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Related Concept Videos

Variability: Analysis01:11

Variability: Analysis

156
Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
The range is a simple measure of variability, indicating the difference between the highest and...
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Variance01:15

Variance

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 The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
The standard deviation measures the spread in the same units as the...
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Variation01:19

Variation

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An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
When independent and dependent variables are plotted on a scatter plot, the slope of a line is a value that describes the rate of change between the two...
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Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

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The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...
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Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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What is Variation?01:14

What is Variation?

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Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of any data set is its variation or spread. In some data sets, the data values are concentrated closely near the mean; in others, the data values are more widely spread out from the mean.
The range, standard deviation, standard error, and variance are the different measures of variation.
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Updated: Jul 15, 2025

Application of Voltage in Dynamic Light Scattering Particle Size Analysis
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Application of Voltage in Dynamic Light Scattering Particle Size Analysis

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Variance analysis of dynamic light scattering data.

Pietro Anzini1, Davide Biganzoli1, Ihor Cherniukh2

  • 1Dipartimento di Scienza e Alta Tecnologia and To.Sca.Lab, Università degli Studi dell'Insubria, Via Valleggio 11, I-22100 Como, Italy.

The Review of Scientific Instruments
|September 27, 2023
PubMed
Summary
This summary is machine-generated.

A new particle sizing method analyzes scattered light variance, eliminating the need for a correlator used in Dynamic Light Scattering (DLS). This variance (VAR) method accurately determines nanoparticle size and offers comparable performance to DLS.

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Area of Science:

  • Materials Science
  • Physical Chemistry
  • Nanotechnology

Background:

  • Dynamic Light Scattering (DLS) is a standard technique for nanoparticle sizing.
  • DLS relies on analyzing the correlation function of scattered light intensity.
  • Limitations exist in DLS, prompting the search for alternative methods.

Purpose of the Study:

  • Introduce a novel particle sizing method as an alternative to DLS.
  • Develop a technique that bypasses the need for a correlator.
  • Validate the performance of the new method against DLS.

Main Methods:

  • The proposed method utilizes the variance (VAR) of the scattered light signal.
  • It analyzes the behavior of VAR as a function of sampling time (Δt).
  • The correlation time (τc) is recovered using a wide range of sampling times, enabling hydrodynamic diameter calculation via the Stokes-Einstein relation.

Main Results:

  • The variance (VAR) method demonstrated comparable performance to DLS in simulations.
  • The technique was validated on both monodisperse and narrow polydisperse samples.
  • Experimental results on polystyrene spheres and perovskite nanoparticles confirmed the method's efficacy across different setups.

Conclusions:

  • The novel VAR method offers a viable alternative to DLS for nanoparticle sizing.
  • This technique eliminates the requirement for a correlator, simplifying the measurement process.
  • The method provides accurate particle size determination with an analytical error bar expression.