Bivariate analysis
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Bivariate analysis is one of the simplest forms of quantitative (statistical) analysis. Earl R. Babbie, ''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) if we know the value of the other variable (possibly the independent variable) (see also correlation and simple linear regression).Bivariate Analysis
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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 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 dependent variable—the one whose value is determined to some extent by the other, independent variable— is a categorical variable, 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 ...
or
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 or
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 or ordered logit 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 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. Ex ...
, 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 correlation analysis may be.


Graphical methods

Graphs 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 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 ...
.


See also

*
Canonical correlation In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have two vectors ''X'' = (''X''1, ..., ''X'n'') and ''Y' ...
*
Coding (social sciences) Coding may refer to: Computer science * Computer programming, the process of creating and maintaining the source code of computer programs * Line coding, in data storage * Source coding, compression used in data transmission * Coding theory * Cha ...
*
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)