Dynamic Data Table Bayes' Rule Calculator Patients Tested: 10000 Event A Patient has Covid Data Table Posteriors: P(Column|Row) Posterior Formulas An uncertain event (eg. having Covid) Covid Not Covid Total P(Test Result) Covid Not Covid Total Covid Not Covid Event B Outcome of a Covid Test Positive 280 192 472 0.0472 Positive 0.593 0.407 1 Positive =L4/N4 =M4/N4 An event that included information about A (eg. a Covid test) Negative 120 9408 9528 0.9528 Negative 0.013 0.987 1 Negative =L5/N5 =M5/N5 Total 400 9600 10000 1 Prior: P(A) 0.04 False Negative Rate Sensitivity = True Positive Rate 0.7 0.3 P(B|A), the probability of a positive test result, given that Covid is present in the patient False Positive Rate Specificity = True Negative Rate 0.98 0.02 P(not B | not A), the probability of a negative test result, given that the patient does not have Covid Covid-19 [SERIES NAME]: [VALUE] [SERIES NAME]: [VALUE] Tested Positive for Covid-19 Tested Negative for Covid-19 280 120 Not Covid-19 [SERIES NAME]: [VALUE] [SERIES NAME]: [VALUE] Tested Positive for Covid-19 Tested Negative for Covid-19 192 9408 Uncertain Prior Bayes' Rule Calculator Sensitivity 0.7 Population 10000 Out of all Covid cases, how many will test positive? The total number of people tested. Specificity 0.98 Prior Probability Out of all Non-Covid cases, how many will test negative? What fraction of people tested do we expect to have Covid? Prior Probability # People with Covid (C) Positive + C Positive + not C Negative + C Negative + not C Total Positives Total Negatives PPV NPV 0 0 0 200 0 9800 200 9800 0.000 1.000 0.01 100 70 198 30 9702 268 9732 0.261 0.997 0.02 200 140 196 60 9604 336 9664 0.417 0.994 0.03 300 210 194 90 9506 404 9596 0.520 0.991 0.04 400 280 192 120 9408 472 9528 0.593 0.987 0.05 500 350 190 150 9310 540 9460 0.648 0.984 0.06 600 420 188 180 9212 608 9392 0.691 0.981 0.07 700 490 186 210 9114 676 9324 0.725 0.977 0.08 800 560 184 240 9016 744 9256 0.753 0.974 0.09 900 630 182 270 8918 812 9188 0.776 0.971 0.1 1000 700 180 300 8820 880 9120 0.795 0.967 0.11 1100 770 178 330 8722 948 9052 0.812 0.964 0.12 1200 840 176 360 8624 1016 8984 0.827 0.960 0.13 1300 910 174 390 8526 1084 8916 0.839 0.956 0.14 1400 980 172 420 8428 1152 8848 0.851 0.953 0.15 1500 1050 170 450 8330 1220 8780 0.861 0.949 0.16 1600 1120 168 480 8232 1288 8712 0.870 0.945 0.17 1700 1190 166 510 8134 1356 8644 0.878 0.941 0.18 1800 1260 164 540 8036 1424 8576 0.885 0.937 0.19 1900 1330 162 570 7938 1492 8508 0.891 0.933 0.2 2000 1400 160 600 7840 1560 8440 0.897 0.929 0.21 2100 1470 158 630 7742 1628 8372 0.903 0.925 0.22 2200 1540 156 660 7644 1696 8304 0.908 0.921 0.23 2300 1610 154 690 7546 1764 8236 0.913 0.916 0.24 2400 1680 152 720 7448 1832 8168 0.917 0.912 0.25 2500 1750 150 750 7350 1900 8100 0.921 0.907 0.26 2600 1820 148 780 7252 1968 8032 0.925 0.903 0.27 2700 1890 146 810 7154 2036 7964 0.928 0.898 0.28 2800 1960 144 840 7056 2104 7896 0.932 0.894 0.29 2900 2030 142 870 6958 2172 7828 0.935 0.889 0.3 3000 2100 140 900 6860 2240 7760 0.938 0.884 0.31 3100 2170 138 930 6762 2308 7692 0.940 0.879 0.32 3200 2240 136 960 6664 2376 7624 0.943 0.874 0.33 3300 2310 134 990 6566 2444 7556 0.945 0.869 0.34 3400 2380 132 1020 6468 2512 7488 0.947 0.864 0.35 3500 2450 130 1050 6370 2580 7420 0.950 0.858 0.36 3600 2520 128 1080 6272 2648 7352 0.952 0.853 0.37 3700 2590 126 1110 6174 2716 7284 0.954 0.848 0.38 3800 2660 124 1140 6076 2784 7216 0.955 0.842 0.39 3900 2730 122 1170 5978 2852 7148 0.957 0.836 0.4 4000 2800 120 1200 5880 2920 7080 0.959 0.831 0.41 4100 2870 118 1230 5782 2988 7012 0.961 0.825 0.42 4200 2940 116 1260 5684 3056 6944 0.962 0.819 0.43 4300 3010 114 1290 5586 3124 6876 0.964 0.812 0.44 4400 3080 112 1320 5488 3192 6808 0.965 0.806 0.45 4500 3150 110 1350 5390 3260 6740 0.966 0.800 0.46 4600 3220 108 1380 5292 3328 6672 0.968 0.793 0.47 4700 3290 106 1410 5194 3396 6604 0.969 0.786 