Pinocchio testing in the forensic analysis of waiting lists: using public waiting list data from Finland and Spain for testing Newcomb-Benford's Law.

Objective: Newcomb-Benford's Law (NBL) proposes a regular distribution for first digits, second digits and digit combinations applicable to many different naturally occurring sources of data. Testing deviations from NBL is used in many datasets as a screening tool for identifying data trustworthiness problems. This study aims to compare public available waiting lists (WL) data from Finland and Spain for testing NBL as an instrument to flag up potential manipulation in WLs.

Design: Analysis of the frequency of Finnish and Spanish WLs first digits to determine if their distribution is similar to the pattern documented by NBL. Deviations from the expected first digit frequency were analysed using Pearson's χ, mean absolute deviation and Kuiper tests.

Setting/participants: Publicly available WL data from Finland and Spain, two countries with universal health insurance and National Health Systems but characterised by different levels of transparency and good governance standards.

Main Outcome Measures: Adjustment of the observed distribution of the numbers reported in Finnish and Spanish WL data to the expected distribution according to NBL.

Results: WL data reported by the Finnish health system fits first digit NBL according to all statistical tests used (p=0.6519 in χ test). For Spanish data, this hypothesis was rejected in all tests (p<0.0001 in χ test).

Conclusions: Testing deviations from NBL distribution can be a useful tool to identify problems with WL data trustworthiness and signalling the need for further testing.