Statistics Definitions > Coefficient Definition
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:
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.
- 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.
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 x2 + 3 x, both 4 and 3 are coefficients. The coefficient of x2, 4, acts on the x2 term and multiplies it by 4. The coefficient of x, 3, acts on the x term and multiplies it by 3.
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