Confusion of the Inverse

An example of the Confusion of the Inverse is the entry-level drug hypothesis : while many hard drug users started using soft drugs, relatively few people get to hard drugs from soft drugs. The entry-level drug hypothesis ignores this asymmetry.

Confusion of the inverse ( Engl. For "confusing the reversal"; also: Conditional Probability Fallacy [ "fallacy of the conditional probability"], inverse fallacy [ "reversal fallacy"], Fallacy of the Transposed Probability [ "fallacy of the transposed probability"] Prosecutor's Fallacy is a logical fallacy that consists in equating a conditional probability with its reversal.

A conditional probability (e.g. the probability that a professor in Germany is a woman: 25%) is by no means identical to its inverse (the probability that a woman is a professor in Germany: 0.03%). With Confusion of the Inverse , however, this difference is not understood and one value is incorrectly used for the other.

The American psychologist Robyn Dawes coined the term Confusion of the Inverse .

Examples

General examples

“As has been shown in a study, almost every second terrorist has completed technical training. Parents who offer their child a technical education should be prepared for the child to embark on a career in terrorism. "

“Most accidents happen at home. To be sure, you should stay at home as little as possible. "

"Most drug addicts have the gateway drug started hashish. Anyone who smokes hashish runs a high risk of later becoming addicted to harder drugs. "

Examples from medicine

The confusion of the inverse is widespread among students and academics and leads to serious and sometimes momentous distortions, especially in the interpretation of medical test results.

Relative size	Vicious	Benign	total
Test positive	0.8 (correct positive)	9.9 (false positive)	10.7
Test negative	0.2 (false negative)	89.1 (correct negative)	89.3
total	1	99	100

One of the best-known examples today is one pointed out by David M. Eddy in 1982. Eddy asked 100 doctors to comment on the following case: A patient has a lump in her breast. A mammography provides the finding that the tumor is malignant. The doctor knows that:

• Only 1% of all breast tumors are malignant.
• Mammograms identify a malignant tumor as such in 80% of the cases (while they incorrectly classify it as benign in 20% of the cases).
• Mammograms identify a benign tumor as such in 90% of the cases (while they incorrectly classify it as malignant in 10% of the cases).

Most of the doctors surveyed by Eddy put the probability that the patient had a malignant tumor at 75% (0.75). Correctly, but calculated using Bayes' theorem , the risk is only 7.5% (0.075).

${\displaystyle {\begin{aligned}&{}\qquad P({\text{bösartig}}|{\text{positiv}})\\[8pt]&={\frac {P({\text{positiv}}|{\text{bösartig}})P({\text{bösartig}})}{P({\text{positiv}}|{\text{bösartig}})P({\text{bösartig}})+P({\text{positiv}}|{\text{gutartig}})P({\text{gutartig}})}}\\[8pt]&={\frac {(0,80\cdot 0,01)}{(0,80\cdot 0,01)+(0,10\cdot 0,99)}}=0,075\end{aligned}}}$

As early as 1979, two researchers from Massachusetts had shown similar systematic misinterpretations in advance of medical prescriptions of amniocenteses in pregnant women.

literature

• Pavel Kalinowski, Fiona Fidler, Geoff Cumming: Overcoming the Inverse Probability Fallacy: A Comparison of Two Teaching Interventions . In: Methodology European Journal of Research Methods for the Behavioral and Social Sciences . tape 4 , no. 4 , January 2008, p. 152-158 .

Web links

• Richardo Franco, Jerome Busemeyer: A quantum probability explanation for the inverse fallacy. Retrieved July 14, 2020 (Indiana University). 

Individual evidence

1. ↑ Christopher J. Wild, Jessica M. Utts, Nicholas J. Horton: What Is Statistics? In: Dani Ben-Zvi, Katie Makar, Joan Garfield (Eds.): International Handbook of Research in Statistics Education . Springer, ISBN 978-3-319-66193-3 , pp. 5–36, here: p. 24 ( limited preview in Google book search).
2. ↑ Scott Plous: The Psychology of Judgment and Decision Making . McGraw-Hill, 1993, ISBN 978-0-07-050477-6 , pp. 132 .
3. ^ Diego Gambetta, Steffen Hertog: Engineers of Jihad: the curious connection between violent extremism and education . Princeton University Press, Princeton, Oxford 2016, ISBN 978-0-691-14517-4 .
4. ↑ ^{a b} David M. Eddy: Probabilistic reasoning in clinical medicine: Problems and opportunity . In: Daniel Kahneman, Paul Slovic, AAmos Tversky (Eds.): Judgment under Uncertainty: Heuristic and Biases . Cambridge University Press, Cambridge 1982, ISBN 978-0-521-28414-1 , pp. 249-267 . Quoted from: Jessica Utts, Robert Heckard: Statistical Ideas and Methods . Thomson, Belmont, CA 2006, ISBN 0-534-40284-4 , pp. 234 ( limited preview in Google Book search).
5. ↑ Susan P. Pauker, Stephen G. Pauker: The amniocentesis decision: an explicit guide for parents . In: Birth Defects Original Article Series . tape 15 , 5C, 1979, pp. 289-324 , PMID 160805 .