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Calculation of test quality criteria for screenings


Screening procedures aim at identifying persons who have a certain (binary) characteristic. They are often used to identify people at risk who later develop mental disorders, diseases or school problems. For the evaluation of the screenings there are a number of characteristic values, of which sensitivity and specificity are the best known. They show how many people were correctly identified by the test as risk and how many as non-risk persons.

Besides these basic data, however, there are a number of other important data, such as the positive and negative predictive values or the relative increase in the hit rate compared to the random hit rate (RIOC); further information and a detailed description of the various parameters can be found in Marx & Lenhard, 2010; see also the glossary).


Online calculator to determine specificity, specificity, predictive value and the Relative Improvement Over Chance

You can use the table to determine various characteristic values for screening procedures. Please enter the absolute case numbers in the table cells.

Area proportions see graphic
please fill in absolute numbers
Predictor
(e. g. from a screening)
positive result negative result
Criteria not affected b

(false positive)
d

(correct negative)
affected a

(correct positive)
c

(false negative)


Quality indicators of the screening:
Sensitivity or Recall
Specificity
Positive predictive value or Precision
Negative predictive value
Contingency Coefficient rPhi
Hit ratio or Accuracy
Random hit ratio
Relative Improvement Over Chance (RIOC)


Concrete test results on the basis of the screening criteria

Ok, let's turn the logic around and look at the numbers of correct positive and false positive diagnoses that result. If the base rate is very low, then screening very quickly reaches its limits and it is then primarily used to pre-select people for further diagnostics. Let us take COVID19 as an example and a fictitious incidence of 100 / 100 000 persons for infections in the last 7 days, which corresponds to a baserate of 0.1%. Good rapid tests have at least a specificity of 99.5% and a sensitivity of 95%. What number of false positive diagnoses results if 1000 people are examined with a rapid test in this infection situation?


Baserate
between 0 and 100 in percent
Sensitivity
between 0 and 100 in percent
Spezifity
between 0 and 100 in percent
Number of persons
Results of the screening:
False Positive
False Negative
Correct Positive
Correct Negative
Share of false positives in all positive results (in percent)
Share of false-negative results in all negative results (percent)


Glossary:


Online tool as Excel table and Java source code

The online tool is available as an Excel sheet and as Source-Code in Java under the General Public License (GPL):



Literature

Marx, P. & Lenhard, W. (2010). Diagnostische Merkmale von Screeningverfahren. In M. Hasselhorn & W. Schneider (Hrsg.), Frühprognose schulischer Kompetenzen. Göttingen: Hogrefe.

Citeable: Lenhard, W. & Lenhard, A. (2014). Calculation of test quality criteria for screenings. available: http://www.psychometrica.de/testkennwerte.html. Dettelbach: Psychometrica.