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<p>This study investigates the impact of design decisions on the outcomes of chi-squared tests when applied to Poisson distributions, using the practical example of arrivals in a parking garage. Through a combination of experiments and simulations, we found that variations in modeling parameters, such as interval length, observation period, and the number of classes, significantly influence the <i>p</i>-values of the chi-squared test. Specifically, increasing interval lengths resulted in reduced sample sizes and greater variance in the average number of events, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>, leading to lower <i>p</i>-values and contrasting previous findings from the literature. Furthermore, we find that biases, such as those arising from disruptions like COVID-19 lockdowns, have a smaller impact than anticipated, whereas sample size is a dominant factor, with larger samples consistently producing lower <i>p</i>-values. Our results highlight the susceptibility of chi-squared tests to parameter choices, emphasizing the risk of misleading conclusions when testing the fit of a Poisson distribution. We recommend that practitioners carefully select model parameters to avoid false claims of statistical significance and urge reviewers to critically assess test setups.</p>

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From Theory to Practice: Exploring the Chi-Squared Goodness-of-Fit Test for Poisson Distributions with Car Parking Data

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月8日

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  • Thomas Müller,
  • Dirk Schweim

摘要

This study investigates the impact of design decisions on the outcomes of chi-squared tests when applied to Poisson distributions, using the practical example of arrivals in a parking garage. Through a combination of experiments and simulations, we found that variations in modeling parameters, such as interval length, observation period, and the number of classes, significantly influence the p-values of the chi-squared test. Specifically, increasing interval lengths resulted in reduced sample sizes and greater variance in the average number of events, \(\lambda\) λ , leading to lower p-values and contrasting previous findings from the literature. Furthermore, we find that biases, such as those arising from disruptions like COVID-19 lockdowns, have a smaller impact than anticipated, whereas sample size is a dominant factor, with larger samples consistently producing lower p-values. Our results highlight the susceptibility of chi-squared tests to parameter choices, emphasizing the risk of misleading conclusions when testing the fit of a Poisson distribution. We recommend that practitioners carefully select model parameters to avoid false claims of statistical significance and urge reviewers to critically assess test setups.