Statistical Calculations

Diagnostic Tests


Centre for Evidence Based Medicine Stats Calculator

Vanderbilt- Power and Sample Size Calculator




Gold standard Positive (condition present)
Gold standard Negative (condition not present)
Test result Positive
True Positive
False Positive
Test result Negative
False Negative
True Negative


Stable Properties:

Sensitivity = True Positives/(True Positives + False Negatives)

Specificity = True Negatives/(False Positive + True Negative)


Frequency Dependent Properties:

Positive Predictive Value = True Positive/(True Positive + False Positive)

Negative Predictive Value = True Negative/(True Negative + False Negative)


Likelihood Ratios

The likelihood ratio for a test result compares the likelihood of that result in patients with disease to the likelihood of that result in patients without disease:

Condition Present
Condition Absent
Test Positive
Test Negative

Positive LR = (a/a+c)/(b/b+d)
Negative LR = (c/a+c)/(d/b+d)


How much do Likelihood Ratios change disease likelihood?

LRs >10 or <0.1 cause large changes in likelihood.
LRs 5-10 or 0.1-0.2 cause moderate changes.
LRs 2-5 or 0.2-0.5 cause small changes.
LRs between <2 and 0.5 cause little or no change.