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Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Accuracy and Errors in Hypothesis Testing

Accuracy and Errors in Hypothesis Testing

Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...

Testing a Claim about Standard Deviation

Testing a Claim about Standard Deviation

A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

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The effect size in uncertainty analysis.

Jan J Barendregt¹

¹School of Population Health, University of Queensland, Herston, QLD, Australia. j.barendregt@sph.uq.edu.au

Value in Health : the Journal of the International Society for Pharmacoeconomics and Outcomes Research

|July 28, 2010

Summary

This summary is machine-generated.

Parametric bootstrapping in health economic evaluations can overestimate relative risks. This study presents two correction methods, with the second recommended for accurately reflecting uncertainty intervals in model-based analyses.

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Area of Science:

Health economics
Biostatistics
Statistical modeling

Background:

Model-based health economic evaluations commonly use parametric bootstrapping for uncertainty analysis.
Specifying probability distributions for uncertain model variables is a prerequisite for this method.
A common assumption for intervention effect sizes (relative risk) is a lognormal distribution.

Purpose of the Study:

To address the bias in bootstrap draws from lognormal distributions where the mean exceeds the true relative risk.
To evaluate two distinct correction methods for this overestimation bias.
To compare the advantages and disadvantages of the proposed correction techniques.

Main Methods:

Investigated two methods to correct the overestimation of relative risk in parametric bootstrapping.
Analyzed the properties of bootstrap draws, specifically the mean and uncertainty interval width.
Compared the outcomes of the correction methods against standard lognormal distribution assumptions.

Main Results:

Both presented methods successfully correct the bootstrap mean to equal the true relative risk.
The first correction method results in an uncertainty interval narrower than the confidence interval.
The second correction method preserves the width of the uncertainty interval, matching the confidence interval.

Conclusions:

The second correction method is preferred for parametric bootstrapping of relative risks in health economic evaluations.
This method ensures accurate representation of uncertainty without artificially narrowing the interval.
Accurate uncertainty quantification is crucial for reliable health economic decision-making.