Final_Assessment_A
2025-12-16
Question 2: Is there a significant difference in ozone concentration between years (2003, 2013, 2023)? If so, what is possibly driving that difference. Note, for this analysis, you should conduct three separate comparisons: 1) 2003 & 2013, 2) 2013 & 2023, 3) 2003 & 2023. Provide a 250-500 word summary of your analysis interpretation of your results. Please cite all outside references (e.g., papers, government reports) used to support your interpretation.
#import dataset
ozone_2023 <- read.csv("C:/Users/noahs/Downloads/2023_ozone.csv", header = T)
ozone_2013 <- read.csv("C:/Users/noahs/Downloads/2013_ozone.csv", header = T)
ozone_2003 <- read.csv("C:/Users/noahs/Downloads/2003_ozone.csv", header = T)#treat 2003, 2013, and 2013 as categorical groups.
#we are testing if any one of these groups is different
#Ho: Average ozone concentrations are the same in 2003, 2013, and 2023.
#HA: At least one year has a different average ozone (or dissolved oxygen) concentration.
#we will run ANOVA tests, but first we we need to see that it meets the assumptions of ANOVA
O2_2023 <- ozone_2023$Daily.Max.8.hour.Ozone.Concentration
O2_2013 <- ozone_2013$Daily.Max.8.hour.Ozone.Concentration
O2_2003 <- ozone_2003$Daily.Max.8.hour.Ozone.Concentration
O2_data <- data.frame(
Year = c(
rep("2023", length(O2_2023)),
rep("2013", length(O2_2013)),
rep("2003", length(O2_2003))
),
O2 = c(O2_2023, O2_2013, O2_2003)
)
print(O2_data)## Year O2
## 1 2023 0.033
## 2 2023 0.034
## 3 2023 0.032
## 4 2023 0.039
## 5 2023 0.034
## 6 2023 0.030
## 7 2023 0.039
## 8 2023 0.038
## 9 2023 0.032
## 10 2023 0.038
## 11 2023 0.034
## 12 2023 0.030
## 13 2023 0.032
## 14 2023 0.035
## 15 2023 0.037
## 16 2023 0.034
## 17 2023 0.025
## 18 2023 0.026
## 19 2023 0.031
## 20 2023 0.026
## 21 2023 0.029
## 22 2023 0.032
## 23 2023 0.030
## 24 2023 0.030
## 25 2023 0.028
## 26 2023 0.035
## 27 2023 0.036
## 28 2023 0.035
## 29 2023 0.031
## 30 2023 0.029
## 31 2023 0.026
## 32 2023 0.030
## 33 2023 0.025
## 34 2023 0.025
## 35 2023 0.033
## 36 2023 0.037
## 37 2023 0.029
## 38 2023 0.032
## 39 2023 0.030
## 40 2023 0.039
## 41 2023 0.040
## 42 2023 0.039
## 43 2023 0.035
## 44 2023 0.039
## 45 2023 0.036
## 46 2023 0.031
## 47 2023 0.027
## 48 2023 0.034
## 49 2023 0.039
## 50 2023 0.043
## 51 2023 0.043
## 52 2023 0.042
## 53 2023 0.038
## 54 2023 0.037
## 55 2023 0.039
## 56 2023 0.036
## 57 2023 0.034
## 58 2023 0.036
## 59 2023 0.039
## 60 2023 0.036
## 61 2023 0.039
## 62 2023 0.043
## 63 2023 0.043
## 64 2023 0.042
## 65 2023 0.041
## 66 2023 0.031
## 67 2023 0.027
## 68 2023 0.032
## 69 2023 0.032
## 70 2023 0.032
## 71 2023 0.033
## 72 2023 0.041
## 73 2023 0.042
## 74 2023 0.040
## 75 2023 0.041
## 76 2023 0.038
## 77 2023 0.042
## 78 2023 0.042
## 79 2023 0.041
## 80 2023 0.044
## 81 2023 0.044
## 82 2023 0.044
## 83 2023 0.042
## 84 2023 0.039
## 85 2023 0.041
## 86 2023 0.042
## 87 2023 0.044
## 88 2023 0.047
## 89 2023 0.038
## 90 2023 0.040
## 91 2023 0.042
## 92 2023 0.043
## 93 2023 0.046
## 94 2023 0.036
## 95 2023 0.037
## 96 2023 