Calculating the Base Rate in Polygraph Populations and the Posterior Confidence in the Obtained Results in the Comparison Question Test, Built upon the Proportion of Outcomes: the Case of Israel Police

Background & Context

One of the most persistent challenges in polygraph science is the "base rate problem"—the question of how much confidence we can place in any individual test result given the underlying prevalence of truthfulness versus deception in tested populations. This 2023 paper by Avital Ginton demonstrates a combined statistical and algebraic method for computing base rates of deceptive versus truthful examinees in defined polygraph populations based on the proportions of deceptive and truthful test outcomes, and evaluates the degree to which a specific CQT examination result can be trusted to be correct.

The work builds upon Ginton's earlier innovative research developing ground-truth-free methods for estimating polygraph accuracy using paired examinations. Rather than debating specific accuracy rates, this paper targets a more fundamental dilemma: assuming a specified accuracy rate—whether 90%, 80%, 70%, or any other number—how much can we trust a given result to represent ground truth, or in other words, what is the posterior probability of the polygraph result being correct?

This question has profound implications for legal admissibility and investigative use of polygraph results. In Israel, polygraph test results are not admissible in criminal trials, and the fact that a witness or accused person took a polygraph test or refused to take it is not allowed to be mentioned during trial. The posterior probability calculations demonstrated in this paper help explain why such caution is warranted.

Research Design & Methodology

The paper presents the posterior probability question as a conditional probability query, which can be solved within the Bayes' Theorem framework, though the paper demonstrates an alternative algebraic approach. The study utilizes real operational data from the Israel Police polygraph laboratories as a concrete test case for the mathematical model.

For the analysis, the author relied on accuracy estimates obtained from the Israel Police population: approximately 84% accuracy for truth-tellers and 94% accuracy for liars (Ginton et al. 1982; Ginton 2013), noting that most other estimates for the probable-lie CQT are close to these figures. These accuracy figures serve as inputs to the computational model.

Key methodological elements include:

• Using data showing that in Israel Police field polygraph labs, NDI (No Deception Indicated) findings constitute 65% of total findings and DI (Deception Indicated) findings constitute 35%
• Algebraic manipulation of true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN) to back-calculate base rates from outcome proportions
• Application to both the specific Israel Police case and generalization across hypothetical outcome proportion ranges

Results & Key Findings

The study's most striking finding reveals a profound asymmetry in the reliability of polygraph outcomes. The confidence with which a deceptive outcome (DI) can be trusted to be correct is only about 0.65 (65%), while in contrast, the posterior probability of a truthful outcome (NDI) to be correct is 0.98 (98%).

This dramatic difference means that:

• Deceptive results have substantial error risk: When the Israel Police CQT indicates deception, there is approximately a 35% chance the result is wrong
• Truthful results are highly reliable: When the test indicates no deception, there is only about a 2% chance of error
• Base rate effects dominate: These posterior probabilities differ markedly from the test's intrinsic accuracy rates because they incorporate the base rate of actual deception in the tested population

The mathematical model successfully demonstrates how test outcome distributions can be used to infer underlying population base rates. The method is generalized to a wide range of hypothetical proportions of outcomes, with significance discussed concerning the dilemma of using polygraph results as evidence in court.

Discussion & Significance

This research provides crucial insight into the base rate fallacy as it applies to polygraph testing. The findings demonstrate that even with reasonably good test accuracy (~84-94%), the interpretation of positive (deceptive) findings requires extreme caution when the base rate of actual deception is relatively low in the tested population. The 65% posterior confidence in deceptive outcomes is far below what would be needed for high-stakes decisions.

The asymmetry between DI and NDI reliability has important practical implications: polygraph results may be more valuable for exoneration than for inculpation. The 98% posterior probability for truthful outcomes suggests the test is quite effective at identifying honest individuals, while the 65% confidence for deceptive outcomes indicates substantial risk of false accusation.

The paper contributes a methodologically innovative approach that avoids reliance on external ground truth criteria. By using the proportions of test outcomes themselves combined with established accuracy estimates, Ginton demonstrates how to calculate both base rates and posterior probabilities—quantities that are typically unknown in operational settings but critical for proper interpretation of results.

Limitations & Considerations

The calculations depend critically on the accuracy estimates used as inputs. While some scientists support the ~84-94% accuracy figures, quite a few do not accept them, with some claiming much lower accuracy particularly with truthful examinees, while others say there are not enough data to indicate any reliable accuracy rate. If true accuracy is lower than assumed, posterior probabilities would be even less favorable.

The Israel Police outcome distribution (65% NDI, 35% DI) may not generalize to other polygraph populations with different referral patterns, investigative contexts, or examiner practices. Different base rates would yield different posterior probabilities even with identical test accuracy.

The author acknowledges that applying different scoring cut scores to Israel Police examinations would affect outcome proportions to some degree, though assumes the effect would not be substantial. This assumption merits empirical verification.

Practical Applications

For polygraph examiners and investigators, this research underscores the need for caution in interpreting deceptive outcomes. A DI result with only 65% posterior confidence should not be treated as definitive proof of deception. Instead, such results might best serve as an investigative lead warranting further inquiry rather than a dispositive conclusion.

For policymakers and courts, the findings support restrictive admissibility standards for polygraph evidence, particularly for inculpatory results. The substantial false positive risk for DI outcomes helps explain why many jurisdictions exclude polygraph evidence or limit its use to specific contexts.

The analytical framework presented can be applied by any polygraph program to estimate base rates and posterior probabilities from their own outcome distributions and accuracy estimates, enabling evidence-based assessment of result reliability in their specific operational context.