Science follows the path of intuitive exploration-an endeavor to find answers to the unknown. Guided by, and founded upon, the use of mathematics, science tests and confirms the conjectures of creative scientific thinking, resulting in a corpus of collective knowledge that has been robustly examined and can be reproduced by a community following the scientific method. This scientific method is thus based on the systematic collection and scrutiny of empirical evidence attained through precise measurement. As such, the means employed to measure phenomena are as important as the methods used for analysis. Choosing an inappropriate mathematical framework to analyze our data or overconstraining the way in which data are gathered or measured can often derail the path of scientific inquiry. Constrained methodology and/or inappropriate methods of analysis are often reflected in a constrained, dogmatic one-sided view of a phenomenology that is ungeneralizable to the broader context-an inherent feature of the replication crisis now facing psychology (Francis 2012a, 2012b, 2012c, 2012d and see Chapter 11). This crisis has had a profound effect on the academic field of inquiry at large, leading to increased scrutiny and questioning of methodologies employed. Yet more importantly, this epidemic implies that psychological results are not conducive to generalizable knowledge that may benefit humanity at large-that is, they are unlikely to build toward lawlike findings that we can trust as general rules to integrate into the foundations for further inquiry. Indeed, building a core foundational corpus of knowledge to spawn further scientific inquiry and discovery is at the heart of the scientific method. Thus, modes of inquiry, the methods of data gathering, and analysis techniques in fields that deal with mental health and psychological phenomena, including those within a clinical setting, are arguably more an art than a science-as defined by the scientific method. This section aims to expose some of the issues that we need to address in the specific field of autism spectrum disorder (ASD) research if we are to make progress in posing proper lines of inquiry to begin defining the phenomena surrounding this constellation of disorders. Drawing on mathematical principles, these chapters aim to illustrate the importance of the concrete application of sound instrumentation to measure phenomena at all levels-including complex human behaviors. Methods to analyze and scrutinize data that can be applied within this broad context will be introduced in an attempt to showcase how the field can move toward applications that can invariably hold stable across different cultures and historical time periods for generalizable, replicable data.
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