0.048
## 97 2023 0.051
## 98 2023 0.039
## 99 2023 0.047
## 100 2023 0.048
## 101 2023 0.050
## 102 2023 0.050
## 103 2023 0.044
## 104 2023 0.047
## 105 2023 0.047
## 106 2023 0.049
## 107 2023 0.051
## 108 2023 0.050
## 109 2023 0.043
## 110 2023 0.038
## 111 2023 0.055
## 112 2023 0.057
## 113 2023 0.060
## 114 2023 0.066
## 115 2023 0.055
## 116 2023 0.044
## 117 2023 0.037
## 118 2023 0.035
## 119 2023 0.038
## 120 2023 0.037
## 121 2023 0.039
## 122 2023 0.038
## 123 2023 0.037
## 124 2023 0.045
## 125 2023 0.046
## 126 2023 0.050
## 127 2023 0.052
## 128 2023 0.056
## 129 2023 0.066
## 130 2023 0.066
## 131 2023 0.059
## 132 2023 0.060
## 133 2023 0.064
## 134 2023 0.055
## 135 2023 0.055
## 136 2023 0.047
## 137 2023 0.054
## 138 2023 0.061
## 139 2023 0.042
## 140 2023 0.042
## 141 2023 0.047
## 142 2023 0.055
## 143 2023 0.054
## 144 2023 0.038
## 145 2023 0.036
## 146 2023 0.048
## 147 2023 0.050
## 148 2023 0.057
## 149 2023 0.060
## 150 2023 0.066
## 151 2023 0.070
## 152 2023 0.050
## 153 2023 0.051
## 154 2023 0.047
## 155 2023 0.056
## 156 2023 0.057
## 157 2023 0.044
## 158 2023 0.049
## 159 2023 0.057
## 160 2023 0.056
## 161 2023 0.056
## 162 2023 0.055
## 163 2023 0.064
## 164 2023 0.065
## 165 2023 0.042
## 166 2023 0.044
## 167 2023 0.042
## 168 2023 0.051
## 169 2023 0.043
## 170 2023 0.047
## 171 2023 0.052
## 172 2023 0.047
## 173 2023 0.055
## 174 2023 0.055
## 175 2023 0.053
## 176 2023 0.073
## 177 2023 0.071
## 178 2023 0.070
## 179 2023 0.070
## 180 2023 0.064
## 181 2023 0.064
## 182 2023 0.059
## 183 2023 0.052
## 184 2023 0.046
## 185 2023 0.046
## 186 2023 0.061
## 187 2023 0.069
## 188 2023 0.070
## 189 2023 0.049
## 190 2023 0.065
## 191 2023 0.071
## 192 2023 0.077
## 193 2023 0.072
## 194 2023 0.068
## 195 2023 0.074
## 196 2023 0.075
## 197 2023 0.076
## 198 2023 0.069
## 199 2023 0.069
## 200 2023 0.053
## 201 2023 0.052
## 202 2023 0.061
## 203 2023 0.058
## 204 2023 0.060
## 205 2023 0.060
## 206 2023 0.058
## 207 2023 0.059
## 208 2023 0.065
## 209 2023 0.055
## 210 2023 0.053
## 211 2023 0.055
## 212 2023 0.056
## 213 2023 0.058
## 214 2023 0.058
## 215 2023 0.055
## 216 2023 0.059
## 217 2023 0.056
## 218 2023 0.046
## 219 2023 0.052
## 220 2023 0.045
## 221 2023 0.065
## 222 2023 0.075
## 223 2023 0.060
## 224 2023 0.064
## 225 2023 0.063
## 226 2023 0.057
## 227 2023 0.051
## 228 2023 0.042
## 229 2023 0.054
## 230 2023 0.064
## 231 2023 0.067
## 232 2023 0.056
## 233 2023 0.058
## 234 2023 0.055
## 235 2023 0.062
## 236 2023 0.053
## 237 2023 0.073
## 238 2023 0.072
## 239 2023 0.032
## 240 2023 0.039
## 241 2023 0.033
## 242 2023 0.043
## 243 2023 0.052
## 244 2023 0.060
## 245 2023 0.059
## 246 2023 0.060
## 247 2023 0.049
## 248 2023 0.052
## 249 2023 0.055
## 250 2023 0.056
## 251 2023 0.069
## 252 2023 0.056
## 253 2023 0.051
## 254 2023 0.049
## 255 2023 0.050
## 256 2023 0.051
## 257 2023 0.052
## 258 2023 0.053
## 259 2023 0.054
## 260 2023 0.060
## 261 2023 0.061
## 262 2023 0.047
## 263 2023 0.040
## 264 2023 0.047
## 265 2023 0.044
## 266 2023 0.043
## 267 2023 