What Bayes theorem tell us
Mar 31, 2017
What-Bayes theorem tell us
###If a person is infected by the disease, the probability of a positive test result will be 90%. However, if someone is not infected, there still will have 9% chances to get the positive result. We have already known that the prevalence of this disease is 1%.
##If I am tested to be positive, what is the probability of getting a true infection?
##70%?
##60%?
##50%?
##40%?
##10%?
Answer
Just 9%, the key is not the reliability of the test but the prevalence of this disease
| the prevalence of this disease | the probability of true positive |
|---|---|
| 1% | 9.17% |
| 2% | 16.95% |
| 3% | 23.62% |
| 6% | 38.96% |
| 9% | 49.72% |
| 12% | 57.69% |
| 15% | 63.83% |
| 18% | 68.7% |
| 21% | 72.66% |
| 24% | 75.95% |
| 27% | 78.72% |
| 30% | 81.08% |
| 33% | 83.12% |
| 36% | 84.91% |
| 39% | 86.47% |
| 42% | 87.87% |
| 45% | 89.11% |
| 48% | 90.23% |
| 51% | 91.23% |
| 54% | 92.15% |
| 57% | 92.99% |
| 60% | 93.75% |
| 63% | 94.45% |
| 66% | 95.1% |
| 69% | 95.7% |
| 72% | 96.26% |
| 75% | 96.77% |
| 78% | 97.26% |
| 81% | 97.71% |
| 84% | 98.13% |
| 87% | 98.53% |
| 90% | 98.9% |
| 93% | 99.25% |
| 96% | 99.59% |
| 99% | 99.9% |
| the probability of a positive test result if infected | the probability of a positive test result if not infected |
|---|---|
| 90% | 3% |
| the prevalence of this disease | the probability of true positive |
|---|---|
| 1% | 23.26% |
| 2% | 37.97% |
| 3% | 48.13% |
| 6% | 65.69% |
| 9% | 74.79% |
| 12% | 80.36% |
| 15% | 84.11% |
| 18% | 86.82% |
| 21% | 88.86% |
| 24% | 90.45% |
| 27% | 91.73% |
| 30% | 92.78% |
| 33% | 93.66% |
| 36% | 94.41% |
| 39% | 95.04% |
| 42% | 95.6% |
| 45% | 96.09% |
| 48% | 96.51% |
| 51% | 96.9% |
| 54% | 97.24% |
| 57% | 97.55% |
| 60% | 97.83% |
| 63% | 98.08% |
| 66% | 98.31% |
| 69% | 98.52% |
| 72% | 98.72% |
| 75% | 98.9% |
| 78% | 99.07% |
| 81% | 99.22% |
| 84% | 99.37% |
| 87% | 99.5% |
| 90% | 99.63% |
| 93% | 99.75% |
| 96% | 99.86% |
| 99% | 99.97% |
| the probability of a positive test result if infected | the probability of a positive test result if not infected |
|---|---|
| 80% | 3% |
| the prevalence of this disease | the probability of true positive |
|---|---|
| 1% | 23.26% |
| 2% | 37.97% |
| 3% | 45.2% |
| 6% | 62.99% |
| 9% | 72.51% |
| 12% | 78.43% |
| 15% | 82.47% |
| 18% | 85.41% |
| 21% | 87.64% |
| 24% | 89.39% |
| 27% | 90.79% |
| 30% | 91.95% |
| 33% | 92.93% |
| 36% | 93.75% |
| 39% | 94.46% |
| 42% | 95.08% |
| 45% | 95.62% |
| 48% | 96.1% |
| 51% | 96.52% |
| 54% | 96.9% |
| 57% | 97.25% |
| 60% | 97.56% |
| 63% | 97.85% |
| 66% | 98.1% |
| 69% | 98.34% |
| 72% | 98.56% |
| 75% | 98.77% |
| 78% | 98.95% |
| 81% | 99.13% |
| 84% | 99.29% |
| 87% | 99.44% |
| 90% | 99.59% |
| 93% | 99.72% |
| 96% | 99.84% |
| 99% | 99.96% |