0.48 4800 3360 104 1440 5096 3464 6536 0.970 0.780 0.49 4900 3430 102 1470 4998 3532 6468 0.971 0.773 0.5 5000 3500 100 1500 4900 3600 6400 0.972 0.766 0.51 5100 3570 98 1530 4802 3668 6332 0.973 0.758 0.52 5200 3640 96 1560 4704 3736 6264 0.974 0.751 0.53 5300 3710 94 1590 4606 3804 6196 0.975 0.743 0.54 5400 3780 92 1620 4508 3872 6128 0.976 0.736 0.55 5500 3850 90 1650 4410 3940 6060 0.977 0.728 0.56 5600 3920 88 1680 4312 4008 5992 0.978 0.720 0.57 5700 3990 86 1710 4214 4076 5924 0.979 0.711 0.58 5800 4060 84 1740 4116 4144 5856 0.980 0.703 0.59 5900 4130 82 1770 4018 4212 5788 0.981 0.694 0.6 6000 4200 80 1800 3920 4280 5720 0.981 0.685 0.61 6100 4270 78 1830 3822 4348 5652 0.982 0.676 0.62 6200 4340 76 1860 3724 4416 5584 0.983 0.667 0.63 6300 4410 74 1890 3626 4484 5516 0.983 0.657 0.64 6400 4480 72 1920 3528 4552 5448 0.984 0.648 0.65 6500 4550 70 1950 3430 4620 5380 0.985 0.638 0.66 6600 4620 68 1980 3332 4688 5312 0.985 0.627 0.67 6700 4690 66 2010 3234 4756 5244 0.986 0.617 0.68 6800 4760 64 2040 3136 4824 5176 0.987 0.606 0.69 6900 4830 62 2070 3038 4892 5108 0.987 0.595 0.7 7000 4900 60 2100 2940 4960 5040 0.988 0.583 0.71 7100 4970 58 2130 2842 5028 4972 0.988 0.572 0.72 7200 5040 56 2160 2744 5096 4904 0.989 0.560 0.73 7300 5110 54 2190 2646 5164 4836 0.990 0.547 0.74 7400 5180 52 2220 2548 5232 4768 0.990 0.534 0.75 7500 5250 50 2250 2450 5300 4700 0.991 0.521 0.76 7600 5320 48 2280 2352 5368 4632 0.991 0.508 0.77 7700 5390 46 2310 2254 5436 4564 0.992 0.494 0.78 7800 5460 44 2340 2156 5504 4496 0.992 0.480 0.79 7900 5530 42 2370 2058 5572 4428 0.992 0.465 0.8 8000 5600 40 2400 1960 5640 4360 0.993 0.450 0.81 8100 5670 38 2430 1862 5708 4292 0.993 0.434 0.82 8200 5740 36 2460 1764 5776 4224 0.994 0.418 0.83 8300 5810 34 2490 1666 5844 4156 0.994 0.401 0.84 8400 5880 32 2520 1568 5912 4088 0.995 0.384 0.85 8500 5950 30 2550 1470 5980 4020 0.995 0.366 0.86 8600 6020 28 2580 1372 6048 3952 0.995 0.347 0.87 8700 6090 26 2610 1274 6116 3884 0.996 0.328 0.88 8800 6160 24 2640 1176 6184 3816 0.996 0.308 0.89 8900 6230 22 2670 1078 6252 3748 0.996 0.288 0.9 9000 6300 20 2700 980 6320 3680 0.997 0.266 0.91 9100 6370 18 2730 882 6388 3612 0.997 0.244 0.92 9200 6440 16 2760 784 6456 3544 0.998 0.221 0.93 9300 6510 14 2790 686 6524 3476 0.998 0.197 0.94 9400 6580 12 2820 588 6592 3408 0.998 0.173 0.95 9500 6650 10 2850 490 6660 3340 0.998 0.147 0.96 9600 6720 8 2880 392 6728 3272 0.999 0.120 0.97 9700 6790 6 2910 294 6796 3204 0.999 0.092 0.98 9800 6860 4 2940 196 6864 3136 0.999 0.063 0.99 9900 6930 2 2970 98 6932 3068 1.000 0.032 1 10000 7000 0 3000 0 7000 3000 1.000 0.000 Posterior Probabilities for Varying Prior PPV 0 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28000000000000003 0.28999999999999998 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55000000000000004 0.56000000000000005 0.56999999999999995 0.57999999999999996 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 0 0.26119402985074608 0.41666666666666646 0.5198019801980196 0.5932203389830506 0.64814814814814792 0.69078947368421029 0.72485207100591698 0.75268817204301053 0.77586206896551702 0.7954545454545453 0.81223628691983107 0.82677165354330695 0.83948339483394818 0.85069444444444442 0.86065573770491788 0.86956521739130421 0.87758112094395269 0.88483146067415719 0.89142091152814995 0.89743589743589736 0.90294840294840284 0.90801886792452813 0.91269841269841256 0.91703056768558944 0.92105263157894723 0.92479674796747957 0.92829076620825135 0.93155893536121659 0.93462246777163893 0.9375 0.9402079722703639 0.9427609427609428 0.94517184942716859 0.94745222929936301 0.94961240310077522 0.95166163141993954 0.95360824742268047 0.95545977011494254 0.95722300140252459 0.95890410958904104 0.96050870147255685 0.9620418848167539 0.96350832266325226 0.96491228070175439 0.96625766871165641 0.96754807692307687 0.96878680800942285 0.96997690531177827 0.97112117780294449 