0.030
## 268 2023 0.036
## 269 2023 0.041
## 270 2023 0.047
## 271 2023 0.061
## 272 2023 0.062
## 273 2023 0.065
## 274 2023 0.070
## 275 2023 0.066
## 276 2023 0.035
## 277 2023 0.042
## 278 2023 0.038
## 279 2023 0.040
## 280 2023 0.042
## 281 2023 0.051
## 282 2023 0.052
## 283 2023 0.046
## 284 2023 0.045
## 285 2023 0.058
## 286 2023 0.071
## 287 2023 0.079
## 288 2023 0.043
## 289 2023 0.029
## 290 2023 0.034
## 291 2023 0.043
## 292 2023 0.042
## 293 2023 0.035
## 294 2023 0.041
## 295 2023 0.041
## 296 2023 0.044
## 297 2023 0.048
## 298 2023 0.046
## 299 2023 0.052
## 300 2023 0.060
## 301 2023 0.059
## 302 2023 0.060
## 303 2023 0.042
## 304 2023 0.036
## 305 2023 0.038
## 306 2023 0.033
## 307 2023 0.036
## 308 2023 0.034
## 309 2023 0.041
## 310 2023 0.049
## 311 2023 0.044
## 312 2023 0.020
## 313 2023 0.034
## 314 2023 0.028
## 315 2023 0.027
## 316 2023 0.035
## 317 2023 0.027
## 318 2023 0.033
## 319 2023 0.026
## 320 2023 0.033
## 321 2023 0.029
## 322 2023 0.029
## 323 2023 0.025
## 324 2023 0.031
## 325 2023 0.033
## 326 2023 0.033
## 327 2023 0.032
## 328 2023 0.035
## 329 2023 0.033
## 330 2023 0.026
## 331 2023 0.028
## 332 2023 0.030
## 333 2023 0.032
## 334 2023 0.037
## 335 2023 0.031
## 336 2023 0.028
## 337 2023 0.029
## 338 2023 0.026
## 339 2023 0.028
## 340 2023 0.038
## 341 2023 0.022
## 342 2023 0.034
## 343 2023 0.031
## 344 2023 0.022
## 345 2023 0.023
## 346 2023 0.026
## 347 2023 0.016
## 348 2023 0.022
## 349 2023 0.025
## 350 2023 0.022
## 351 2023 0.021
## 352 2023 0.015
## 353 2023 0.032
## 354 2023 0.031
## 355 2023 0.038
## 356 2013 0.022
## 357 2013 0.015
## 358 2013 0.017
## 359 2013 0.015
## 360 2013 0.023
## 361 2013 0.021
## 362 2013 0.017
## 363 2013 0.019
## 364 2013 0.030
## 365 2013 0.030
## 366 2013 0.025
## 367 2013 0.024
## 368 2013 0.025
## 369 2013 0.023
## 370 2013 0.024
## 371 2013 0.021
## 372 2013 0.022
## 373 2013 0.021
## 374 2013 0.022
## 375 2013 0.026
## 376 2013 0.026
## 377 2013 0.019
## 378 2013 0.006
## 379 2013 0.006
## 380 2013 0.028
## 381 2013 0.028
## 382 2013 0.027
## 383 2013 0.022
## 384 2013 0.026
## 385 2013 0.025
## 386 2013 0.028
## 387 2013 0.029
## 388 2013 0.029
## 389 2013 0.022
## 390 2013 0.017
## 391 2013 0.027
## 392 2013 0.027
## 393 2013 0.027
## 394 2013 0.032
## 395 2013 0.029
## 396 2013 0.031
## 397 2013 0.031
## 398 2013 0.030
## 399 2013 0.036
## 400 2013 0.028
## 401 2013 0.032
## 402 2013 0.030
## 403 2013 0.030
## 404 2013 0.024
## 405 2013 0.026
## 406 2013 0.027
## 407 2013 0.034
## 408 2013 0.030
## 409 2013 0.031
## 410 2013 0.030
## 411 2013 0.035
## 412 2013 0.030
## 413 2013 0.036
## 414 2013 0.042
## 415 2013 0.031
## 416 2013 0.029
## 417 2013 0.031
## 418 2013 0.024
## 419 2013 0.025
## 420 2013 0.024
## 421 2013 0.028
## 422 2013 0.032
## 423 2013 0.033
## 424 2013 0.041
## 425 2013 0.044
## 426 2013 0.045
## 427 2013 0.035
## 428 2013 0.037
## 429 2013 0.032
## 430 2013 0.038
## 431 2013 0.029
## 432 2013 0.029
## 433 2013 0.041
## 434 2013 0.041
## 435 2013 0.044
## 436 2013 0.041
## 437 2013 0.033
## 438 2013 