FreeCalc sample size estimation Inputs Test sensitivity 0.9 Test specificity 0.95 Population size 1,00E+06 Design prevalence 0.05 Diseased elements 50000 Analysis method Simple binomial (large population) Target Type I error 0.05 Target Type II error 0.05 Population threshold for infinite probability formula 10000 Maximum sample size 3200 Results Required sample size: 398 Cut-point number of reactors: 27 Type I error: 0.0489 Type II error: 0.0456 Herd-level sensitivity: 0.9511 Herd-level specificity: 0.9544 Interpretation: If a random sample of 398 units is taken from a population of 1e+06 and 27 or fewer reactors are found, the probability that the population is diseased at a prevalence of 0.05 is 0.0489. Method: Simple binomial (large population) Detailed Results 1 1 0.0925 0.95 0 0.9075 0.05 2 100 0.447 0.9718 9 0.553 0.0282 3 200 0.7632 0.9556 15 0.2368 0.0444 4 300 0.8968 0.9514 21 0.1032 0.0486 5 400 0.9541 0.952 27 0.0459 0.048 6 301 0.8572 0.9698 22 0.1428 0.0302 7 302 0.8612 0.9689 22 0.1388 0.0311 8 303 0.865 0.9678 22 0.135 0.0322 9 304 0.8688 0.9668 22 0.1312 0.0332 10 305 0.8725 0.9657 22 0.1275 0.0343 11 306 0.8761 0.9646 22 0.1239 0.0354 12 307 0.8797 0.9635 22 0.1203 0.0365 13 308 0.8831 0.9624 22 0.1169 0.0376 14 309 0.8865 0.9612 22 0.1135 0.0387999999999999 15 310 0.8898 0.96 22 0.1102 0.04 16 311 0.893 0.9588 22 0.107 0.0412 17 312 0.8962 0.9575 22 0.1038 0.0425 18 313 0.8993 0.9562 22 0.1007 0.0438 19 314 0.9023 0.9549 22 0.0977 0.0451 20 315 0.9052 0.9536 22 0.0948 0.0464 21 316 0.9081 0.9522 22 0.0919 0.0478 22 317 0.9109 0.9508 22 0.0891 0.0492 23 318 0.876 0.9691 23 0.124 0.0309 24 319 0.8794 0.9681 23 0.1206 0.0319 25 320 0.8828 0.9671 23 0.1172 0.0329 26 321 0.8862 0.9661 23 0.1138 0.0339 27 322 0.8894 0.965 23 0.1106 0.035 28 323 0.8926 0.9639 23 0.1074 0.0361 29 324 0.8957 0.9628 23 0.1043 0.0372 30 325 0.8987 0.9617 23 0.1013 0.0383 31 326 0.9017 0.9605 23 0.0983 0.0395 32 327 0.9046 0.9594 23 0.0954 0.0406 33 328 0.9074 0.9582 23 0.0926 0.0418 34 329 0.9102 0.9569 23 0.0898 0.0431 35 330 0.9129 0.9557 23 0.0871 0.0443 36 331 0.9155 0.9544 23 0.0845 0.0456 37 332 0.9181 0.9531 23 0.0819 0.0469 38 333 0.9205 0.9517 23 0.0795 0.0483 39 334 0.923 0.9504 23 0.077 0.0496 40 335 0.8923 0.9684 24 0.1077 0.0316 41 336 0.8953 0.9675 24 0.1047 0.0325 42 337 0.8983 0.9665 24 0.1017 0.0335 43 338 0.9012 0.9654 24 0.0988 0.0346 44 339 0.9041 0.9644 24 0.0959 0.0356 45 340 0.9069 0.9633 24 0.0931 0.0367 46 341 0.9096 0.9622 24 0.0904 0.0377999999999999 47 342 0.9123 0.9611 24 0.0877 0.0389 48 343 0.9149 0.96 24 0.0851 0.04 49 344 0.9174 0.9588 24 0.0826 0.0412 50 345 0.9199 0.9577 24 0.0801 0.0423 51 346 0.9223 0.9564 24 0.0777 0.0436 52 347 0.9246 0.9552 24 0.0754 0.0448 53 348 0.9269 0.9539 24 0.0731 0.0461 54 349 0.9291 0.9527 24 0.0709 0.0473 55 350 0.9313 0.9513 24 0.0687 0.0487 56 351 0.9334 0.95 24 0.0666 0.05 57 352 0.9064 0.9679 25 0.0936 0.0321 58 353 0.9091 0.9669 25 0.0909 0.0331 59 354 0.9117 0.9659 25 0.0883 0.0341 60 355 0.9143 0.9649 25 0.0857 0.0351 61 356 0.9168 0.9639 25 0.0832 0.0361 62 357 0.9192 0.9628 25 0.0808 0.0372 63 358 0.9216 0.9618 25 0.0784 0.0382 64 359 0.924 0.9607 25 0.076 0.0393 65 360 0.9262 0.9596 25 0.0738 0.0404 66 361 0.9284 0.9584 25 0.0716 0.0416 67 362 0.9306 0.9573 25 0.0694 0.0427 68 363 0.9327 0.9561 25 0.0673 0.0439 69 364 0.9347 0.9549 25 0.0653 0.0451 70 365 0.9367 0.9536 25 0.0633 0.0464 71 366 0.9387 0.9524 25 0.0613 0.0476 72 367 0.9406 0.9511 25 0.0594 0.0489000000000001 73 368 0.9163 0.9683 26 0.0837 0.0317 74 369 0.9187 0.9674 26 0.0813 0.0326 75 370 0.9211 0.9664 26 0.0789 0.0336 76 371 0.9234 0.9655 26 0.0766 0.0345 77 372 0.9256 0.9645 26 0.0744 0.0355 78 373 0.9278 0.9635 26 0.0722 0.0365 79 374 0.93 0.9624 26 0.07 0.0376 80 375 0.9321 0.9614 26 0.0679 0.0386 81 376 0.9341 0.9603 26 0.0659 0.0397 82 377 0.9361 0.9592 26 0.0639 0.0408 83 378 0.938 0.9581 26 0.062 0.0419 84 379 0.9399 0.9569 26 0.0601 0.0431 85 380 0.9417 0.9558 26 0.0583 0.0442 86 381 0.9435 0.9546 26 0.0565 0.0454 87 382 0.9452 0.9534 26 0.0548 0.0466 88 383 0.9469 0.9521 26 0.0531 0.0479000000000001 89 384 0.9486 0.9509 26 0.0514 0.0491 90 385 0.9273 0.9679 27 0.0727 0.0321 91 386 0.9294 0.967 27 0.0706 0.033 92 387 0.9315 0.966 27 0.0685 0.034 93 388 0.9335 0.9651 27 0.0665 0.0349 94 389 0.9355 0.9641 27 0.0645 0.0359 95 390 0.9374 0.9631 27 0.0626 0.0369 96 391 0.9393 0.9621 27 0.0607 0.0379 97 392 0.9411 0.9611 27 0.0589 0.0389 98 393 0.9429 0.96 27 0.0571 0.04 99 394 0.9446 0.9589 27 0.0554 0.0411 100 395 0.9463 0.9578 27 0.0537 0.0422 101 396 0.9479 0.9567 27 0.0521 0.0433 102 397 0.9495 0.9556 27 0.0505 0.0444 103 398 0.9511 0.9544 27 0.0489 0.0456