## 3 Method  
To study how the frequency of delays changes under different passenger volumes, we perform a Chi-square goodness of fit test. Using intervals for the delay size rather than a binary approach not only shows the frequency of delays but also the most common delay sizes. We limit ourselves to delays ranging between 1 and 120 s. This range is based on the most frequent delay sizes found in our data. In addition to this, we include situations where there is no delay. We then perform a Chi-square goodness of fit test between the frequency distribution under different passenger volumes and the unconditional frequency distribution based on the distribution of delays when not taking passenger volumes into account. When performing a Chi-square goodness of fit, the expected frequencies should at least be five. In order to fulfil this criterion, we grouped our data based on delay sizes and passenger volumes prior to the statistical test. Passenger volumes were grouped into intervals of ten passengers, and delay sizes into intervals of fifteen seconds.  
A drawback of using a Chi-square goodness of fit test is that it only confirms the existence of any differences in the frequency distribution and does not provide insights into the nature of these differences. We, therefore, perform several post hoc tests to understand the influence of passenger volumes on the frequency of dwell time delays when statistically significant results are found. The post hoc tests consist of performing a visual graphical analysis of the frequency distributions, a pairwise post hoc comparison using the Bonferroni correction as suggested by [27], and computing Cohen's W to determine the effect sizes.  
The visual graphical analysis is performed to understand the nature of any differences in the frequency distribution that were found to be statistically significant. Visual graphical analysis is an explorative technique that can aid in the analysis and interpretation of the data by visually representing the information [28; 29; 30; 31]. This technique is commonly used in railway research to, for example, visualize the on-time performance of train lines by plotting delay profiles [32; 33]. Pairwise comparisons are made between the observed and expected values for each delay size at different passenger volumes individually. A Bonferroni correction, which adjusts the critical value for the alpha by dividing the critical \(p\) value by the number of tests, is performed to control for a potential familywise error rate for multiple comparisons, as suggested by [34]. We then compute Cohen's W effect sizes. Effect sizes are important here since we run the risk of a large sample size fallacy where small, irrelevant effects show up to be statistically significant as a result of the number of observations in our sample size [35]. The effect size, denoted at [PERSON]'s W, is based on the difference between observed and expected proportions. Here, we consider the observed and expected proportion for the dwell time delay sizes under different passenger volumes. Effect sizes are categorized based on the values provided by [36], where effects are said to be small (W = 0.1), medium (W = 0.3), or large (W = 0.5).