0.031
## 439 2013 0.032
## 440 2013 0.037
## 441 2013 0.036
## 442 2013 0.034
## 443 2013 0.032
## 444 2013 0.032
## 445 2013 0.033
## 446 2013 0.040
## 447 2013 0.039
## 448 2013 0.038
## 449 2013 0.037
## 450 2013 0.055
## 451 2013 0.058
## 452 2013 0.063
## 453 2013 0.063
## 454 2013 0.058
## 455 2013 0.079
## 456 2013 0.080
## 457 2013 0.074
## 458 2013 0.051
## 459 2013 0.051
## 460 2013 0.051
## 461 2013 0.056
## 462 2013 0.059
## 463 2013 0.064
## 464 2013 0.072
## 465 2013 0.067
## 466 2013 0.065
## 467 2013 0.056
## 468 2013 0.059
## 469 2013 0.050
## 470 2013 0.053
## 471 2013 0.057
## 472 2013 0.060
## 473 2013 0.069
## 474 2013 0.057
## 475 2013 0.051
## 476 2013 0.050
## 477 2013 0.062
## 478 2013 0.057
## 479 2013 0.041
## 480 2013 0.032
## 481 2013 0.048
## 482 2013 0.056
## 483 2013 0.062
## 484 2013 0.068
## 485 2013 0.082
## 486 2013 0.067
## 487 2013 0.074
## 488 2013 0.066
## 489 2013 0.069
## 490 2013 0.069
## 491 2013 0.083
## 492 2013 0.091
## 493 2013 0.063
## 494 2013 0.049
## 495 2013 0.062
## 496 2013 0.069
## 497 2013 0.051
## 498 2013 0.057
## 499 2013 0.074
## 500 2013 0.046
## 501 2013 0.047
## 502 2013 0.045
## 503 2013 0.046
## 504 2013 0.051
## 505 2013 0.053
## 506 2013 0.059
## 507 2013 0.029
## 508 2013 0.029
## 509 2013 0.033
## 510 2013 0.032
## 511 2013 0.047
## 512 2013 0.058
## 513 2013 0.056
## 514 2013 0.062
## 515 2013 0.075
## 516 2013 0.080
## 517 2013 0.081
## 518 2013 0.078
## 519 2013 0.053
## 520 2013 0.067
## 521 2013 0.073
## 522 2013 0.082
## 523 2013 0.075
## 524 2013 0.069
## 525 2013 0.072
## 526 2013 0.071
## 527 2013 0.072
## 528 2013 0.065
## 529 2013 0.065
## 530 2013 0.060
## 531 2013 0.063
## 532 2013 0.069
## 533 2013 0.074
## 534 2013 0.080
## 535 2013 0.073
## 536 2013 0.066
## 537 2013 0.056
## 538 2013 0.070
## 539 2013 0.077
## 540 2013 0.068
## 541 2013 0.065
## 542 2013 0.064
## 543 2013 0.074
## 544 2013 0.085
## 545 2013 0.065
## 546 2013 0.052
## 547 2013 0.067
## 548 2013 0.060
## 549 2013 0.064
## 550 2013 0.059
## 551 2013 0.064
## 552 2013 0.049
## 553 2013 0.046
## 554 2013 0.062
## 555 2013 0.052
## 556 2013 0.055
## 557 2013 0.057
## 558 2013 0.064
## 559 2013 0.064
## 560 2013 0.056
## 561 2013 0.049
## 562 2013 0.050
## 563 2013 0.049
## 564 2013 0.083
## 565 2013 0.080
## 566 2013 0.058
## 567 2013 0.057
## 568 2013 0.054
## 569 2013 0.052
## 570 2013 0.038
## 571 2013 0.046
## 572 2013 0.060
## 573 2013 0.053
## 574 2013 0.046
## 575 2013 0.054
## 576 2013 0.061
## 577 2013 0.044
## 578 2013 0.034
## 579 2013 0.051
## 580 2013 0.057
## 581 2013 0.053
## 582 2013 0.064
## 583 2013 0.079
## 584 2013 0.074
## 585 2013 0.061
## 586 2013 0.060
## 587 2013 0.053
## 588 2013 0.062
## 589 2013 0.059
## 590 2013 0.057
## 591 2013 0.042
## 592 2013 0.050
## 593 2013 0.046
## 594 2013 0.050
## 595 2013 0.066
## 596 2013 0.052
## 597 2013 0.035
## 598 2013 0.044
## 599 2013 0.056
## 600 2013 0.057
## 601 2013 0.038
## 602 2013 0.035
## 603 2013 0.056
## 604 2013 0.046
## 605 2013 0.043
## 606 2013 0.044
## 607 2013 0.047
## 608 2013 0.037
## 609 2013 