0.97222222222222221 0.97328244274809161 0.97430406852248397 0.97528916929547849 0.97623966942148765 0.97715736040609136 0.97804391217564868 0.97890088321884194 0.9797297297297296 0.98053181386514721 0.98130841121495327 0.98206071757129709 0.98278985507246375 0.98349687778768957 0.98418277680140598 0.98484848484848486 0.98549488054607504 0.9861227922624054 0.98673300165837474 0.98732624693376947 0.98790322580645162 0.98846459824980115 0.98901098901098905 0.98954298993028655 0.99006116207951067 0.99056603773584906 0.99105812220566314 0.99153789551140548 0.99200581395348841 0.99246231155778897 0.99290780141843971 0.99334267694463907 0.99376731301939059 0.99418206707734424 0.99458728010825437 0.99498327759197325 0.99537037037037035 0.99574885546108571 0.99611901681759374 0.99648112603966732 0.99683544303797467 0.99718221665623041 0.99752168525402729 0.99785407725321884 0.99817961165048541 0.99849849849849848 0.99881093935790721 0.99911712772218952 0.99941724941724941 0.99971148297749568 1 NPV 0 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28000000000000003 0.28999999999999998 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55000000000000004 0.56000000000000005 0.56999999999999995 0.57999999999999996 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 1 0.99691738594327994 0.99379139072847678 0.99062109212171734 0.9874055415617129 0.9841437632135307 0.98083475298126066 0.97747747747747749 0.97407087294727746 0.97061384414453633 0.96710526315789469 0.96354396818382682 0.95992876224398926 0.95625841184387617 0.95253164556962022 0.94874715261958997 0.94490358126721763 0.94099953725127261 0.93703358208955223 0.93300423131170662 0.92890995260663511 0.92474916387959871 0.92052023121387283 0.91622146673142302 0.91185112634671894 0.90740740740740744 0.90288844621513942 0.89829231541938726 0.8936170212765957 0.88886050076647927 0.884020618556701 0.87909516380655228 0.87408184679958023 0.86897829539438853 0.86378205128205132 0.85849056603773588 0.85310119695320996 0.84761120263591438 0.84 20177383592018 0.83631785114717405 0.83050847457627119 0.8245864232743868 0.81854838709677424 0.81239092495637 0.80611045828437133 0.79970326409495551 0.79316546762589923 0.78649303452453057 0.7796817625458996 0.77272727272727271 0.765625 0.75837018319646243 0.75095785440613028 0.74338282763072949 0.73563968668407309 0.7277227722772277 0.71962616822429892 0.71134368669817694 0.70286885245901642 0.69419488597097445 0.68531468531468531 0.67622080679405516 0.66690544412607455 0.65736040609137059 0.64757709251101325 0.63754646840148699 0.62725903614457834 0.6167048054919908 0.60587326120556395 0.59475332811276438 0.58333333333333337 0.57160096540627514 0.55954323001631323 0.54714640198511166 0.53439597315436238 0.52127659574468088 0.50777202072538863 0.49386503067484661 0.47953736654804269 0.46476964769647694 0.44954128440366975 0.43383038210624397 0.41761363636363635 0.40086621751684309 0.38356164383561642 0.36567164179104472 0.34716599190283398 0.32801235839340881 0.3081761006289308 0.28762006403415152 0.26630434782608692 0.24418604651162787 0.22121896162528215 0.19735327963176061 0.1725352112676056 0.1467065868263473 0.11980440097799509 9.1760299625468153E-2 6.2499999999999993E-2 3.1942633637548887E-2 0 Prior Probability Posterior Probability Uncertain Sensitivity Bayes' Rule Calculator Sensitivity Unknown Population 10000 Out of all Covid cases, how many will test positive? The total number of people tested. Specificity 0.96 Prior 0.6 Out of all Non-Covid cases, how many will test negative? What fraction of people tested do we expect to have Covid? Sensitivity # People with Covid (C) Positive + C Positive + not C Negative + C Negative + not C Total Positives Total Negatives % Correct Positives % Correct Negatives 0 6000 0 160 6000 3840 160 9840 0.000 0.390 0.01 6000 60 160 5940 3840 220 9780 0.273 0.393 0.02 6000 120 160 5880 3840 280 9720 0.429 0.395 0.03 6000 180 160 5820 