## 1 Introduction  
The study of the statistical significance  
## 1 Introduction  
In clinical medicine, precise determination of the concentration of a given compound is essential. For instance, in the case of suspected heart attack, the concentration of specific biomarkers must be determined accurately in a blood sample of the patient to support the diagnosis. Inaccurate mathematical calculations based on laboratory measurements may lead to erroneous biomarker concentrations and misdiagnosis. Therefore, mathematical calculations are heavily relied upon in daily clinical and laboratory practices, but it is crucial to ensure that the underlying assumptions of these calculations are satisfied. This report addresses one such assumption, namely parallelism.  
Demonstration of parallelism is crucial for the accuracy of any test based on calculating sample concentration from a standard curve [1]. However, it has been noted that there is no widely adopted universal strategy for assessing parallelism in bioassays. Without assurance of parallelism, investigators are unable to calculate reliable estimates for serum antibody concentrations [1]. To address this issue, it has been suggested to visually compare the slope of logistic-log curves, for which a series of excellent examples have been provided. The authors cautioned against purely statistical assessments of parallelism, as the methods of computation are complex, not readily available in software packages, prone to error unless interpreted correctly, and overly sensitive to negligible departures from parallelism when model precision is high. Furthermore, no guidance was provided on how to interpret the data in cases where there is partial non-parallelism, which may make it challenging for users to determine the appropriate course of action. Notwithstanding this constraint, the parallelism plots initially proposed [1] continue to serve as a valuable graphical tool for evaluating parallelism in laboratory tests, and their significance has been acknowledged in subsequent research. According to this authoritative perspective [2], the experimental validation of parallelism remains a challenging and pivotal aspect in the validation of bioanalytical methods to this day, an assertion that was reiterated in a highly influential white paper [3].  
Regulatory authorities impose strict requirements for the approval of an assay, including the demonstration of parallelism. As per the latest guidelines by the Food and Drug Administration (FDA) and European Medical Agency (EMA), parallelism is defined as \"Parallelism demonstrates that the serially diluted incurred sample response curve is parallel to the calibration curve\" [4]. The guideline provides explicit laboratory instructions for conducting the study, involving the dilution of a high-concentration study sample to at least three concentrations with a blank matrix. However, the interpretation of results becomes more ambiguous. The guideline states that the consistency of back-calculated concentrations between samples in a dilution series should not exceed a 30% coefficient of variation (CV). Nevertheless, it is essential to carefully monitor the data, as results meeting this criterion may still indicate trends of non-parallelism. In cases where the sample does not dilute linearly, a predefined procedure for reporting results should be established. In this report, I propose a simple graphical approach for such a procedure, as it may offer greater intuitiveness and be less susceptible to the limitations previously recognised in purely numerical methods [1,2].  
The concept of parallelism may appear simple at first glance, but it can be difficult to understand upon further examination. Additionally, numerically driven, statistical representations of parallelism may not be intuitive for individuals without a statistical background. This lack of understanding can be problematic for regulatory authorities and mixed expertise panels tasked with making decisions in laboratory-based research.