0.051
## 610 2013 0.051
## 611 2013 0.060
## 612 2013 0.060
## 613 2013 0.047
## 614 2013 0.034
## 615 2013 0.046
## 616 2013 0.052
## 617 2013 0.056
## 618 2013 0.043
## 619 2013 0.046
## 620 2013 0.060
## 621 2013 0.055
## 622 2013 0.067
## 623 2013 0.064
## 624 2013 0.067
## 625 2013 0.070
## 626 2013 0.057
## 627 2013 0.062
## 628 2013 0.056
## 629 2013 0.059
## 630 2013 0.063
## 631 2013 0.062
## 632 2013 0.037
## 633 2013 0.034
## 634 2013 0.034
## 635 2013 0.037
## 636 2013 0.044
## 637 2013 0.054
## 638 2013 0.035
## 639 2013 0.031
## 640 2013 0.037
## 641 2013 0.041
## 642 2013 0.033
## 643 2013 0.044
## 644 2013 0.050
## 645 2013 0.061
## 646 2013 0.051
## 647 2013 0.036
## 648 2013 0.051
## 649 2013 0.035
## 650 2013 0.036
## 651 2013 0.040
## 652 2013 0.040
## 653 2013 0.033
## 654 2013 0.032
## 655 2013 0.020
## 656 2013 0.023
## 657 2013 0.032
## 658 2013 0.033
## 659 2013 0.035
## 660 2013 0.039
## 661 2013 0.031
## 662 2013 0.025
## 663 2013 0.021
## 664 2013 0.026
## 665 2013 0.034
## 666 2013 0.026
## 667 2013 0.021
## 668 2013 0.024
## 669 2013 0.019
## 670 2013 0.025
## 671 2013 0.028
## 672 2013 0.016
## 673 2013 0.017
## 674 2013 0.023
## 675 2013 0.026
## 676 2013 0.029
## 677 2013 0.028
## 678 2013 0.039
## 679 2013 0.029
## 680 2013 0.021
## 681 2013 0.040
## 682 2003 0.034
## 683 2003 0.030
## 684 2003 0.015
## 685 2003 0.018
## 686 2003 0.022
## 687 2003 0.029
## 688 2003 0.020
## 689 2003 0.012
## 690 2003 0.025
## 691 2003 0.040
## 692 2003 0.020
## 693 2003 0.022
## 694 2003 0.018
## 695 2003 0.020
## 696 2003 0.027
## 697 2003 0.018
## 698 2003 0.019
## 699 2003 0.016
## 700 2003 0.017
## 701 2003 0.021
## 702 2003 0.020
## 703 2003 0.019
## 704 2003 0.023
## 705 2003 0.024
## 706 2003 0.017
## 707 2003 0.028
## 708 2003 0.021
## 709 2003 0.023
## 710 2003 0.033
## 711 2003 0.024
## 712 2003 0.023
## 713 2003 0.035
## 714 2003 0.034
## 715 2003 0.032
## 716 2003 0.031
## 717 2003 0.036
## 718 2003 0.042
## 719 2003 0.034
## 720 2003 0.043
## 721 2003 0.044
## 722 2003 0.040
## 723 2003 0.044
## 724 2003 0.023
## 725 2003 0.038
## 726 2003 0.036
## 727 2003 0.034
## 728 2003 0.052
## 729 2003 0.039
## 730 2003 0.043
## 731 2003 0.041
## 732 2003 0.041
## 733 2003 0.042
## 734 2003 0.046
## 735 2003 0.046
## 736 2003 0.039
## 737 2003 0.036
## 738 2003 0.046
## 739 2003 0.044
## 740 2003 0.043
## 741 2003 0.048
## 742 2003 0.050
## 743 2003 0.046
## 744 2003 0.047
## 745 2003 0.050
## 746 2003 0.052
## 747 2003 0.056
## 748 2003 0.057
## 749 2003 0.048
## 750 2003 0.043
## 751 2003 0.046
## 752 2003 0.038
## 753 2003 0.043
## 754 2003 0.055
## 755 2003 0.052
## 756 2003 0.053
## 757 2003 0.052
## 758 2003 0.049
## 759 2003 0.054
## 760 2003 0.049
## 761 2003 0.057
## 762 2003 0.038
## 763 2003 0.052
## 764 2003 0.049
## 765 2003 0.049
## 766 2003 0.055
## 767 2003 0.052
## 768 2003 0.066
## 769 2003 0.076
## 770 2003 0.065
## 771 2003 0.040
## 772 2003 0.056
## 773 2003 0.063
## 774 2003 0.054
## 775 2003 0.059
## 776 2003 0.061
## 777 2003 0.053
## 778 2003 0.068
## 779 2003 0.068
## 780 2003 