Bivariate data

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In statistics, bivariate data is data on each of two variables, where each value of one of the variables is paired with a value of the other variable.^[1] It is a specific but very common case of multivariate data. The association can be studied via a tabular or graphical display, or via sample statistics which might be used for inference. Typically it would be of interest to investigate the possible association between the two variables.^[2] The method used to investigate the association would depend on the level of measurement of the variable. This association that involves exactly two variables can be termed a bivariate correlation, or bivariate association.

For two quantitative variables (interval or ratio in level of measurement), a scatterplot can be used and a correlation coefficient or regression model can be used to quantify the association.^[3] For two qualitative variables (nominal or ordinal in level of measurement), a contingency table can be used to view the data, and a measure of association or a test of independence could be used.^[3]

If the variables are quantitative, the pairs of values of these two variables are often represented as individual points in a plane using a scatter plot. This is done so that the relationship (if any) between the variables is easily seen.^[4] For example, bivariate data on a scatter plot could be used to study the relationship between stride length and length of legs. In a bivariate correlation, outliers can be incredibly problematic when they involve both extreme scores on both variables. The best way to look for these outliers is to look at the scatterplots and see if any data points stand out between the variables.