Frequentist Approach

The frequentist (or classical) approach is a branch of statistics that currently represents the predominant methodology used in empirical data analysis and inference. Frequentist statistics emerged as a prevailing method for inference in the 20th century, particularly due to work by Fisher and, subsequently, by Neyman and Pearson. Given that distinct differences exist between the research conducted by these authors, however, frequentist inference may also be subcategorized as being either Fisherian or Neyman-Pearson in nature, although some view the Fisherian approach to be a distinct philosophy apart from frequentist statistics altogether.

Frequentist methods are often contrasted with those of Bayesian statistics, as these two schools of thought represent the more widely considered approaches through which formal inference is undertaken to analyze data and to incorporate robust measurements of uncertainty. Although frequentist and Bayesian statistics do share certain similarities, important divergence between the approaches should also be noted. In this context, the central tenets that differentiate the frequentist paradigm from other statistical methods (e.g., Bayesian) involve (a) the foundational definition of probability that is employed and (b) the limited framework through which extraneous information (i.e., prior information) is assessed from sources outside of the immediate experiment being conducted. Ultimately, these characteristics affect the breadth of research design and statistical inference. By formally focusing primarily on data that emanate from an immediate experiment being conducted (e.g., a randomized clinical trial) and not on additional sources of information (e.g., prior research or the current state of knowledge), results of a frequentist analysis are essentially confined to an immediate study. Reliance is thus often placed on a more informal process to consider extraneous data from sources beyond the immediate study. Although this issue has, in part, led to its theoretic appeal among both regulatory agencies and scientists as being an “objective” method of inference (e.g., the conclusions of a single study do not allow for other findings to affect statistical inference), the frequentist approach has also been viewed as lacking a full rigor that parallels the comprehensive aspects of scientific inquiry and decision theory. Despite a lengthy debate concerning these philosophical issues, the frequentist approach remains the most commonly used method of statistical inquiry. When correctly applied and interpreted, frequentist statistics also represent a robust standard for point estimation, interval estimation, and statistical/hypothesis testing. Consideration of the frequentist approach is additionally important when addressing the overall study design, sample size calculations, and effect sizes.

Within the frequentist paradigm, probability is defined as a long-run expected limit of relative frequency within a large number of trials or via a frequency concept of probability that denotes the proportion of time when similar events will occur if an experiment is repeated several times. Hence, classical statistical analysis and inference yields interpretations only within a context of repeated samples or experiments. While the theory of infinitely repeatable samples may be viewed as a largely hypothetical issue for an analyst (i.e., because researchers typically obtain only one random draw from a population), the concept becomes of fundamental importance in interpreting results within the frequentist paradigm. Furthermore, the assumption of infinite repeated samples imparts asymptotic properties (e.g., the law of large numbers, convergence, the central limit theorem), which are required for robust inference under the frequentist approach.

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