Abstract

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are interpreted as classical probabilities, and this interpretation of equally likely chance outcomes is applied to statistical inference using urn models. These are used to address Bayesian criticisms of frequentist methods. Recent descriptions of p-values, confidence intervals, and power are viewed through the lens of classical probability based on a single random sample from the population.

Highlights

  • Frequentist inference, as a subset of statistical inference, appears to require hypothetical repeated sampling

  • The same is true for probability: a probability model describes the distribution of the population and a single random sample is better described in terms of a proportion rather than an infinite limit of frequencies obtained by hypothetical random samples

  • We compare these interpretations with the standard frequentist interpretation: the observed 95% confidence interval 1.01 < θ < 16.0 either does or does not contain θpop, 95% refers to the procedure that generated this interval and this procedure produces intervals that cover the population parameter value θpop at least 95% of the time

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Summary

Introduction

Frequentist inference, as a subset of statistical inference, appears to require hypothetical repeated sampling. Arguments involving probability only via its (hypothetical) long-run frequency interpretation are called frequentist. We define procedures for assessing evidence that are calibrated by how they would perform were they used repeatedly. In that sense they do not differ from other measuring instruments. The entry “Frequency Interpretation in Probability and Statistical Inference” in the Encyclopedia of Statistical Sciences (ESS) restricts the interpretation to repeated trials

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Frequentist statistical inference
Inference for a deck of cards
The p-value and model percentiles
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Definition versus interpretation
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Two interpretations
Criticism of these interpretations
Common understanding of probability
ESS example
Gambling examples
Clinical trial example
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Relationship between the interpretations
Scope-specific or generic
Focus-population or model
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Urn models
Population urn
Model urns
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Compared to repeated sampling
Confidence intervals
Comparing the interpretations
Clinical trial example revisited
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P-values
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10 Discussion
Findings
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Full Text

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