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Confidence interval based parameter estimation--a new SOCR applet and activity.

Christou N, Dinov ID - PLoS ONE (2011)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, University of California Los Angeles, Los Angeles, California, United States of America.

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.

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Results of 100 simulations (samples include N = 2,000 random observations from Beta distribution) of 0.99 confidence intervals for the population proportion (using the exact method) provide effective coverage of 95%.Five of the 100 simulations miss the real population proportion p = 0.47, which represents the shaded area below the Beta density function. This proportion indicates a healthy US unemployment rate between .
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pone-0019178-g022: Results of 100 simulations (samples include N = 2,000 random observations from Beta distribution) of 0.99 confidence intervals for the population proportion (using the exact method) provide effective coverage of 95%.Five of the 100 simulations miss the real population proportion p = 0.47, which represents the shaded area below the Beta density function. This proportion indicates a healthy US unemployment rate between .

Mentions: Then, we can run a simulation and estimate the confidence interval for the proportion of unemployment population to be within the desirable range of (note that is considered “full employment”). Figure 21 shows the confidence interval simulation settings panel, and Figure 22 illustrates the results of the simulation. The 100 simulations of confidence intervals for the population proportion use the exact method and provide effective coverage of . In other words, 5 of the 100 simulations miss the real population proportion ( representing the shaded area below the Beta density function on Figure 22, which indicates a healthy unemployment rate between ). Note that each of the 100 samples contains random observations from Beta distribution. The discrepancy between the expected coverage and the observed coverage rates for the simulated confidence intervals of the population proportion can be explained by random sampling variation or the small number of intervals (100). A larger number of simulations using 1,000 confidence intervals cover the population proportion of interest () of the time (or ).


Confidence interval based parameter estimation--a new SOCR applet and activity.

Christou N, Dinov ID - PLoS ONE (2011)

Results of 100 simulations (samples include N = 2,000 random observations from Beta distribution) of 0.99 confidence intervals for the population proportion (using the exact method) provide effective coverage of 95%.Five of the 100 simulations miss the real population proportion p = 0.47, which represents the shaded area below the Beta density function. This proportion indicates a healthy US unemployment rate between .
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3104980&req=5

pone-0019178-g022: Results of 100 simulations (samples include N = 2,000 random observations from Beta distribution) of 0.99 confidence intervals for the population proportion (using the exact method) provide effective coverage of 95%.Five of the 100 simulations miss the real population proportion p = 0.47, which represents the shaded area below the Beta density function. This proportion indicates a healthy US unemployment rate between .
Mentions: Then, we can run a simulation and estimate the confidence interval for the proportion of unemployment population to be within the desirable range of (note that is considered “full employment”). Figure 21 shows the confidence interval simulation settings panel, and Figure 22 illustrates the results of the simulation. The 100 simulations of confidence intervals for the population proportion use the exact method and provide effective coverage of . In other words, 5 of the 100 simulations miss the real population proportion ( representing the shaded area below the Beta density function on Figure 22, which indicates a healthy unemployment rate between ). Note that each of the 100 samples contains random observations from Beta distribution. The discrepancy between the expected coverage and the observed coverage rates for the simulated confidence intervals of the population proportion can be explained by random sampling variation or the small number of intervals (100). A larger number of simulations using 1,000 confidence intervals cover the population proportion of interest () of the time (or ).

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, University of California Los Angeles, Los Angeles, California, United States of America.

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.

Show MeSH
Related in: MedlinePlus