3840 340 9660 0.529 0.398 0.04 6000 240 160 5760 3840 400 9600 0.600 0.400 0.05 6000 300 160 5700 3840 460 9540 0.652 0.403 0.06 6000 360 160 5640 3840 520 9480 0.692 0.405 0.07 6000 420 160 5580 3840 580 9420 0.724 0.408 0.08 6000 480 160 5520 3840 640 9360 0.750 0.410 0.09 6000 540 160 5460 3840 700 9300 0.771 0.413 0.1 6000 600 160 5400 3840 760 9240 0.789 0.416 0.11 6000 660 160 5340 3840 820 9180 0.805 0.418 0.12 6000 720 160 5280 3840 880 9120 0.818 0.421 0.13 6000 780 160 5220 3840 940 9060 0.830 0.424 0.14 6000 840 160 5160 3840 1000 9000 0.840 0.427 0.15 6000 900 160 5100 3840 1060 8940 0.849 0.430 0.16 6000 960 160 5040 3840 1120 8880 0.857 0.432 0.17 6000 1020 160 4980 3840 1180 8820 0.864 0.435 0.18 6000 1080 160 4920 3840 1240 8760 0.871 0.438 0.19 6000 1140 160 4860 3840 1300 8700 0.877 0.441 0.2 6000 1200 160 4800 3840 1360 8640 0.882 0.444 0.21 6000 1260 160 4740 3840 1420 8580 0.887 0.448 0.22 6000 1320 160 4680 3840 1480 8520 0.892 0.451 0.23 6000 1380 160 4620 3840 1540 8460 0.896 0.454 0.24 6000 1440 160 4560 3840 1600 8400 0.900 0.457 0.25 6000 1500 160 4500 3840 1660 8340 0.904 0.460 0.26 6000 1560 160 4440 3840 1720 8280 0.907 0.464 0.27 6000 1620 160 4380 3840 1780 8220 0.910 0.467 0.28 6000 1680 160 4320 3840 1840 8160 0.913 0.471 0.29 6000 1740 160 4260 3840 1900 8100 0.916 0.474 0.3 6000 1800 160 4200 3840 1960 8040 0.918 0.478 0.31 6000 1860 160 4140 3840 2020 7980 0.921 0.481 0.32 6000 1920 160 4080 3840 2080 7920 0.923 0.485 0.33 6000 1980 160 4020 3840 2140 7860 0.925 0.489 0.34 6000 2040 160 3960 3840 2200 7800 0.927 0.492 0.35 6000 2100 160 3900 3840 2260 7740 0.929 0.496 0.36 6000 2160 160 3840 3840 2320 7680 0.931 0.500 0.37 6000 2220 160 3780 3840 2380 7620 0.933 0.504 0.38 6000 2280 160 3720 3840 2440 7560 0.934 0.508 0.39 6000 2340 160 3660 3840 2500 7500 0.936 0.512 0.4 6000 2400 160 3600 3840 2560 7440 0.938 0.516 0.41 6000 2460 160 3540 3840 2620 7380 0.939 0.520 0.42 6000 2520 160 3480 3840 2680 7320 0.940 0.525 0.43 6000 2580 160 3420 3840 2740 7260 0.942 0.529 0.44 6000 2640 160 3360 3840 2800 7200 0.943 0.533 0.45 6000 2700 160 3300 3840 2860 7140 0.944 0.538 0.46 6000 2760 160 3240 3840 2920 7080 0.945 0.542 0.47 6000 2820 160 3180 3840 2980 7020 0.946 0.547 0.48 6000 2880 160 3120 3840 3040 6960 0.947 0.552 0.49 6000 2940 160 3060 3840 3100 6900 0.948 0.557 0.5 6000 3000 160 3000 3840 3160 6840 0.949 0.561 0.51 6000 3060 160 2940 3840 3220 6780 0.950 0.566 0.52 6000 3120 160 2880 3840 3280 6720 0.951 0.571 0.53 6000 3180 160 2820 3840 3340 6660 0.952 0.577 0.54 6000 3240 160 2760 3840 3400 6600 0.953 0.582 0.55 6000 3300 160 2700 3840 3460 6540 0.954 0.587 0.56 6000 3360 160 2640 3840 3520 6480 0.955 0.593 0.57 6000 3420 160 2580 3840 3580 6420 0.955 0.598 0.58 6000 3480 160 2520 3840 3640 6360 0.956 0.604 0.59 6000 3540 160 2460 3840 3700 6300 0.957 0.610 0.6 6000 3600 160 2400 3840 3760 6240 0.957 0.615 0.61 6000 3660 160 2340 3840 3820 6180 0.958 0.621 0.62 6000 3720 160 2280 3840 3880 6120 0.959 0.627 0.63 6000 3780 160 2220 3840 3940 6060 0.959 0.634 0.64 6000 3840 160 2160 3840 4000 6000 0.960 0.640 0.65 6000 3900 160 2100 3840 4060 5940 0.961 0.646 0.66 6000 3960 160 2040 3840 4120 5880 0.961 0.653 0.67 6000 4020 160 1980 3840 4180 5820 0.962 0.660 0.68 6000 4080 160 1920 3840 4240 5760 0.962 0.667 0.69 6000 4140 160 1860 3840 4300 5700 0.963 0.674 0.7 6000 4200 160 1800 3840 4360 5640 0.963 0.681 0.71 6000 4260 160 1740 3840 4420 5580 0.964 0.688 0.72 6000 4320 160 1680 3840 4480 5520 0.964 0.696 0.73 6000 4380 160 1620 3840 4540 5460 0.965 0.703 0.74 6000 4440 160 1560 3840 4600 5400 0.965 0.711 0.75 6000 4500 160 1500 3840 4660 5340 0.966 0.719 0.76 6000 4560 160 1440 3840 4720 5280 0.966 0.727 0.77 6000 4620 160 1380 3840 4780 5220 0.967 0.736 0.78 6000 4680 160 1320 3840 4840 5160 0.967 0.744 0.79 6000 4740 160 1260 3840 4900 5100 0.967 0.753 0.8 6000 4800 160 1200 3840 4960 5040 0.968 0.762 