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Test for Homogeneity01:23

Test for Homogeneity

The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can be stated as...
One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
One-Way ANOVA01:18

One-Way ANOVA

One-way ANOVA analyzes more than three samples categorized by one factor. For example, it can compare the average mileage of sports bikes. Here, the data is categorized by one factor - the company. However, one-way ANOVA cannot be used to simultaneously compare the sample mean of three or more samples categorized by two factors. An example of two factors would be sports bikes from different companies driven in different terrains, such as a desert or snowy landscape. Here, two-way ANOVA is used...
One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

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 from...
Multiple Allele Traits01:49

Multiple Allele Traits

The Concept of Multiple Allelism

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Related Experiment Video

Updated: May 27, 2026

Crack Monitoring in Resonance Fatigue Testing of Welded Specimens Using Digital Image Correlation
05:30

Crack Monitoring in Resonance Fatigue Testing of Welded Specimens Using Digital Image Correlation

Published on: September 29, 2019

Crack front dynamics across a single heterogeneity.

J Chopin1, A Prevost, A Boudaoud

  • 1Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Paris 06, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France.

Physical Review Letters
|November 24, 2011
PubMed
Summary
This summary is machine-generated.

Crack front dynamics at an elastomer-substrate interface reveal nonlinear motion. A standard theory accurately predicts steady states but fails during dynamic crack propagation and detachment from defects.

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Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method
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Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method

Published on: January 16, 2019

Related Experiment Videos

Last Updated: May 27, 2026

Crack Monitoring in Resonance Fatigue Testing of Welded Specimens Using Digital Image Correlation
05:30

Crack Monitoring in Resonance Fatigue Testing of Welded Specimens Using Digital Image Correlation

Published on: September 29, 2019

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method
07:37

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method

Published on: January 16, 2019

Area of Science:

  • Materials Science
  • Solid Mechanics
  • Fracture Mechanics

Background:

  • Crack propagation at interfaces is crucial for material durability.
  • Understanding crack front dynamics in heterogeneous materials remains challenging.

Purpose of the Study:

  • To investigate the spatiotemporal dynamics of crack fronts.
  • To analyze crack behavior on homogeneous and patterned elastomer-substrate interfaces.
  • To evaluate the applicability of existing theories to dynamic crack phenomena.

Main Methods:

  • Characterization of crack front kinematics.
  • Analysis of crack profiles on patterned substrates.
  • Comparison of experimental observations with nonlocal elasticity theory.

Main Results:

  • The equation of motion for crack fronts on homogeneous substrates is intrinsically nonlinear.
  • Nonlocal elasticity theory accurately describes steady crack profiles, except for large slopes.
  • The standard theory fails to predict dynamic crack relaxation and pinch-off behavior after defect interaction.

Conclusions:

  • Existing linear theories with nonlocal elasticity have limitations in describing dynamic crack front behavior.
  • Heterogeneities significantly influence crack front dynamics.
  • Further research is needed to develop more comprehensive models for crack propagation in complex media.