloadslide.com 698 Chapter 1

- Page 725 and 726:
700 Chapter 13 The Analysis of Vari

- Page 727 and 728:
702 Chapter 13 The Analysis of Vari

- Page 729 and 730:
704 Chapter 13 The Analysis of Vari

- Page 731 and 732:
www.downloadslide.com 706 Chapter 1

- Page 733 and 734:
www.downloadslide.com 708 Chapter 1

- Page 735 and 736:
710 Chapter 13 The Analysis of Vari

- Page 737 and 738:
www.downloadslide.com 712 Chapter 1

- Page 739 and 740:
714 Chapter 14 Analysis of Categori

- Page 741 and 742:
716 Chapter 14 Analysis of Categori

- Page 743 and 744:
718 Chapter 14 Analysis of Categori

- Page 745 and 746: www.downloadslide.com 720 Chapter 1
- Page 747 and 748: 722 Chapter 14 Analysis of Categori
- Page 749 and 750: 724 Chapter 14 Analysis of Categori
- Page 751 and 752: 726 Chapter 14 Analysis of Categori
- Page 753 and 754: www.downloadslide.com 728 Chapter 1
- Page 755 and 756: 730 Chapter 14 Analysis of Categori
- Page 757 and 758: www.downloadslide.com 732 Chapter 1
- Page 759 and 760: 734 Chapter 14 Analysis of Categori
- Page 761 and 762: 736 Chapter 14 Analysis of Categori
- Page 763 and 764: www.downloadslide.com 738 Chapter 1
- Page 765 and 766: 740 Chapter 14 Analysis of Categori
- Page 767 and 768: 742 Chapter 15 Nonparametric Statis
- Page 769 and 770: 744 Chapter 15 Nonparametric Statis
- Page 771 and 772: 746 Chapter 15 Nonparametric Statis
- Page 773 and 774: www.downloadslide.com 748 Chapter 1
- Page 775 and 776: 750 Chapter 15 Nonparametric Statis
- Page 777 and 778: 752 Chapter 15 Nonparametric Statis
- Page 779 and 780: www.downloadslide.com 754 Chapter 1
- Page 781 and 782: 756 Chapter 15 Nonparametric Statis
- Page 783 and 784: 758 Chapter 15 Nonparametric Statis
- Page 785 and 786: 760 Chapter 15 Nonparametric Statis
- Page 787 and 788: 762 Chapter 15 Nonparametric Statis
- Page 789 and 790: www.downloadslide.com 764 Chapter 1
- Page 791 and 792: 766 Chapter 15 Nonparametric Statis
- Page 793 and 794: 768 Chapter 15 Nonparametric Statis
- Page 795: 770 Chapter 15 Nonparametric Statis
- Page 799 and 800: www.downloadslide.com 774 Chapter 1
- Page 801 and 802: 776 Chapter 15 Nonparametric Statis
- Page 803 and 804: 778 Chapter 15 Nonparametric Statis
- Page 805 and 806: 780 Chapter 15 Nonparametric Statis
- Page 807 and 808: www.downloadslide.com 782 Chapter 1
- Page 809 and 810: 784 Chapter 15 Nonparametric Statis
- Page 811 and 812: 786 Chapter 15 Nonparametric Statis
- Page 813 and 814: www.downloadslide.com 788 Chapter 1
- Page 815 and 816: 790 Chapter 15 Nonparametric Statis
- Page 817 and 818: 792 Chapter 15 Nonparametric Statis
- Page 819 and 820: 794 Chapter 15 Nonparametric Statis
- Page 821 and 822: www.downloadslide.com CHAPTER 16 In
- Page 823 and 824: www.downloadslide.com 798 Chapter 1
- Page 825 and 826: www.downloadslide.com 800 Chapter 1
- Page 827 and 828: www.downloadslide.com 802 Chapter 1
- Page 829 and 830: www.downloadslide.com 804 Chapter 1
- Page 831 and 832: www.downloadslide.com 806 Chapter 1
- Page 833 and 834: www.downloadslide.com 808 Chapter 1
- Page 835 and 836: www.downloadslide.com 810 Chapter 1
- Page 837 and 838: www.downloadslide.com 812 Chapter 1
- Page 839 and 840: www.downloadslide.com 814 Chapter 1
- Page 841 and 842: www.downloadslide.com 816 Chapter 1
- Page 843 and 844: www.downloadslide.com 818 Chapter 1
- Page 845 and 846: www.downloadslide.com This page int
- Page 847 and 848:
www.downloadslide.com 822 Appendix

