# Free statistical calculators

## Diagnostic test evaluation

Instructions: enter the number of cases in the diseased group that test
positive (*a*) and negative (*b*); and the number of cases in the
non-diseased group that test
positive (*c*) and negative (*d*).

Next click the **Test** button.

## Results

Statistic | Formula | Value | 95% CI |
---|---|---|---|

Sensitivity | |||

Specificity | |||

Positive Likelihood Ratio | |||

Negative Likelihood Ratio | |||

Disease prevalence | (*) | ||

Positive Predictive Value | (*) | ||

Negative Predictive Value | (*) |

## Definitions

*Sensitivity*: probability that a test result will be positive when the disease is present (true positive rate).

= a / (a+b)*Specificity*: probability that a test result will be negative when the disease is not present (true negative rate).

= d / (c+d)*Positive likelihood ratio*: ratio between the probability of a positive test result given the*presence*of the disease and the probability of a positive test result given the*absence*of the disease, i.e.

= True positive rate / False positive rate = Sensitivity / (1-Specificity)*Negative likelihood ratio*: ratio between the probability of a negative test result given the*presence*of the disease and the probability of a negative test result given the*absence*of the disease, i.e.

= False negative rate / True negative rate = (1-Sensitivity) / Specificity*Positive predictive value*: probability that the disease is present when the test is positive.

= a / (a+c)*Negative predictive value*: probability that the disease is not present when the test is negative.

= d / (b+d)

Sensitivity, specificity, positive and negative predictive value as well as disease prevalence are expressed as percentages for ease of interpretation. Their confidence intervals are "exact" Clopper-Pearson confidence intervals.

Confidence intervals for the likelihood ratios are calculated using the "Log method" as given on page 109 of Altman et al. 2000.

## (*) Note

If the sample sizes in the positive (Disease present) and the negative (Disease absent) groups do not reflect the real prevalence of the disease, then the Positive and Negative predicted values cannot be estimated and you should ignore those values.

Alternatively, when the disease prevalence is known then the positive and negative predictive values can be calculated using the following formula's based on Bayes' theorem:

and

## Literature

- Altman DG, Machin D, Bryant TN, Gardner MJ (Eds) (2000) Statistics with confidence, 2
^{nd}ed. BMJ Books. - Gardner IA, Greiner M (2006) Receiver-operating characteristic curves and likelihood ratios: improvements over traditional methods for the evaluation and application of veterinary clinical pathology tests. Veterinary Clinical Pathology, 35:8-17. [Abstract]
- Griner PF, Mayewski RJ, Mushlin AI, Greenland P (1981) Selection and interpretation of diagnostic tests and procedures. Annals of Internal Medicine, 94, 555-600. [Abstract]
- Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143, 29-36. [Abstract]
- Metz CE (1978) Basic principles of ROC analysis. Seminars in Nuclear Medicine, 8, 283-298. [Abstract]
- Zhou XH, NA Obuchowski, DK McClish (2002) Statistical methods in diagnostic medicine. New York: Wiley.
- Zweig MH, Campbell G (1993) Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clinical Chemistry, 39, 561-577. [Abstract]

## External links

- Binomial proportion confidence interval on Wikipedia.