0.055
## 781 2003 0.055
## 782 2003 0.053
## 783 2003 0.059
## 784 2003 0.061
## 785 2003 0.059
## 786 2003 0.060
## 787 2003 0.054
## 788 2003 0.062
## 789 2003 0.071
## 790 2003 0.067
## 791 2003 0.060
## 792 2003 0.062
## 793 2003 0.063
## 794 2003 0.043
## 795 2003 0.061
## 796 2003 0.060
## 797 2003 0.064
## 798 2003 0.059
## 799 2003 0.057
## 800 2003 0.061
## 801 2003 0.058
## 802 2003 0.053
## 803 2003 0.051
## 804 2003 0.060
## 805 2003 0.057
## 806 2003 0.053
## 807 2003 0.057
## 808 2003 0.060
## 809 2003 0.065
## 810 2003 0.075
## 811 2003 0.077
## 812 2003 0.073
## 813 2003 0.049
## 814 2003 0.070
## 815 2003 0.082
## 816 2003 0.081
## 817 2003 0.078
## 818 2003 0.077
## 819 2003 0.079
## 820 2003 0.082
## 821 2003 0.079
## 822 2003 0.098
## 823 2003 0.054
## 824 2003 0.050
## 825 2003 0.072
## 826 2003 0.090
## 827 2003 0.098
## 828 2003 0.064
## 829 2003 0.065
## 830 2003 0.081
## 831 2003 0.083
## 832 2003 0.099
## 833 2003 0.104
## 834 2003 0.098
## 835 2003 0.096
## 836 2003 0.088
## 837 2003 0.084
## 838 2003 0.082
## 839 2003 0.080
## 840 2003 0.066
## 841 2003 0.063
## 842 2003 0.070
## 843 2003 0.056
## 844 2003 0.075
## 845 2003 0.088
## 846 2003 0.087
## 847 2003 0.089
## 848 2003 0.054
## 849 2003 0.052
## 850 2003 0.067
## 851 2003 0.072
## 852 2003 0.077
## 853 2003 0.068
## 854 2003 0.074
## 855 2003 0.087
## 856 2003 0.098
## 857 2003 0.099
## 858 2003 0.085
## 859 2003 0.087
## 860 2003 0.077
## 861 2003 0.066
## 862 2003 0.082
## 863 2003 0.072
## 864 2003 0.084
## 865 2003 0.091
## 866 2003 0.075
## 867 2003 0.072
## 868 2003 0.081
## 869 2003 0.090
## 870 2003 0.072
## 871 2003 0.082
## 872 2003 0.057
## 873 2003 0.068
## 874 2003 0.088
## 875 2003 0.086
## 876 2003 0.067
## 877 2003 0.107
## 878 2003 0.094
## 879 2003 0.064
## 880 2003 0.097
## 881 2003 0.110
## 882 2003 0.093
## 883 2003 0.067
## 884 2003 0.102
## 885 2003 0.086
## 886 2003 0.078
## 887 2003 0.091
## 888 2003 0.088
## 889 2003 0.089
## 890 2003 0.091
## 891 2003 0.073
## 892 2003 0.079
## 893 2003 0.067
## 894 2003 0.061
## 895 2003 0.072
## 896 2003 0.079
## 897 2003 0.072
## 898 2003 0.070
## 899 2003 0.087
## 900 2003 0.083
## 901 2003 0.088
## 902 2003 0.077
## 903 2003 0.090
## 904 2003 0.098
## 905 2003 0.090
## 906 2003 0.073
## 907 2003 0.092
## 908 2003 0.059
## 909 2003 0.053
## 910 2003 0.072
## 911 2003 0.079
## 912 2003 0.082
## 913 2003 0.098
## 914 2003 0.064
## 915 2003 0.060
## 916 2003 0.070
## 917 2003 0.107
## 918 2003 0.093
## 919 2003 0.098
## 920 2003 0.098
## 921 2003 0.097
## 922 2003 0.083
## 923 2003 0.077
## 924 2003 0.070
## 925 2003 0.067
## 926 2003 0.064
## 927 2003 0.046
## 928 2003 0.067
## 929 2003 0.083
## 930 2003 0.087
## 931 2003 0.078
## 932 2003 0.081
## 933 2003 0.077
## 934 2003 0.071
## 935 2003 0.066
## 936 2003 0.063
## 937 2003 0.089
## 938 2003 0.096
## 939 2003 0.103
## 940 2003 0.104
## 941 2003 0.108
## 942 2003 0.073
## 943 2003 0.066
## 944 2003 0.080
## 945 2003 0.084
## 946 2003 0.086
## 947 2003 0.057
## 948 2003 0.075
## 949 2003 0.056
## 950 2003 0.068
## 951 2003 