All figures are fictional.
1. Urine colony count. A calibrated 1 microlitre (0.001 mL) loop is used and 50 colonies grow. CFU/mL = 50 / 0.001 = 50,000 (5 x 10^4) CFU/mL. With a 10 microlitre loop, the same 50 colonies would mean 50 / 0.01 = 5,000 CFU/mL. Always check the loop volume first.
2. Viable count from a dilution. 0.1 mL of a 10^-6 dilution is spread on a plate and 45 colonies grow. CFU/mL = 45 / (0.1 x 10^-6) = 4.5 x 10^8 CFU/mL in the original sample. Use plates with roughly 30 to 300 colonies for a reliable count.
3. Diagnostic test accuracy. A rapid test is compared with culture in 1,000 patients:
| Culture positive | Culture negative |
|---|
| Test positive | 90 (true positive) | 30 (false positive) |
| Test negative | 10 (false negative) | 870 (true negative) |
- Sensitivity = 90 / 100 = 90%
- Specificity = 870 / 900 = 96.67%
- Positive predictive value = 90 / 120 = 75%
- Negative predictive value = 870 / 880 = 98.86%
Prevalence here is 10%. At 1% prevalence, the same test in 1,000 people gives 9 true positives and about 33 false positives, so the PPV falls to about 21.4%. Sensitivity and specificity stay the same; predictive values change with prevalence.
4. Blood culture contamination rate. 18 of 600 blood culture sets grow a likely contaminant: 18 / 600 x 100 = 3.0%.