0.81 6000 4860 160 1140 3840 5020 4980 0.968 0.771 0.82 6000 4920 160 1080 3840 5080 4920 0.969 0.780 0.83 6000 4980 160 1020 3840 5140 4860 0.969 0.790 0.84 6000 5040 160 960 3840 5200 4800 0.969 0.800 0.85 6000 5100 160 900 3840 5260 4740 0.970 0.810 0.86 6000 5160 160 840 3840 5320 4680 0.970 0.821 0.87 6000 5220 160 780 3840 5380 4620 0.970 0.831 0.88 6000 5280 160 720 3840 5440 4560 0.971 0.842 0.89 6000 5340 160 660 3840 5500 4500 0.971 0.853 0.9 6000 5400 160 600 3840 5560 4440 0.971 0.865 0.91 6000 5460 160 540 3840 5620 4380 0.972 0.877 0.92 6000 5520 160 480 3840 5680 4320 0.972 0.889 0.93 6000 5580 160 420 3840 5740 4260 0.972 0.901 0.94 6000 5640 160 360 3840 5800 4200 0.972 0.914 0.95 6000 5700 160 300 3840 5860 4140 0.973 0.928 0.96 6000 5760 160 240 3840 5920 4080 0.973 0.941 0.97 6000 5820 160 180 3840 5980 4020 0.973 0.955 0.98 6000 5880 160 120 3840 6040 3960 0.974 0.970 0.99 6000 5940 160 60 3840 6100 3900 0.974 0.985 1 6000 6000 160 0 3840 6160 3840 0.974 1.000 Posterior Probabilities by Sensitivity % Correct Positives 0 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28000000000000003 0.28999999999999998 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55000000000000004 0.56000000000000005 0.56999999999999995 0.57999999999999996 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 0 0.27272727272727254 0.42857142857142838 0.52941176470588214 0.59999999999999987 0.65217391304347805 0.69230769230769218 0.72413793103448254 0.74999999999999989 0.77142857142857135 0.78947368421052622 0.80487804878048774 0.81818181818181812 0.82978723404255306 0.84 0.84905660377358472 0.85714285714285698 0.86440677966101687 0.87096774193548376 0.87692307692307681 0.88235294117647045 0.88732394366197165 0.89189189189189177 0.89610389610389596 0.89999999999999991 0.90361445783132521 0.90697674418604635 0.91011235955056169 0.91304347826086951 0.91578947368421038 0.91836734693877542 0.92079207920792072 0.92307692307692313 0.92523364485981308 0.92727272727272714 0.92920353982300885 0.93103448275862066 0.9327731092436975 0.93442622950819676 0.93600000000000005 0.9375 0.93893129770992367 0.94029850746268662 0.94160583941605835 0.94285714285714284 0.94405594405594406 0.9452054794520548 0.94630872483221473 0.94736842105263153 0.94838709677419353 0.94936708860759489 0.9503105590062112 0.95121951219512191 0.95209580838323349 0.95294117647058818 0.95375722543352603 0.95454545454545459 0.95530726256983245 0.95604395604395609 0.95675675675675675 0.95744680851063835 0.95811518324607325 0.95876288659793818 0.95939086294416243 0.96 0.96059113300492616 0.96116504854368934 0.96172248803827742 0.96226415094339612 0.96279069767441861 0.96330275229357798 0.96380090497737558 0.9642857142857143 0.96475770925110127 0.9652173913043478 0.96566523605150212 0.96610169491525422 0.96652719665271969 0.96694214876033058 0.96734693877551026 0.967741935483871 0.96812749003984067 0.96850393700787396 0.9688715953307393 0.96923076923076923 0.96958174904942962 0.96992481203007519 0.97026022304832715 0.97058823529411764 0.97090909090909094 0.97122302158273377 0.97153024911032027 0.971830985915493 0.97212543554006969 0.97241379310344822 0.97269624573378843 0.97297297297297303 0.97324414715719065 0.97350993377483441 0.97377049180327868 0.97402597402597402 % Correct Negatives 0 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28000000000000003 0.28999999999999998 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55000000000000004 0.56000000000000005 0.56999999999999995 0.57999999999999996 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 0.3902439024390244 0.39263803680981596 0.39506172839506171 0.39751552795031053 0.4 0.40251572327044027 0.4050632911392405 0.40764331210191085 0.41025641025641024 0.41290322580645161 0.41558441558441561 0.41830065359477125 0.42105263157894735 0.42384105960264901 0.42666666666666669 0.42953020134228187 0.43243243243243246 0.43537414965986393 