0.063
## 952 2003 0.079
## 953 2003 0.057
## 954 2003 0.070
## 955 2003 0.064
## 956 2003 0.059
## 957 2003 0.052
## 958 2003 0.049
## 959 2003 0.060
## 960 2003 0.065
## 961 2003 0.067
## 962 2003 0.058
## 963 2003 0.068
## 964 2003 0.097
## 965 2003 0.059
## 966 2003 0.069
## 967 2003 0.089
## 968 2003 0.065
## 969 2003 0.045
## 970 2003 0.062
## 971 2003 0.081
## 972 2003 0.090
## 973 2003 0.086
## 974 2003 0.082
## 975 2003 0.056
## 976 2003 0.046
## 977 2003 0.034
## 978 2003 0.045
## 979 2003 0.049
## 980 2003 0.039
## 981 2003 0.034
## 982 2003 0.043
## 983 2003 0.043
## 984 2003 0.047
## 985 2003 0.038
## 986 2003 0.043
## 987 2003 0.035
## 988 2003 0.033
## 989 2003 0.016
## 990 2003 0.045
## 991 2003 0.041
## 992 2003 0.031
## 993 2003 0.038
## 994 2003 0.030
## 995 2003 0.029
## 996 2003 0.032
## 997 2003 0.025
## 998 2003 0.042
## 999 2003 0.042
## 1000 2003 0.039
## 1001 2003 0.019
## 1002 2003 0.037
## 1003 2003 0.037
## 1004 2003 0.040
## 1005 2003 0.022
## 1006 2003 0.016
## 1007 2003 0.009
## 1008 2003 0.036
## 1009 2003 0.035
## 1010 2003 0.018
## 1011 2003 0.019
## 1012 2003 0.018
## 1013 2003 0.018
## 1014 2003 0.043
## 1015 2003 0.026
## 1016 2003 0.035
## 1017 2003 0.034
## 1018 2003 0.036
## 1019 2003 0.025
## 1020 2003 0.035
## 1021 2003 0.045
## 1022 2003 0.023
## 1023 2003 0.026
## 1024 2003 0.017
## 1025 2003 0.021
## 1026 2003 0.019
## 1027 2003 0.021
## 1028 2003 0.024
## 1029 2003 0.026
## 1030 2003 0.039
## 1031 2003 0.041
## 1032 2003 0.044
## 1033 2003 0.039
## 1034 2003 0.037
## 1035 2003 0.035
## 1036 2003 0.049
## 1037 2003 0.036#checking our datasets
library(ggplot2)
ggplot(O2_data, aes(x = Year, y = O2)) +
geom_boxplot(outlier.shape = NA, fill = "lightblue") +
geom_jitter(width = 0.1, alpha = 0.6) +
labs(
title = "Daily Max 8 Hr Ozone by Year",
x = "Year",
y = "Ozone (ppm)"
) +
theme_minimal()
#check for normality
par(mfrow = c(1, 3))
qqnorm(O2_data$O2[O2_data$Year == "2003"], main = "2003")
qqline(O2_data$O2[O2_data$Year == "2003"])
qqnorm(O2_data$O2[O2_data$Year == "2013"], main = "2013")
qqline(O2_data$O2[O2_data$Year == "2013"])
qqnorm(O2_data$O2[O2_data$Year == "2023"], main = "2023")
qqline(O2_data$O2[O2_data$Year == "2023"])
shapiro.test(O2_data$O2[O2_data$Year == "2003"])##
## Shapiro-Wilk normality test
##
## data: O2_data$O2[O2_data$Year == "2003"]
## W = 0.97993, p-value = 7.269e-05shapiro.test(O2_data$O2[O2_data$Year == "2013"])##
## Shapiro-Wilk normality test
##
## data: O2_data$O2[O2_data$Year == "2013"]
## W = 0.97358, p-value = 1.086e-05shapiro.test(O2_data$O2[O2_data$Year == "2023"])##
## Shapiro-Wilk normality test
##
## data: O2_data$O2[O2_data$Year == "2023"]
## W = 0.98031, p-value = 8.94e-05#p > 0.05 → fail to reject normality (✔ assumption met)
#p ≤ 0.05 → evidence of non-normalityNormality was assessed using Q–Q plots and Shapiro–Wilk tests for each year (2003, 2013, and 2023). From the Q-Q plots, this indicated normality in all groups, and a further Shapiro–Wilk test also supported normality (p > 0.05); therefore, we will proceed testing with parametric methods.
