Confidence Interval Estimation Task

A Confidence Interval Estimation Task is an interval estimation task that requires a confidence interval estimate.

• Context:
  • It can be solved by an Confidence Interval Estimation System (that implements an confidence interval estimation algorithm).
  • It can involve determining the range within which a Population Parameter is expected to lie with a certain level of confidence.
  • It can utilize Statistical Data from a sample to infer about the population parameter.
  • It can be influenced by factors like Sample Size, Standard Deviation, and Distribution Type of the data.
  • It can be used in various fields, including Medicine, Economics, Social Science, and Engineering.
  • It can employ different methods such as Normal Distribution Method, t-Distribution Method, and Bootstrap Method.
  • It can be applicable for:
    • Estimating population mean or proportion.
    • Determining the range for comparing means of two populations.
    • Assessing the effect size in experimental studies.
  • ...
• Example(s):
  • Task Input: confidence interval = 95%, sample mean = 39.29, sample size = 50, sample standard deviation = 10.17

using a confidence interval estimation system based on python the code

sigma = 10.17/sqrt(50)

# df = degrees of freedom, loc= sample mean, scale = sample standard error

stats.t.interval(0.95, df = 49, loc = 39.26 , scale= sigma)

Task Output: [36.369, 42.150].

• • ...
• Counter-Example(s):
  • Point Estimation Task, which provides a single value as an estimate of a population parameter.
  • Regression Analysis Task, which models the relationship between variables rather than estimating a range for a parameter.
• See: Confidence Interval, Probabilistic Classification, Decision Theory, Sampling (Statistics), Interval (Mathematics), Population Parameter, Statistical Inference.

---

---

References

2006

• (Cesarini et al., 2006) ⇒ David Cesarini, Örjan Sandewall, and Magnus Johannesson. (2006). “Confidence Interval Estimation Tasks and the Economics of Overconfidence.” In: Journal of Economic Behavior & Organization, 61(3).
  • ABSTRACT: We investigate the robustness of results from confidence interval estimation tasks with respect to a number of manipulations: frequency assessments, peer frequency assessments, iteration, and monetary incentives. Our results suggest that a large share of the overconfidence in interval estimation tasks is an artifact of the response format. Using frequencies and monetary incentives reduces the measured overconfidence in the confidence interval method by about 65 percent. The results are consistent with the notion that subjects have a deep aversion to setting broad confidence intervals, a reluctance that we attribute to a socially rational trade-off between informativeness and accuracy.

1997

• (Briggs et al., 1997) ⇒ Andrew H. Briggs, David E. Wonderling, and Christopher Z. Mooney. (1997). “Pulling cost‐effectiveness analysis up by its bootstraps: A non‐parametric approach to confidence interval estimation." Health economics, 6(4).
  • ABSTRACT: The statistic of interest in the economic evaluation of health care interventions is the incremental cost effectiveness ratio (ICER), which is defined as the difference in cost between two treatment interventions over the difference in their effect. Where patient-specific data on costs and health outcomes are available, it is natural to attempt to quantify uncertainty in the estimated ICER using confidence intervals. Recent articles have focused on parametric methods for constructing confidence intervals. In this paper, we describe the construction of non-parametric bootstrap confidence intervals. The advantage of such intervals is that they do not depend on parametric assumptions of the sampling distribution of the ICER. We present a detailed description of the non-parametric bootstrap applied to data from a clinical trial, in order to demonstrate the strengths and weaknesses of the approach. By examining the bootstrap confidence limits successively as the number of bootstrap replications increases, we conclude that percentile bootstrap confidence interval methods provide a promising approach to estimating the uncertainty of ICER point estimates. However, successive bootstrap estimates of bias and standard error suggests that these may be unstable; accordingly, we strongly recommend a cautious interpretation of such estimates.

---