0.43835616438356162 0.44137931034482758 0.44444444444444442 0.44755244755244755 0.45070422535211269 0.45390070921985815 0.45714285714285713 0.46043165467625902 0.46376811594202899 0.46715328467153283 0.47058823529411764 0.47407407407407409 0.47761194029850745 0.48120300751879697 0.48484848484848486 0.48854961832061067 0.49230769230769234 0.49612403100775193 0.5 0.50393700787401574 0.50793650793650791 0.51200000000000001 0.5161290322580645 0.52032520325203258 0.52459016393442626 0.52892561983471076 0.53333333333333333 0.53781512605042014 0.5423728813559322 0.54700854700854706 0.55172413793103448 0.55652173913043479 0.56140350877192979 0.5663716814159292 0.5714285714285714 0.57657657657657657 0.58181818181818179 0.58715596330275233 0.59259259259259256 0.59813084112149528 0.60377358490566035 0.60952380952380958 0.61538461538461542 0.62135922330097082 0.62745098039215685 0.63366336633663367 0.64 0.64646464646464652 0.65306122448979587 0.65979381443298968 0.66666666666666663 0.67368421052631577 0.68085106382978722 0.68817204301075274 0.69565217391304346 0.70329670329670335 0.71111111111111114 0.7191011235955056 0.72727272727272729 0.73563218390804597 0.7441860465116279 0.75294117647058822 0.76190476190476186 0.77108433734939763 0.78048780487804881 0.79012345679012341 0.8 0.810126582278481 0.82051282051282048 0.83116883116883122 0.84210526315789469 0.85333333333333339 0.86486486486486491 0.87671232876712324 0.88888888888888884 0.90140845070422537 0.91428571428571426 0.92753623188405798 0.94117647058823528 0.95522388059701491 0.96969696969696972 0.98461538461538467 1 Sensitivity Posterior Probability Uncertain Specificity Bayes' Rule Calculator Sensitivity 0.9 Population 10000 Out of all Covid cases, how many will test positive? The total number of people tested. Specificity Unknown Prior 0.6 Out of all Non-Covid cases, how many will test negative? What fraction of people tested do we expect to have Covid? Specificity # People with Covid (C) Positive + C Positive + not C Negative + C Negative + not C Total Positives Total Negatives % Correct Positives % Correct Negatives 0 6000 5400 4000 600 0 9400 600 0.574 0.000 0.01 6000 5400 3960 600 40 9360 640 0.577 0.063 0.02 6000 5400 3920 600 80 9320 680 0.579 0.118 0.03 6000 5400 3880 600 120 9280 720 0.582 0.167 0.04 6000 5400 3840 600 160 9240 760 0.584 0.211 0.05 6000 5400 3800 600 200 9200 800 0.587 0.250 0.06 6000 5400 3760 600 240 9160 840 0.590 0.286 0.07 6000 5400 3720 600 280 9120 880 0.592 0.318 0.08 6000 5400 3680 600 320 9080 920 0.595 0.348 0.09 6000 5400 3640 600 360 9040 960 0.597 0.375 0.1 6000 5400 3600 600 400 9000 1000 0.600 0.400 0.11 6000 5400 3560 600 440 8960 1040 0.603 0.423 0.12 6000 5400 3520 600 480 8920 1080 0.605 0.444 0.13 6000 5400 3480 600 520 8880 1120 0.608 0.464 0.14 6000 5400 3440 600 560 8840 1160 0.611 0.483 0.15 6000 5400 3400 600 600 8800 1200 0.614 0.500 0.16 6000 5400 3360 600 640 8760 1240 0.616 0.516 0.17 6000 5400 3320 600 680 8720 1280 0.619 0.531 0.18 6000 5400 3280 600 720 8680 1320 0.622 0.545 0.19 6000 5400 3240 600 760 8640 1360 0.625 0.559 0.2 6000 5400 3200 600 800 8600 1400 0.628 0.571 0.21 6000 5400 3160 600 840 8560 1440 0.631 0.583 0.22 6000 5400 3120 600 880 8520 1480 0.634 0.595 0.23 6000 5400 3080 600 920 8480 1520 0.637 0.605 0.24 6000 5400 3040 600 960 8440 1560 0.640 0.615 0.25 6000 5400 3000 600 1000 8400 1600 0.643 0.625 0.26 6000 5400 2960 600 1040 8360 1640 0.646 0.634 0.27 6000 5400 2920 600 1080 8320 1680 0.649 0.643 0.28 6000 5400 2880 600 1120 8280 1720 0.652 0.651 0.29 6000 5400 2840 600 1160 8240 1760 0.655 0.659 0.3 6000 5400 2800 600 1200 8200 1800 0.659 0.667 0.31 6000 5400 2760 600 1240 8160 1840 0.662 0.674 0.32 6000 5400 2720 600 1280 8120 1880 0.665 0.681 0.33 6000 5400 2680 600 1320 8080 1920 0.668 0.688 0.34 6000 5400 2640 600 1360 8040 1960 0.672 0.694 0.35 6000 5400 2600 600 1400 8000 2000 0.675 0.700 0.36 6000 5400 2560 600 1440 7960 