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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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Related in: MedlinePlus

Results of 10 runs of the experiment.
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pone-0019178-g007: Results of 10 runs of the experiment.

Mentions: We observe that all the input parameters are recorded on the right margin of the applet's main window (Figure 6). There are two displays on this window. The top display shows the distribution mean and the sample values ( in our example) selected for each interval (we have constructed 20 intervals). The second display depicts the actual 20 intervals which are constructed from the 20 random samples (red segments). When a confidence interval misses the true mean (here ) a green dot is shown to indicate this discrepancy. Observe that in this example because we have assumed that the population standard deviation is known () all the intervals have the same length. The confidence level was chosen to be and therefore it is not surprising that among the 20 intervals only one missed the target parameter (). If we choose to run the experiment multiple times (for example 10 times), we simply select the “Number of Experiments  = 10” and then click on the “Run” button. The results from each run of these 10 experiments are recorded on the right margin of the applet and are shown on Figure 7. In general, as these are random simulations, repeats of the experiment using the same parameter settings would generate different outcomes (sample instances and corresponding confidence intervals).


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

Christou N, Dinov ID - PLoS ONE (2011)

Results of 10 runs of the experiment.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0019178-g007: Results of 10 runs of the experiment.
Mentions: We observe that all the input parameters are recorded on the right margin of the applet's main window (Figure 6). There are two displays on this window. The top display shows the distribution mean and the sample values ( in our example) selected for each interval (we have constructed 20 intervals). The second display depicts the actual 20 intervals which are constructed from the 20 random samples (red segments). When a confidence interval misses the true mean (here ) a green dot is shown to indicate this discrepancy. Observe that in this example because we have assumed that the population standard deviation is known () all the intervals have the same length. The confidence level was chosen to be and therefore it is not surprising that among the 20 intervals only one missed the target parameter (). If we choose to run the experiment multiple times (for example 10 times), we simply select the “Number of Experiments  = 10” and then click on the “Run” button. The results from each run of these 10 experiments are recorded on the right margin of the applet and are shown on Figure 7. In general, as these are random simulations, repeats of the experiment using the same parameter settings would generate different outcomes (sample instances and corresponding confidence intervals).

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