# Free statistical calculators

## Diagnostic test evaluation calculator

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.

 Disease Test Present n Absent n Total Positive True Positive a= False Positive c= a + c Negative False Negative b= True Negative d= b + d Total a + b c + d

## Results

Statistic Formula Value 95% CI
Sensitivity Specificity Positive Likelihood Ratio Negative Likelihood Ratio Disease prevalence (*)
Positive Predictive Value (*)
Negative Predictive Value (*)
Accuracy (*)

## 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)
• Accuracy: overall probability that a patient will be correctly classified .
= (a+d) / (a+b+d+c)

Sensitivity, specificity, positive and negative predictive value as well as disease prevalence are expressed as percentages.

Confidence intervals for sensitivity, specificity and accuracy 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.

Confidence intervals for the predictive values are the standard logit confidence intervals given by Mercaldo et al. 2007.

## (*) 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, and Accucary, 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 formulas based on Bayes' theorem: and ## External links

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