Bivariate analysis is one of the simplest forms of quantitative (statistical) analysis.

Earl R. Babbie Earl Robert Babbie (born January 8, 1938), is an American sociologist who holds the position of Campbell Professor Emeritus in Behavioral Sciences at Chapman University. He is best known for his book ''The Practice of Social Research'' (first ...

, ''The Practice of Social Research'', 12th edition, Wadsworth Publishing, 2009, , pp. 436–440 It involves the analysis of two variables (often denoted as ''X'', ''Y''), for the purpose of determining the empirical relationship between them. Bivariate analysis can be helpful in testing simple hypotheses of

association Association may refer to: *Club (organization), an association of two or more people united by a common interest or goal *Trade association, an organization founded and funded by businesses that operate in a specific industry *Voluntary associatio ...

. Bivariate analysis can help determine to what extent it becomes easier to know and predict a value for one variable (possibly a

dependent variable Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...

) if we know the value of the other variable (possibly the independent variable) (see also

correlation In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...

and

simple linear regression In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the ''x'' and ...

).Bivariate Analysis
Sociology Index> Bivariate analysis can be contrasted with

univariate analysis Univariate analysis is perhaps the simplest form of statistical analysis. Like other forms of statistics, it can be inferential or descriptive. The key fact is that only one variable is involved. Univariate analysis can yield misleading results i ...

in which only one variable is analysed. Like univariate analysis, bivariate analysis can be

descriptive In the study of language, description or descriptive linguistics is the work of objectively analyzing and describing how language is actually used (or how it was used in the past) by a speech community. François & Ponsonnet (2013). All acad ...

or inferential. It is the analysis of the relationship between the two variables. Bivariate analysis is a simple (two variable) special case of

multivariate analysis Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate statistics concerns understanding the different aims and background of each of the dif ...

(where multiple relations between multiple variables are examined simultaneously).

When there is a dependent variable

If the

—the one whose value is determined to some extent by the other, independent variable— is a

categorical variable In statistics, a categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or ...

, such as the preferred brand of cereal, then

probit In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. It has applications in data analysis and machine learning, in particular exploratory statistical graphics and s ...

logit In statistics, the logit ( ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations. Mathematically, the logit is the ...

regression (or

multinomial probit In statistics and econometrics, the multinomial probit model is a generalization of the probit model used when there are several possible categories that the dependent variable can fall into. As such, it is an alternative to the multinomial log ...

multinomial logit In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the prob ...

) can be used. If both variables are ordinal, meaning they are ranked in a sequence as first, second, etc., then a

rank correlation In statistics, a rank correlation is any of several statistics that measure an ordinal association—the relationship between rankings of different ordinal variables or different rankings of the same variable, where a "ranking" is the assignment o ...

coefficient can be computed. If just the dependent variable is ordinal,

ordered probit In statistics, ordered probit is a generalization of the widely used probit analysis to the case of more than two outcomes of an ordinal dependent variable (a dependent variable for which the potential values have a natural ordering, as in poor, ...

ordered logit In statistics, the ordered logit model (also ordered logistic regression or proportional odds model) is an ordinal regression model—that is, a regression model for ordinal dependent variables—first considered by Peter McCullagh. For exampl ...

can be used. If the dependent variable is continuous—either interval level or ratio level, such as a temperature scale or an income scale—then

simple regression In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the ''x'' an ...

can be used. If both variables are

time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...

, a particular type of causality known as

Granger causality The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969. Ordinarily, regressions reflect "mere" correlations, but Clive Granger argued that cau ...

can be tested for, and

vector autoregression Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of stochastic process model. VAR models generalize the single-variable (univariate) autoregres ...

can be performed to examine the intertemporal linkages between the variables.

When there is not a dependent variable

When neither variable can be regarded as dependent on the other, regression is not appropriate but some form of

analysis may be.

Graphical methods

Graphs Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

that are appropriate for bivariate analysis depend on the type of variable. For two continuous variables, a

scatterplot A scatter plot (also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram) is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. ...

is a common graph. When one variable is categorical and the other continuous, a

box plot In descriptive statistics, a box plot or boxplot is a method for graphically demonstrating the locality, spread and skewness groups of numerical data through their quartiles. In addition to the box on a box plot, there can be lines (which are ca ...

is common and when both are categorical a

mosaic plot A mosaic is a pattern or image made of small regular or irregular pieces of colored stone, glass or ceramic, held in place by plaster/mortar, and covering a surface. Mosaics are often used as floor and wall decoration, and were particularly pop ...

is common. These graphs are part of

descriptive statistics A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and an ...

External links

* Discriminant correlation analysis (DCA)M. Haghighat, M. Abdel-Mottaleb, & W. Alhalabi (2016)
Discriminant Correlation Analysis: Real-Time Feature Level Fusion for Multimodal Biometric Recognition
IEEE Transactions on Information Forensics and Security, 11(9), 1984-1996.

References

{{Statistics Multivariate statistics 2 (number)

When there is a dependent variable

When there is not a dependent variable

Graphical methods

See also

External links

References