Interval Variable Versus Interval Variable

Robert Gilmore Pontius, Clark University

Abstract

This chapter gives methods to compare Y versus X when both variables indicate a phenomenon with the same units on an interval scale. The analysis’ begins with a visual examination of a square scatter plot of where each observation is a point (X,Y) plotted relative to the line Y = X. Mean Deviation is the average Y minus the average X. Mean Absolute Deviation is the average vertical distance between the Y = X line and the points in the scatter plot. Mean Absolute Deviation is the sum of two components: Quantity and Allocation. Correlation is an index on the continuous interval [−1,1] concerning the strength and sign of a linear relationship between Y and X. The slope of the least squares line indicates the change in Y for each increment increase in X. Each of those four metrics measures a distinct concept. Relevant software includes the diffeR package available at https://cran.r-project.org/web/packages/diffeR/index.html (Pontius Jr and Santacruz 2015).