Martyn Richard Jones, A Coruña 18th January 2025

Frequentist inference is a type of statistical inference based on frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample data by means of emphasizing the frequency or proportion of findings in the data. Frequentist inference underlies frequentist statistics, in which the well-established methodologies of statistical hypothesis testing and confidence intervals are founded.

http://en.wikipedia.org/wiki/Frequentist_inference

Consider this: Frequentist inference is a branch of statistical inference that focuses on drawing conclusions from data based on the concept of frequency or long-term behaviour of repeated samples. It is one of two major schools of statistical thought, the other being Bayesian inference.

In short, frequentist inference is a fundamental framework for making data-driven decisions based on the long-term properties of estimators and test statistics. It is particularly suited to applications where objectivity, standardization, and simplicity are prioritised.

When to use: When you know what you are doing.

When not to use: When you don’t know what you are doing.

Strengths: There are three key areas where this approach excels:

• Objectivity: Results depend only on the data and the model, not on prior beliefs.
• Standardization: Most commonly used methods (e.g., p-values, confidence intervals) are well understood and standardized across disciplines.
• Simplicity: Often computationally simpler than Bayesian methods for standard problems.

Weaknesses: The key weaknesses of this approach are:

• Lack of flexibility: Limited in incorporating prior information or expert knowledge.
• Criticism of p-values: Over-reliance on p-values ​​can lead to misinterpretations (e.g. p-hacking or arbitrary thresholds).
• Interpretation of confidence intervals: Confidence intervals do not provide a direct probability statement about the parameter, which can be confusing.

Frequentist: “The parameter is fixed; the interval varies.”

Bayesian: “The interval reflects the probability that the parameter lies within it.”

Passing comments: “There is something in the unselfish and self-sacrificing love of a brute, which goes directly to the heart of him who has had frequent occasion to test the paltry friendship and gossamer fidelity of mere Man.” – Edgar Allan Poe.