Statistical Interval Estimate

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.

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References

2023

• (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/Interval_estimation Retrieved:2023-11-26.
  • In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a parameter of interest. This is in contrast to point estimation, which gives a single value.
    • The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method);
    • less common forms include likelihood intervals and fiducial intervals.
    • Other forms of statistical intervals include tolerance intervals (covering a proportion of a sampled population) and prediction intervals (an estimate of a future observation, used mainly in regression analysis).
    • Non-statistical methods that can lead to interval estimates include fuzzy logic.

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.

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