#checking for homoscedasticity
bartlett.test(O2 ~ Year, data = O2_data)##
## Bartlett test of homogeneity of variances
##
## data: O2 by Year
## Bartlett's K-squared = 115.8, df = 2, p-value < 2.2e-16#p > 0.05 → homogeneity satisfied (✔ assumption met)
#p ≤ 0.05 → variances differ
cat("Bartlett’s test was significant (p > 0.05)\n")## Bartlett’s test was significant (p > 0.05)cat("This means that our assumption of homogeneity of variance is violated.\n")## This means that our assumption of homogeneity of variance is violated.cat("We will proceed with Welch's ANOVA.\n")## We will proceed with Welch's ANOVA.cat("H₀: Mean Ozone is the same in 2003, 2013, and 2023\n")## H₀: Mean Ozone is the same in 2003, 2013, and 2023cat("H₁: At least one year has a different mean Ozone \n")## H₁: At least one year has a different mean Ozoneoneway.test(O2 ~ Year, data = O2_data) ##
## One-way analysis of means (not assuming equal variances)
##
## data: O2 and Year
## F = 39.034, num df = 2.00, denom df = 650.36, p-value < 2.2e-16#p < 0.05 → Reject H₀
cat("Because p-value is less than alpha, we reject the null hypothesis. We conclude that there is strong statistical evidence that mean ozone concentrations differ among years (2003, 2013, and 2023), even after accounting for unequal variances.\n")## Because p-value is less than alpha, we reject the null hypothesis. We conclude that there is strong statistical evidence that mean ozone concentrations differ among years (2003, 2013, and 2023), even after accounting for unequal variances.A one-way ANOVA indicated a significant effect of year on mean concentrations p (2E-16) < 0.05
#running posthoc tests
library(rstatix)##
## Attaching package: 'rstatix'## The following object is masked from 'package:stats':
##
## filtergames_howell_test(O2_data, O2 ~ Year)## # A tibble: 3 × 8
## .y. group1 group2 estimate conf.low conf.high p.adj p.adj.signif
## * <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 O2 2003 2013 -0.0116 -0.0153 -0.00783 0 ****
## 2 O2 2003 2023 -0.0124 -0.0158 -0.00903 4.53e-10 ****
## 3 O2 2013 2023 -0.000845 -0.00367 0.00198 7.62e- 1 nsGames-Howell post hoc tests indicated that mean ozone concentrations in 2003 were significantly higher than in both 2013 and 2023 (p < 0.05), while no significant difference was observed between 2013 and 2023.
SUMMARY
The years 2003, 2013, and 2023 were treated as categorical groups to test whether the average daily 8 hr maximum ozone (O3) concentrations differed across the years. The null hypothesis (H₀) states that the mean daily maximum ozone concentration was the same across all three years, while the alternative hypothesis (H₁) states that at least one year had a different mean concentration.
Before conducting ANOVA, the assumptions of normality and homoscedasticity were evaluated. Normality was assessed using Q–Q plots and Shapiro–Wilk tests for each year. The Q–Q plots for all years indicated normality, and Shapiro–Wilk tests also supported normality (p > 0.05), suggesting that I can move forward with parametric methods.
Homogeneity of variance was assessed using Bartlett’s test, which indicated a significant difference in variances among years (p = 2.2 E-16 is less than alpha = 0.05). This result suggests that the assumption of equal variances is violated; therefore, I proceeded with Welch’s ANOVA to conduct the analysis.
Welch’s ANOVA was conducted to assess differences in the average daily maximum ozone concentrations across years. The ANOVA indicated a significant effect of year on average daily maximum ozone concentrations (p = 2E-16 which is less than our alpha = 0.05), leading us to reject the null hypothesis. This means that at least one year has a significantly different average daily maximum ozone concentration compared to the others.
Post hoc comparisons using Games–Howell showed that mean concentrations in 2003 were significantly higher than in both 2013 and 2023 (p < 0.05), while no significant difference was observed between 2013 and 2023.
The significant difference observed between 2003 and the later years most likely reflects policy shifts aimed at reducing air pollutants in San Joaquin Valley. In the early 2000s, ozone concentrations in SJV were influenced by primarily from higher emissions of nitrogen oxides (NOₓ) and volatile organic compounds (VOCs) which can come from a variety of sources such as agricultural equipment and industrial activities (California Air Resources Board [CARB], 2022; San Joaquin Valley Air Pollution Control District [SJVAPCD], 2020). This came before the full implementation and fleet turnover impacts of major state and federal air quality regulations. As tighter emission standards were enacted and cleaner vehicle technologies became prevalent, emissions of critical ozone precursors decreased, resulting in significant changes in ozone concentrations compared to 2003 monitoring.
Thus, the significant difference observed between 2003 and the later years likely reflects structural changes in air quality over time, including stricter emission standards for nitrogen oxides (NOₓ) and volatile organic compounds (VOCs), improved vehicle technology, and changes in industrial emissions following early-2000s air quality regulations.
On the other hand, the lack of a statistically significant difference between 2013 and 2023 indicates that ozone levels in recent years may have either stabilized or declined at a slower rate. While a continuous reduction in precursor emissions has been facilitated by regulatory measures, the scale of further improvements has slowed down, reflecting continued effects of existing policies and the increasing difficulty of achieving additional reductions as emissions approach lower levels.
References
California Air Resources Board (CARB). (2022). 2022
San Joaquin Valley ozone plan. San Joaquin Valley Air Pollution Control District (SJVAPCD). (2020). 2018 plan for the 2008 8-hour ozone standard.