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Correlations

Correlations

Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...

Correlation

Correlation

In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:

Coefficient of Correlation

Coefficient of Correlation

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the strength of the linear...

Correlation and Causation

Correlation and Causation

Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
Correlation versus Causation
If the dependent variable increases or decreases when the independent variable increases, there is a positive or negative...

Correlation and Regression

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...

Network Covalent Solids

Network Covalent Solids

Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...

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Related Experiment Video

Updated: May 19, 2026

Determining the Mechanical Strength of Ultra-Fine-Grained Metals

Determining the Mechanical Strength of Ultra-Fine-Grained Metals

Published on: November 22, 2021

Strongly correlated materials.

Emilia Morosan¹, Douglas Natelson, Andriy H Nevidomskyy

¹Department of Physics and Astronomy MS 61, Rice University, 6100 Main St., Houston, TX 77005, USA.

Advanced Materials (Deerfield Beach, Fla.)

|August 16, 2012

Summary

This summary is machine-generated.

Strongly correlated materials exhibit unique electronic and magnetic properties due to electron-electron interactions. Research at Rice University explores their quantum phase transitions, novel phases, and potential technological applications.

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Area of Science:

Condensed Matter Physics
Materials Science

Background:

Strongly correlated materials are significantly influenced by electron-electron repulsion, unlike common materials like silicon.
These materials display remarkable properties and phase transitions with distinct electronic and magnetic orders.

Purpose of the Study:

To explore research on strongly correlated materials conducted at Rice University.
To highlight the fundamental science and technological potential of these materials.

Main Methods:

Investigating quantum phase transitions in heavy fermion materials and iron pnictide superconductors.
Utilizing computational ab initio methods combined with analytical theory for correlated materials.
Examining layered dichalcogenides and correlated oxides (VO₂, Fe₃O₄) using nanostructure methods.

Main Results:

Layered dichalcogenides exhibit tunable phases like charge density waves, superconductivity, and ferromagnetism.
Metal-insulator transitions in VO₂ and Fe₃O₄ can be controlled via nanoscale doping and non-equilibrium driving.
Quantum criticality and phase transitions are observed in heavy fermion and iron pnictide systems.

Conclusions:

Strongly correlated materials offer fascinating fundamental science insights.
These materials present significant opportunities for future technological applications.