2040 0.678 0.706 0.37 6000 5400 2520 600 1480 7920 2080 0.682 0.712 0.38 6000 5400 2480 600 1520 7880 2120 0.685 0.717 0.39 6000 5400 2440 600 1560 7840 2160 0.689 0.722 0.4 6000 5400 2400 600 1600 7800 2200 0.692 0.727 0.41 6000 5400 2360 600 1640 7760 2240 0.696 0.732 0.42 6000 5400 2320 600 1680 7720 2280 0.699 0.737 0.43 6000 5400 2280 600 1720 7680 2320 0.703 0.741 0.44 6000 5400 2240 600 1760 7640 2360 0.707 0.746 0.45 6000 5400 2200 600 1800 7600 2400 0.711 0.750 0.46 6000 5400 2160 600 1840 7560 2440 0.714 0.754 0.47 6000 5400 2120 600 1880 7520 2480 0.718 0.758 0.48 6000 5400 2080 600 1920 7480 2520 0.722 0.762 0.49 6000 5400 2040 600 1960 7440 2560 0.726 0.766 0.5 6000 5400 2000 600 2000 7400 2600 0.730 0.769 0.51 6000 5400 1960 600 2040 7360 2640 0.734 0.773 0.52 6000 5400 1920 600 2080 7320 2680 0.738 0.776 0.53 6000 5400 1880 600 2120 7280 2720 0.742 0.779 0.54 6000 5400 1840 600 2160 7240 2760 0.746 0.783 0.55 6000 5400 1800 600 2200 7200 2800 0.750 0.786 0.56 6000 5400 1760 600 2240 7160 2840 0.754 0.789 0.57 6000 5400 1720 600 2280 7120 2880 0.758 0.792 0.58 6000 5400 1680 600 2320 7080 2920 0.763 0.795 0.59 6000 5400 1640 600 2360 7040 2960 0.767 0.797 0.6 6000 5400 1600 600 2400 7000 3000 0.771 0.800 0.61 6000 5400 1560 600 2440 6960 3040 0.776 0.803 0.62 6000 5400 1520 600 2480 6920 3080 0.780 0.805 0.63 6000 5400 1480 600 2520 6880 3120 0.785 0.808 0.64 6000 5400 1440 600 2560 6840 3160 0.789 0.810 0.65 6000 5400 1400 600 2600 6800 3200 0.794 0.813 0.66 6000 5400 1360 600 2640 6760 3240 0.799 0.815 0.67 6000 5400 1320 600 2680 6720 3280 0.804 0.817 0.68 6000 5400 1280 600 2720 6680 3320 0.808 0.819 0.69 6000 5400 1240 600 2760 6640 3360 0.813 0.821 0.7 6000 5400 1200 600 2800 6600 3400 0.818 0.824 0.71 6000 5400 1160 600 2840 6560 3440 0.823 0.826 0.72 6000 5400 1120 600 2880 6520 3480 0.828 0.828 0.73 6000 5400 1080 600 2920 6480 3520 0.833 0.830 0.74 6000 5400 1040 600 2960 6440 3560 0.839 0.831 0.75 6000 5400 1000 600 3000 6400 3600 0.844 0.833 0.76 6000 5400 960 600 3040 6360 3640 0.849 0.835 0.77 6000 5400 920 600 3080 6320 3680 0.854 0.837 0.78 6000 5400 880 600 3120 6280 3720 0.860 0.839 0.79 6000 5400 840 600 3160 6240 3760 0.865 0.840 0.8 6000 5400 800 600 3200 6200 3800 0.871 0.842 0.81 6000 5400 760 600 3240 6160 3840 0.877 0.844 0.82 6000 5400 720 600 3280 6120 3880 0.882 0.845 0.83 6000 5400 680 600 3320 6080 3920 0.888 0.847 0.84 6000 5400 640 600 3360 6040 3960 0.894 0.848 0.85 6000 5400 600 600 3400 6000 4000 0.900 0.850 0.86 6000 5400 560 600 3440 5960 4040 0.906 0.851 0.87 6000 5400 520 600 3480 5920 4080 0.912 0.853 0.88 6000 5400 480 600 3520 5880 4120 0.918 0.854 0.89 6000 5400 440 600 3560 5840 4160 0.925 0.856 0.9 6000 5400 400 600 3600 5800 4200 0.931 0.857 0.91 6000 5400 360 600 3640 5760 4240 0.938 0.858 0.92 6000 5400 320 600 3680 5720 4280 0.944 0.860 0.93 6000 5400 280 600 3720 5680 4320 0.951 0.861 0.94 6000 5400 240 600 3760 5640 4360 0.957 0.862 0.95 6000 5400 200 600 3800 5600 4400 0.964 0.864 0.96 6000 5400 160 600 3840 5560 4440 0.971 0.865 0.97 6000 5400 120 600 3880 5520 4480 0.978 0.866 0.98 6000 5400 80 600 3920 5480 4520 0.985 0.867 0.99 6000 5400 40 600 3960 5440 4560 0.993 0.868 1 6000 5400 0 600 4000 5400 4600 1.000 0.870 Posterior Probabilities by Specificity % Correct Positives 0 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28000000000000003 0.28999999999999998 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55000000000000004 0.56000000000000005 0.56999999999999995 0.57999999999999996 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 0.57446808510638303 0.57692307692307687 0.57939914163090134 0.5818965517241379 0.58441558441558439 0.58695652173913049 0.58951965065502188 0.59210526315789469 0.59471365638766516 0.59734513274336287 0.6 0.6026785714285714 0.60538116591928248 0.60810810810810811 0.61085972850678738 0.61363636363636365 0.61643835616438358 0.61926605504587151 