coefficient

Chemistry

(noun)

A constant by which an algebraic term is multiplied.

Related Terms

  • law of conservation of mass
  • mole
Algebra

(noun)

A quantity (usually a number) that remains the same in value within a problem.

Related Terms

  • parameter
  • coefficients
  • term
  • parameters
  • variable
  • unknown
  • linear
  • degree
  • polynomial
  • trinomial

Examples of coefficient in the following topics:

  • Calculating the Emission and Absorption Coefficients

    • We can write the emission and absorption coefficients in terms of the Einstein coefficients that we have just examined.
    • The emission coefficient $j_\nu$ has units of energy per unit time per unit volume per unit frequency per unit solid angle!
    • The Einstein coefficient $A_{21}$ gives spontaneous emission rate per atom, so dimensional analysis quickly gives
    • We can now write the absorption coefficient and the source function using the relationships between the Einstein coefficients as
  • 95% Critical Values of the Sample Correlation Coefficient Table

  • Rank Correlation

    • It is common to regard these rank correlation coefficients as alternatives to Pearson's coefficient, used either to reduce the amount of calculation or to make the coefficient less sensitive to non-normality in distributions.
    • However, this view has little mathematical basis, as rank correlation coefficients measure a different type of relationship than the Pearson product-moment correlation coefficient.
    • The coefficient is inside the interval $[-1, 1]$ and assumes the value:
    • This means that we have a perfect rank correlation and both Spearman's correlation coefficient and Kendall's correlation coefficient are 1.
    • For example, for the three pairs $(1, 1)$, $(2, 3)$, $(3, 2)$, Spearman's coefficient is $\frac{1}{2}$, while Kendall's coefficient is $\frac{1}{3}$.
  • A Physical Aside: Einstein coefficients

    • The Einstein coefficients seem to say something magical about the properties of atoms, electrons and photons.
    • It turns out that the relationships between Einstein coefficients (1917) are an example of Fermi's Golden Rule (late 1920s).
  • Coefficient of Correlation

    • The most common coefficient of correlation is known as the Pearson product-moment correlation coefficient, or Pearson's $r$.
    • Pearson's correlation coefficient when applied to a population is commonly represented by the Greek letter $\rho$ (rho) and may be referred to as the population correlation coefficient or the population Pearson correlation coefficient.
    • Pearson's correlation coefficient when applied to a sample is commonly represented by the letter $r$ and may be referred to as the sample correlation coefficient or the sample Pearson correlation coefficient.
    • This fact holds for both the population and sample Pearson correlation coefficients.
    • Put the summary statistics into the correlation coefficient formula and solve for $r$, the correlation coefficient.
  • Overview of How to Assess Stand-Alone Risk

    • It is able to accomplish this because the correlation coefficient, R, has been removed from Beta.
    • Another statistical measure that can be used to assess stand-alone risk is the coefficient of variation.
    • In probability theory and statistics, the coefficient of variation is a normalized measure of dispersion of a probability distribution.
    • It is also known as unitized risk or the variation coefficient.
    • A lower coefficient of variation indicates a higher expected return with less risk.
  • Hypothesis Tests with the Pearson Correlation

    • We need to look at both the value of the correlation coefficient $r$ and the sample size $n$, together.
    • We decide this based on the sample correlation coefficient $r$ and the sample size $n$.
    • If the test concludes that the correlation coefficient is significantly different from 0, we say that the correlation coefficient is "significant."
    • If the test concludes that the correlation coefficient is not significantly different from 0 (it is close to 0), we say that correlation coefficient is "not significant. "
    • Our null hypothesis will be that the correlation coefficient IS NOT significantly different from 0.
  • Economic measures

    • The Gini coefficient measures the inequality among values of a frequency distribution.
    • A Gini coefficient of zero expresses perfect equality, where all values are the same (for example, where everyone has the same income).
    • A Gini coefficient of one (or 100%) expresses maximal inequality among values (for example where only one person has all the income).
    • The Gini coefficient was originally proposed as a measure of inequality of income or wealth.
    • The global income inequality Gini coefficient in 2005, for all human beings taken together, has been estimated to be between 0.61 and 0.68.
  • The Coefficient of Determination

    • r2 is called the coefficient of determination. r2 is the square of the correlation coefficient , but is usually stated as a percent, rather than in decimal form. r2 has an interpretation in the context of the data:
  • Testing the Significance of the Correlation Coefficient

    • The sample correlation coefficient, r, is our estimate of the unknown population correlation coefficient.
    • If the test concludes that the correlation coefficient is significantly different from 0, we say that the correlation coefficient is "significant".
    • If the test concludes that the correlation coefficient is not significantly different from 0 (it is close to 0), we say that correlation coefficient is "not significant".
    • The test statistic t has the same sign as the correlation coefficient r.
    • Suppose you computed the following correlation coefficients.
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