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The Uncertainty Principle04:08

The Uncertainty Principle

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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Uncertainty in Measurement: Reading Instruments02:46

Uncertainty in Measurement: Reading Instruments

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Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
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pH Scale02:41

pH Scale

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Hydronium and hydroxide ions are present both in pure water and in all aqueous solutions, and their concentrations are inversely proportional as determined by the ion product of water (Kw). The concentrations of these ions in a solution are often critical determinants of the solution’s properties and the chemical behaviors of its other solutes. Two different solutions can differ in their hydronium or hydroxide ion concentrations by a million, billion, or even trillion times. A common means of...
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Uncertainty: Overview00:59

Uncertainty: Overview

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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.
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Uncertainty in Measurement: Significant Figures03:34

Uncertainty in Measurement: Significant Figures

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All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.
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Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

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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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Related Experiment Video

Updated: Feb 6, 2026

Gene Expression Analyses in Human Follicles
09:09

Gene Expression Analyses in Human Follicles

Published on: February 17, 2023

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Incorporating Scale Uncertainty into Differential Expression Analyses Using ALDEx2.

Scott J Dos Santos1, Gregory B Gloor1

  • 1Department of Biochemistry, Schulich School of Medicine and Dentistry, Western University, Ontario, Canada.

Current Protocols
|February 4, 2026
PubMed
Summary
This summary is machine-generated.

Differential abundance analyses in sequencing data are improved by accounting for sample scale uncertainty. ALDEx2

Keywords:
ALDEx2RNA‐seqdifferential abundancedifferential expressionmetagenomics

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Area of Science:

  • Microbiology
  • Bioinformatics
  • Genomics

Background:

  • Differential abundance and expression analyses are standard for sequencing data.
  • Current methods often lack information on true sample scale, leading to technical variation misinterpretation.
  • Existing normalization techniques make flawed assumptions about biological scale, increasing false discovery rates.

Purpose of the Study:

  • To demonstrate incorporating scale models into differential expression analysis for RNA-seq, transcriptome, and metatranscriptome data.
  • To highlight the impact of scale modeling on analysis outcomes.
  • To present visualization methods for ALDEx2 outputs.

Main Methods:

  • Utilizing the ALDEx2 R package to build and apply scale models.
  • Performing differential expression analyses on bulk transcriptome and metatranscriptome datasets.
  • Applying principal component analysis for data visualization.

Main Results:

  • Scale models mitigate incorrect assumptions in normalization, reducing false discovery rates.
  • Incorporating scale models improves the accuracy of differential expression analysis.
  • ALDEx2 outputs can be effectively visualized using compositional principal component analysis.

Conclusions:

  • Accounting for sample scale uncertainty via scale models is crucial for accurate differential abundance and expression analyses.
  • ALDEx2 provides a framework for integrating scale modeling into standard bioinformatics workflows.
  • This approach enhances the reliability of findings from high-throughput sequencing data.