- Page 849 and 850:
www.downloadslide.com 824 Appendix

- Page 851 and 852:
www.downloadslide.com 826 Appendix

- Page 853 and 854:
www.downloadslide.com 828 Appendix

- Page 855 and 856:
www.downloadslide.com 830 Appendix

- Page 857 and 858:
www.downloadslide.com 832 Appendix

- Page 859 and 860:
www.downloadslide.com 834 Appendix

- Page 861 and 862:
www.downloadslide.com 836 Appendix

- Page 863 and 864:
www.downloadslide.com 838 Appendix

- Page 865 and 866:
www.downloadslide.com 840 Appendix

- Page 867 and 868:
www.downloadslide.com 842 Appendix

- Page 869 and 870:
www.downloadslide.com 844 Appendix

- Page 871 and 872:
www.downloadslide.com 846 Appendix

- Page 873 and 874:
www.downloadslide.com 848 Appendix

- Page 875 and 876:
www.downloadslide.com 850 Appendix

- Page 877 and 878:
www.downloadslide.com 852 Appendix

- Page 879 and 880:
www.downloadslide.com 854 Appendix

- Page 881 and 882:
www.downloadslide.com 856 Appendix

- Page 883 and 884:
www.downloadslide.com 858 Appendix

- Page 885 and 886:
www.downloadslide.com 860 Appendix

- Page 887 and 888:
www.downloadslide.com 862 Appendix

- Page 889 and 890:
www.downloadslide.com 864 Appendix

- Page 891 and 892:
www.downloadslide.com 866 Appendix

- Page 893 and 894:
www.downloadslide.com 868 Appendix

- Page 895 and 896:
www.downloadslide.com 870 Appendix

- Page 897 and 898:
www.downloadslide.com 872 Appendix

- Page 900:
www.downloadslide.com Table 12 (Con

- Page 904:
www.downloadslide.com Table 12 (Con

- Page 907 and 908:
www.downloadslide.com 878 Answers 2

- Page 909 and 910:
www.downloadslide.com 880 Answers 3

- Page 911 and 912:
www.downloadslide.com 882 Answers d

- Page 913 and 914:
www.downloadslide.com 884 Answers (

- Page 915 and 916:
www.downloadslide.com 886 Answers 5

- Page 917 and 918:
www.downloadslide.com 888 Answers 7

- Page 919 and 920:
www.downloadslide.com 890 Answers

- Page 921 and 922:
www.downloadslide.com 892 Answers

- Page 923 and 924:
www.downloadslide.com 894 Answers 1

- Page 925 and 926:
www.downloadslide.com Answers 895 1

- Page 927 and 928:
www.downloadslide.com Index 897 Bet

- Page 929 and 930:
www.downloadslide.com Index 899 Den

- Page 931 and 932:
www.downloadslide.com Index 901 Exp

- Page 933 and 934:
www.downloadslide.com Index 903 Inf

- Page 935 and 936:
www.downloadslide.com Index 905 Met

- Page 937 and 938:
www.downloadslide.com Index 907 Par

- Page 939 and 940:
www.downloadslide.com Index 909 Ran

- Page 941 and 942:
www.downloadslide.com Index 911 Sum

- Page 943 and 944:
www.downloadslide.com Normal Curve