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Related Concept Videos

Uncertainty: Confidence Intervals00:54

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...
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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.
Propagation of Uncertainty from Systematic Error01:10

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
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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...
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Interpretation of Confidence Intervals

A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...

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Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
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Information theoretic quantification of diagnostic uncertainty.

M Brandon Westover1, Nathaniel A Eiseman, Sydney S Cash

  • 1Neurology Department, Massachusetts General Hospital, Wang 720, Boston, MA 02114, USA.

The Open Medical Informatics Journal
|January 11, 2013
PubMed
Summary

Physicians struggle with diagnostic test interpretation due to probabilistic reasoning challenges. This work introduces information theory as an accessible framework to better quantify diagnostic uncertainty, especially when estimating pre-test probabilities.

Keywords:
Bayes’ rulediagnosisinformationprobabilityuncertainty.

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Area of Science:

  • Medical Diagnostics
  • Clinical Decision Making
  • Information Theory

Background:

  • Diagnostic test interpretation is challenging for physicians.
  • Bayes' rule is commonly taught but often misapplied, especially with unexpected results.
  • Information theory offers a framework for quantifying uncertainty but is unfamiliar to clinicians.

Purpose of the Study:

  • To present information theory concepts accessibly for physicians.
  • To extend previous work on pre-test probability uncertainty using an information theoretic framework.
  • To address obstacles hindering physicians' application of information theory in diagnostics.

Main Methods:

  • Review and explanation of core information theory concepts.
  • Application of information theory to diagnostic uncertainty and pre-test probability estimation.
  • Discussion of terminology and mathematical assumptions in information theory for clinical use.

Main Results:

  • Information theory provides a principled framework for understanding diagnostic uncertainty.
  • The study addresses challenges in applying information theory, including terminology and mathematical assumptions.
  • It illustrates how ranges, not just point estimates, of pre-test probability affect diagnostic uncertainty.

Conclusions:

  • Information theory offers a valuable alternative for diagnostic test interpretation.
  • Overcoming terminology and mathematical hurdles can facilitate physician adoption.
  • Considering uncertainty in pre-test probability estimation is crucial for accurate diagnosis.