Clinical Calculator 1
From an Observed Sample: Estimates of Population Prevalence, Sensitivity, Specificity, Predictive Values, and Likelihood Ratios
Given a sample of subjects cross-classified according to whether a certain condition is present or absent, and according to whether a test designed to indicate the presence of that condition proves positive or negative, this page will calculate the estimated population midpoints and 95% confidence intervals for To proceed, enter the observed frequencies for each of the four cross- classifications into the designated cells, then click the «Calculate» button. To perform a new analysis with a new set of data, click the «Reset» button.

Condition Totals
 Absent 
Present
 Test Positive 



 Test Negative 



 Totals 


   Calculate         Reset   
Estimated
Value

95% Confidence Interval
Lower Limit Upper Limit
Prevalence



Sensitivity



Specificity



For any particular test result, the probability that it will be:
Positive



Negative



For any particular positive test result, the probability that it is:
True Positive
(Positive Predictive Value)



False Positive



For any particular negative test result, the probability that it is:
True Negative
(Negative Predictive Value)



False Negative



likelihood Ratios:
   [C] = conventional
   [W] = weighted by prevalence      [definitions]
Positive [C]



Negative [C]



Positive [W]



Negative [W]



The entry 'NaN' in any of the above cells means that
the calculation cannot be performed because the values
entered include one or more instances of zero.
Technical note on calculation of confidence intervals.

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©Richard Lowry 2001-
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Technical Note on Calculation of Confidence Intervals

95% confidence intervals for proportions (which include all but the last four of the above) are calculated according to the efficient-score method (corrected for continuity) described by Robert Newcombe, based on the procedure outlined by E. B. Wilson in 1927. As Newcombe notes in his 1998 paper, the familiar Gaussian approximation
± 1.96 × p(1-p)/n
is ill suited to situations where the proportion is quite small, as is often the case with prevalence measures, or quite large, as is optimally the case with measures of sensitivity and specificity.

References:
Newcombe, Robert G. "Two-Sided Confidence Intervals for the Single Proportion: Comparison of Seven Methods," Statistics in Medicine, 17, 857-872 (1998).

Wilson, E. B. "Probable Inference, the Law of Succession, and Statistical Inference," Journal of the American Statistical Association, 22, 209-212 (1927).
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Definitions of likelihood Ratios:
Conventional Positive:
=
conditional probability of positive
test result if the condition is present
conditional probability of positive
test result if the condition is absent
=
sensitivity
1-specificity
Conventional Negative:
=
conditional probability of negative
test result if the condition is present
conditional probability of negative
test result if the condition is absent
=
1-sensitivity
specificity
Positive [weighted for prevalence]
=
probability that a positive
test result is a true positive
probability that a positive
test result is a false positive
=
(prevalence)(sensitivity)
(1-prevalence)(1-specificity)
Negative [weighted for prevalence]
=
probability of false negative result
probability of true negative result
=
(prevalence)(1-sensitivity)
(1-prevalence)(specificity)
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