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Related Concept Videos

Correlations02:20

Correlations

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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...
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Correlation and Causation01:27

Correlation and Causation

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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...
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Correlation01:09

Correlation

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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:
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Correlation and Regression00:53

Correlation and Regression

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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...
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Coefficient of Correlation01:12

Coefficient of Correlation

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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...
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Standard Enthalpy of Formation02:37

Standard Enthalpy of Formation

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Enthalpy changes are typically tabulated for reactions in which both the reactants and products are at the same conditions. A standard state is a commonly accepted set of conditions used as a reference point for the determination of properties under other different conditions. For chemists, the IUPAC standard state refers to materials under a pressure of 1 bar and solutions at 1 M and does not specify a temperature. Many thermochemical tables list values with a standard state of 1 atm. Because...
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Transcriptomic Analysis of C. elegans RNA Sequencing Data Through the Tuxedo Suite on the Galaxy Project
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Galaxy Correlation Functions Provide a More Robust Cosmological Standard Ruler.

Stefano Anselmi1,2,3, Glenn D Starkman1, Pier-Stefano Corasaniti2

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A new cosmological standard ruler, the "linear point" in galaxy correlations, offers precise distance measurements unaffected by nonlinear effects. This method simplifies baryon acoustic oscillation data analysis for cosmology.

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Area of Science:

  • Cosmology and extragalactic astronomy
  • Galaxy evolution and large-scale structure

Background:

  • Baryon Acoustic Oscillations (BAO) provide a standard ruler in cosmology.
  • BAO peak location is sensitive to nonlinear effects and model-dependent analysis.

Purpose of the Study:

  • To introduce and validate the 'linear point' in the galaxy two-point correlation function as a redshift-independent standard ruler.
  • To measure cosmological distances using the linear point without relying on model-templates or reconstruction methods.

Main Methods:

  • Analysis of the galaxy two-point correlation function from the BOSS DR12 LOWZ and CMASS samples.
  • Identification and measurement of the characteristic length scale ('linear point').
  • Combination of linear point measurements with Planck cosmic microwave background data to derive distance scales.

Main Results:

  • The linear point is a robust cosmological standard ruler, constant in redshift and precise to 0.5% against nonlinear effects.
  • Measured isotropic-volume distances: D_{V}(0.32) = 1264 ± 28 Mpc and D_{V}(0.57) = 2056 ± 22 Mpc.
  • Results are consistent with existing BOSS Collaboration measurements.

Conclusions:

  • The linear point effectively compresses all distance information from baryon acoustic oscillations into a single, reliable length scale.
  • This method offers a simplified and robust approach to cosmological distance measurements.