Bivariate Statistics

Abstract

Bivariate analysis aims to understand the relationship between two variables x and y. Examples are the length and the width of a fossil, the sodium and potassium content of volcanic glass or the organic matter content along a sediment core. When the two variables are measured on the same object, x is usually identified as the independent variable, and y as the dependent variable. If both variables have been generated in an experiment, the variable manipulated by the experimenter is described as the independent variable. In some cases, neither variable is manipulated and neither is independent. The methods of bivariate statistics aim to describe the strength of the relationship between the two variables, either by a single parameter such as Pearson’s correlation coefficient for linear relationships or by an equation obtained by regression analysis (Fig. 4.1). The equation describing the relationship between x and y can be used to predict the y-response from any arbitrary x within the range of the original data values used for the regression analysis. This is of particular importance if one of the two parameters is difficult to measure. In such a case, the relationship between the two variables is first determined by regression analysis on a small training set of data. The regression equation can then be used to calculate the second parameter.