Abstract
Many scientific investigations depend on obtaining data-driven, accurate, robust and computationally-tractable parameter estimates. In the face of unavoidable intrinsic variability, there are different algorithmic approaches, prior assumptions and fundamental principles for computing point and interval estimates. Efficient and reliable parameter estimation is critical in making inference about observable experiments, summarizing process characteristics and prediction of experimental behaviors. In this manuscript, we demonstrate simulation, construction, validation and interpretation of confidence intervals, under various assumptions, using the interactive web-based tools provided by the Statistics Online Computational Resource (http://www.SOCR.ucla.edu). Specifically, we present confidence interval examples for population means, with known or unknown population standard deviation; population variance; population proportion (exact and approximate), as well as confidence intervals based on bootstrapping or the asymptotic properties of the maximum likelihood estimates. Like all SOCR resources, these confidence interval resources may be openly accessed via an Internet-connected Java-enabled browser. The SOCR confidence interval applet enables the user to empirically explore and investigate the effects of the confidence-level, the sample-size and parameter of interest on the corresponding confidence interval. Two applications of the new interval estimation computational library are presented. The first one is a simulation of confidence interval estimating the US unemployment rate and the second application demonstrates the computations of point and interval estimates of hippocampal surface complexity for Alzheimers disease patients, mild cognitive impairment subjects and asymptomatic controls.
Highlights
Variability and Estimation in Quantitative Studies Solutions to many biological, engineering, social, environmental or health related challenges depend on obtaining accurate, robust and computationally-tractable parameter estimates
The SOCR confidence interval applet is unique in a way that it allows the user to interactively sample from any of the 70z distributions of SOCR (Figure 2), set the specific parameters of the distribution, select the appropriate confidence interval parameter (m,s,p, etc.) and choose the a
Clicking on the ‘‘Step’’ tab on the main applet window will show the results of a single run of the confidence interval (CI) experiment, using the user specified parameters, Figure 5
Summary
Variability and Estimation in Quantitative Studies Solutions to many biological, engineering, social, environmental or health related challenges depend on obtaining accurate, robust and computationally-tractable parameter estimates. Observable phenomena and designed experiments are affected by intrinsically or extrinsically induced variation [1]. Our understanding of such processes frequently revolves around estimating various population parameters of interest based on observed (acquired) data. There are different algorithmic approaches, prior assumptions and principals for computing data-driven parameter estimates. These depend on the distribution of the process of interest, the available computational resources and other criteria that may be desirable [2], e.g., biasness and robustness of the estimates. There are several different situations: 1. Depending upon our knowledge of the population variance (s2), there are two approaches for constructing the confidence interval for the population mean, m
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