Statistical Interval Estimate

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A Statistical Interval Estimate is a statistical estimate that provides a range of values, calculated from a sample, within which a population parameter is expected to lie.

  • Context:
    • It can (typically) be calculated with a Statistical Interval Estimation Task (an interval estimation task).
    • It can be used to indicate the reliability and precision of an estimate of a population parameter.
    • It can be derived from sample data and a specified probability, typically expressed as a confidence level (e.g., 95%).
    • It can vary in width, where a wider interval indicates less precision and a narrower interval indicates more precision.
    • It can be influenced by the sample size, with larger samples typically leading to narrower intervals.
    • It can be constructed for various population parameters, such as means, proportions, variances, and differences between parameters.
    • It can be used for:
      • Estimating a population mean with a confidence interval.
      • Estimating a population proportion with a confidence interval.
      • Estimating the difference between two population means or proportions.
    • ...
  • Example(s):
    • Confidence Interval, which quantifies the uncertainty of an estimate by specifying a range of plausible values for the population parameter.
    • Prediction Interval, which provides a range of values for a single new observation from the population.
    • Tolerance Interval, which covers a specified proportion of the population with a specified level of confidence.
    • Credible Interval, often used in Bayesian analysis, representing a range of values within which an unobservable parameter value lies with a certain probability.
    • ...
  • Counter-Example(s):
    • Point Estimate, which provides a single value as an estimate of a population parameter.
    • Hypothesis Test, which assesses the evidence against a specific hypothesis rather than estimating a range for a parameter.
    • ...
  • See: Confidence Level, Sample Size, Population Parameter, Statistical Inference, Central Limit Theorem, Sampling Distribution.


References

2023

2016

  • (Steiger & Fouladi, 2016) ⇒ James H. Steiger, Ramin T. Fouladi. (2016). “Noncentrality Interval Estimation and the Evaluation of Statistical Models." In: "What if there were no significance tests." [1].
    • Note: This work reviews standard interval estimation procedures and argues for their superiority over traditional significance tests, emphasizing the benefits of interval estimation in statistical model evaluation.

2001

  • (Brown et al., 2001) ⇒ Lawrence D. Brown, T. Tony Cai, Anirban DasGupta. (2001). “Interval Estimation for a Binomial Proportion." In: Statistical Science, 2001. [2].
    • Note: This article critically examines the Wald confidence interval for a binomial proportion and explores alternative interval estimation methods, addressing issues like coverage probability and computational efficiency.

1954

  • (Fieller, 1954) ⇒ E. C. Fieller. (1954). “Some Problems in Interval Estimation." In: Journal of the Royal Statistical Society Series B: Statistical Methodology. [3].
    • Note: This historical paper tackles the challenges in interval estimation within mathematical statistics, focusing on the expectations and limitations of interval estimates for true or population values.