Departamento de Métodos Cuantitativos en Economía y Gestión, Universidad de Las Palmas de Gran Canaria - Campus de Tafira, Las Palmas de Gran Canaria, Spain.
Fundación para el Fomento de la Investigación Sanitaria y Biomédica de la Comunidad Valenciana (FISABIO), Red de Investigación en Servicios de Salud en Enfermedades Crónicas (REDISSEC), València, Spain.
BMJ Open. 2018 May 9;8(5):e022079. doi: 10.1136/bmjopen-2018-022079.
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.
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.
Adjustment of the observed distribution of the numbers reported in Finnish and Spanish WL data to the expected distribution according to NBL.
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).
Testing deviations from NBL distribution can be a useful tool to identify problems with WL data trustworthiness and signalling the need for further testing.
纽博特-本福特定律（NBL）提出了一种适用于许多不同自然发生数据来源的首位数字、次位数字和数字组合的规则分布。在许多数据集，测试与 NBL 的偏差被用作识别数据可信度问题的筛选工具。本研究旨在比较芬兰和西班牙的公共可用等待名单（WL）数据，以测试 NBL 作为标记 WL 中潜在操纵的工具。
分析芬兰和西班牙 WL 首位数字的频率，以确定其分布是否与 NBL 记录的模式相似。使用 Pearson χ 检验、平均绝对偏差和 Kuiper 检验分析偏离预期首位数字频率的情况。
设置/参与者：芬兰和西班牙的公共 WL 数据，这两个国家都有全民健康保险和国家卫生系统，但透明度和良好治理标准不同。
根据 NBL 调整芬兰和西班牙 WL 数据中报告数字的观察分布。
芬兰卫生系统报告的 WL 数据符合所有使用的统计检验的首位数字 NBL（χ 检验中 p=0.6519）。对于西班牙数据，该假设在所有检验中均被拒绝（χ 检验中 p<0.0001）。
测试与 NBL 分布的偏差可以成为识别 WL 数据可信度问题的有用工具，并表示需要进一步测试。
