Statistics Definitions > Coefficient Definition

**Contents:**

## Coefficient Definition: Statistics

A coefficient measures a certain property or characteristic of a data set, phenomenon, or process, given specified conditions. You’ll come across many different coefficient definitions, each of which is specific to a test or procedure:

## Correlation coefficients

These tell us whether two sets of data are connected:

- The
**Pearson’s correlation coefficient(r)**tells us the degree of correlation between two variables. It is probably the most widely used correlation coefficient. - The
**Spearman rank correlation coefficient**is the nonparametric version of the Pearson correlation coefficient. - The
**point biserial correlation coefficient**is another**special case**of Pearson’s correlation coefficient. It measures the relationship between one continuous variable and one naturally binary variable. - The
**validity coefficient**tells you how strong or weak your experiment results are. **Moran’s I**measures how one object is similar to others surrounding it.

## Reliability Coefficients

- The
**coefficient alpha**(Cronbach’s alpha) is a way to measure reliability, or internal consistency of a psychometric instrument. - The
**intraclass correlation coefficient**measures the reliability of ratings or measurements for clusters — data that has been collected as groups or sorted into groups. **Test-Retest reliability coefficients**measure test consistency — the reliability of a test measured over time.

## Coefficients that measure agreement

>Coefficients that measure agreement (e.g. two judges agreeing on a certain ranking) include:

- The
**polychoric correlation coefficient**measures agreement between multiple raters for ordinal variables. - The
**tetrachoric correlation coefficient**is used to measure agreement for binary variables. - The
**coefficient of concordance**is used to assess agreement between different raters.

## Other types of coefficients:

- The
**coefficient of variation**tells us how data points are dispersed around the mean. - The
**gamma coefficient**tells us how closely two pairs of data match. **Pearson’s coefficient of skewness**tells us how much and in what direction data is skewed.- The
**Jaccard similarity coefficient**compares members for two sets to see which members are shared and which are distinct. - The
**Durbin Watson coefficient**is a measure of autocorrelation (also called serial correlation) in residuals from regression analysis. - The
**coefficient of determination**is used to analyze how differences in one variable can be explained by a difference in a second variable. - The
**standardized beta coefficient**compares the strength of the effect of each individual independent variable to the dependent variable. - The
**Phi Coefficient**measures the association between two binary variables. - The
**Kendall Rank Correlation Coefficient**is a non-parametric measure of relationships between columns of ranked data. **Lin’s concordance correlation coefficient**measures bivariate pairs of observations relative to a “gold standard” test or measurement.**Binomial coefficients**tell us how many ways there are to choose k things out of larger set.- The
**multinomial coefficients**are used to find permutations when you have repeating values or duplicate items. - The
**coefficient of dispersion**, which actually has several different definitions; in general, it’s a statistic which measures dispersion.

## Coefficient Definition in Mathematics

In general mathematics, a coefficient is the number or multiplicative factor that goes before a variable in an equation or mathematical sentence.

If coefficients are numbers, they don’t change as the variables change, and we call them *constants*. They act upon the variables in a way that is always the same.

In the equation 4 x^{2} + 3 x, both 4 and 3 are coefficients. The coefficient of x^{2}, 4, acts on the x^{2} term and multiplies it by 4. The coefficient of x, 3, acts on the x term and multiplies it by 3.

## References

Terms Factors and Coefficients

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