0.62211981566820274 0.625 0.62790697674418605 0.63084112149532712 0.63380281690140849 0.6367924528301887 0.6398104265402843 0.6428571428571429 0.64593301435406703 0.64903846153846156 0.65217391304347827 0.65533980582524276 0.65853658536585369 0.66176470588235292 0.66502463054187189 0.66831683168316836 0.67164179104477617 0.67500000000000004 0.67839195979899503 0.68181818181818177 0.68527918781725883 0.68877551020408168 0.69230769230769229 0.69587628865979378 0.69948186528497414 0.703125 0.70680628272251311 0.71052631578947367 0.7142857142857143 0.71808510638297873 0.72192513368983957 0.72580645161290325 0.72972972972972971 0.73369565217391308 0.73770491803278693 0.74175824175824179 0.7458563535911602 0.75 0.75418994413407825 0.7584269662921348 0.76271186440677963 0.76704545454545459 0.77142857142857146 0.77586206896551724 0.78034682080924855 0.78488372093023251 0.78947368421052633 0.79411764705882348 0.79881656804733725 0.8035714285714286 0.80838323353293418 0.81325301204819278 0.81818181818181823 0.82317073170731703 0.82822085889570551 0.83333333333333337 0.83850931677018636 0.84375 0.84905660377358494 0.85443037974683544 0.85987261146496818 0.86538461538461542 0.87096774193548387 0.87662337662337664 0.88235294117647056 0.88815789473684215 0.89403973509933776 0.9 0.90604026845637586 0.91216216216216217 0.91836734693877553 0.92465753424657537 0.93103448275862066 0.9375 0.94405594405594406 0.95070422535211263 0.95744680851063835 0.9642857142857143 0.97122302158273377 0.97826086956521741 0.98540145985401462 0.99264705882352944 1 % Correct Negatives 0 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28000000000000003 0.28999999999999998 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55000000000000004 0.56000000000000005 0.56999999999999995 0.57999999999999996 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 0 6.2500000000000014E-2 0.11764705882352944 0.16666666666666669 0.21052631578947373 0.25000000000000006 0.28571428571428575 0.31818181818181823 0.34782608695652178 0.37500000000000006 0.4 0.42307692307692307 0.44444444444444442 0.4642857142857143 0.48275862068965519 0.5 0.5161290322580645 0.53125 0.54545454545454541 0.55882352941176472 0.5714285714285714 0.58333333333333337 0.59459459459459463 0.60526315789473684 0.61538461538461542 0.625 0.63414634146341464 0.6428571428571429 0.65116279069767447 0.65909090909090906 0.66666666666666663 0.67391304347826086 0.68085106382978722 0.6875 0.69387755102040816 0.7 0.70588235294117652 0.71153846153846156 0.71698113207547165 0.72222222222222221 0.72727272 727272729 0.7321428571428571 0.73684210526315785 0.74137931034482762 0.74576271186440679 0.75 0.75409836065573765 0.75806451612903225 0.76190476190476186 0.765625 0.76923076923076927 0.77272727272727271 0.77611940298507465 0.77941176470588236 0.78260869565217395 0.7857142857142857 0.78873239436619713 0.79166666666666663 0.79452054794520544 0.79729729729729726 0.8 0.80263157894736847 0.80519480519480524 0.80769230769230771 0.810126582278481 0.8125 0.81481481481481477 0.81707317073170727 0.81927710843373491 0.8214285714285714 0.82352941176470584 0.82558139534883723 0.82758620689655171 0.82954545454545459 0.8314606741573034 0.83333333333333337 0.8351648351648352 0.83695652173913049 0.83870967741935487 0.84042553191489366 0.84210526315789469 0.84375 0.84536082474226804 0.84693877551020413 0.84848484848484851 0.85 0.85148514851485146 0.8529411764705882 0.85436893203883491 0.85576923076923073 0.8571428571428571 0.85849056603773588 0.85981308411214952 0.86111111111111116 0.86238532110091748 0.86363636363636365 0.86486486486486491 0.8660714285714286 0.86725663716814161 0.86842105263157898 0.86956521739130432 Specificity Posterior Probability 1 2 3 4 5 6 7 A B C Bayes' Rule Calculator Event A Patient has Covid An uncertain event (eg. having Covid) Event B Outcome of a Covid Test An event that included information about A (eg. a Covid test) Prior: P(A) 0.04