# A Critical Approach to Statistical Inquiry

In scientific analysis, statistical methods are employed to understand the common properties of the entities, the material and its substances. Also, social studies commonly resort to statistical methods and their interpretations to come up with common principles of how the society, its elements and human psyche works. These applications intend to attain universal principles and properties of the workings for the entities and phenomena that are inspected (Chance, 2006). In this sense, statistical inquiry becomes the source of the relation between the inquiries of humanity and the systems that make up the world as a way of interpretation and comprehension of the information that is obtained through the inscribed datum of the particular experiences and experimentation. Statistical inquiry is the practice of reasoning that takes the specific as a base to make a point about the general. Through inductive reasoning, this inquiry mobilizes the specific cases of certain events to find universal regulations that explain the occurring phenomena. In this manner, this article will elaborate on the practical and theoretical applications of statistical inquiry and present the inquiry critically. Thus, what the statistical method can or cannot provide regarding the occurring phenomena and the limitations of the statistical method are going to be put forth to comprehend the inquiry as a whole and to be able to reflect on it.

Statistical inquiry is the act of making sense of the world. To develop the idea of statistics, the theoretical approaches and the tools of the method are needed to be understood. The theories of statistics are regarded as in the field of epistemology because statistical inquiry is an inquiry that aims to develop data processing and producing information and knowledge about the world (Chance, 2006). Theories of statistical inquiry involve and evolve around the idea of probability (Hacking, 2001). Considering the idea of probability as an epistemological property, the singular data or information regarding the particular experiences together make up the possibilities that the circumstances lead to these probable events (Good, 2008). Thus, the statistical approach requires defining a set of events and the circumstances that are leading to that event. In the definition of the set of events, the set is divided into different subsets of probability. The number of the events that correspond to the similar results are involved into the subset of the same determination of probability (Hacking, 2001). Probability is the likelihood of occurrence of an event. By definition, the probability of an event can be certain, impossible, or any degree of possibility in-between the certain and the impossible probability (Hacking, 2006). Mathematically, the probability of a certain event is signified by the value one, and the probability of the impossible event is signified by zero. In this way, the probability of any event can take rational values between one and zero (Feller, 1968). On the other hand, the definition of circumstances that lead to the certain probabilistic function of events incur hypothesis making of the statistical inquiry. A hypothesis is a possible explanation for a phenomenon that is put forth to be the basis of reasoning in the explanation of the phenomenon (Finch, 1981). In this sense, the hypothesis for a set of outcomes is built by defining the circumstances (Cochran, 1983). Hence, the theories of statistics branch in their manner of approaching these tools of statistical inquiry as hypothesis making or obtaining the information of the probability.

Statistical theories are applied in practice as implementations of the ideas of probability and hypothesis into the experiences and experimentation. The idea of probability in an epistemological manner is applied to the practice of statistical inquiry by defining the events and determining circumstances that affect the event (Hacking, 1999). For scientific method, experimentation and collection of data from the particular experiments to deduce a general regulation for how the processes in question works is the main idea of the application of statistical theory into practice (Cochran, 1983). For the fields of chemistry, physics or biology, the numbers of the particular occurrences of the certain types for the tested hypothesis represent the set of the probability of that occurrence, e.g. number of different kinds of particles in a particle collider after collision, different concentrations of different chemical components in a reaction, or populations of different kinds of bacteria species. On the other hand, for social sciences, statistical method is applied by conduct of studies on communities and different populations to come up with an understanding of how the social processes are working for the population or the community under inspection, e.g. economic, cultural or psychological tendencies of different populations (Agresti, 2013). For the former, the conducted statistical analysis may seem to result in concrete regulations of probabilistic distribution. However, in the latter, the biases of the hypothesis building, or interpretation of the probability distributions tend more to rise to the occasion (Nelder, 1999).

The reason behind this simply is that when the eye turns to itself, the subjectivity bias appears more to be at work because the interpretations and hypotheses seem to be built upon the belief system of the analyst unless they elude from their cultural background and belief systems, and the analysis methods could seem to be rooted in the cultural background. Hence, the criticism of the statistical inquiries come forth in these senses of application. The question arises that if statistical inquiry is subject to such biases because of its two main methods, then why does it depend on such tools for interpretation of the world? The reason for the dependence of the statistical epistemic relation on hypothesis building or interpretation of probability distribution is that it is a follow up of an ontological tradition of comprehension of being and entities. Statistical inquiry is a method of interpretation of the world that comes from an ontological assumption to an epistemological method of inductive reasoning (Acree, 2021b). The ontological part of this epistemological understanding is that the world in the broadest sense is applicable and bound to observations and interpretations of particulars. Hence, knowledge of the universal can be obtained through relating the various particular instances to each other, which corresponds to a domain ontology (Titel, (n.d.)), that is inferred by the information science ontologies (Petrov, 2013). This correspondence leads to the method of induction of statistical inquiries.

If statistics is taken as a biased inquiry that atomizes and generalizes the world, then there has to be an alternative to comprehend the world in a different manner rather than the manner of atomization and determination of the circumstances. Developments in data science propose new ways to analyze information in a sense that connects information in different fields that leads to the new ways of comprehension of the world (Kelleher, 2018). However, different ways to comprehend the world rather than determination and atomization could approach the world as rather continuous and connected such that it is chaotic and regularities occur at the same time. Such a theory is chaos theory that investigates the world as a connected entity. However, it emphasizes a sense of determinism in chaos because of its adherence to mathematics (Gleick, 2022). Gleick puts it forth as feeling the order of the iteration of the substance of chaotic world with intuition. Though, this theory leads to a connective and collective understanding of the world. Its loyalty to the deterministic understanding still keeps the same line of ontological properties with the statistical inquiry.

In conclusion, statistical inquiry is a bridge that connects the inquiries of the world with the information of the world as a sense organ, and this sense organ evolves through time. This inquiry operates with the tools of hypothesis making and probability interpreting, which are also the parts that carry its biases. The biases of the tools are not merely by the way they operate, but also because of the ontological assumptions they are rooted in. Hence, the inquiries of the world evolve into new understandings of connected and collective version of the world and different fields of the inquiries as in data science or chaos theory. In this sense, these inquiries lead the way of augmentation of the statistical inquiry. However, for the statistical inquiry to be able to make the generalizations that it claims to be making, an elusion from the determinism is necessary in a way that it includes subjectivity as a receptary feature of analysis rather than as a bias.

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