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What do Frequentist Methods rely on in statistical analysis?

Hypothetical repeatability of outcomes

Frequentist methods rely on the concept of hypothetical repeatability of outcomes, which means that they make inferences based on the idea that if an experiment or study were to be repeated many times under the same conditions, the outcomes would stabilize around a certain value due to the law of large numbers. This approach emphasizes the frequency or proportion of events occurring in a theoretically infinite number of trials.

In frequentist analysis, probabilities are interpreted as long-term relative frequencies of outcomes. For instance, if an event occurs with a certain probability, it means that in a large number of trials, that event would occur approximately that proportion of the time. This foundation leads to hypotheses testing, confidence intervals, and p-values that are derived from observed data without incorporating prior beliefs or individual subjective interpretations.

This contrasts with other approaches, such as Bayesian methods which use prior distributions based on previous knowledge or beliefs, or qualitative assessments that involve non-numeric evaluations of data. Frequentist methods stand firmly on the objective measurement of data trends observed in repeated trials, supporting the conclusion that their validity derives from the repeated observation of events.

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The subjective judgement of analysts

Bayesian prior distributions

Qualitative assessments of data

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