TESTING SIZE-DENSITY RELATIONSHIPS WITHOUT RATIO-VARIABLES,MULTICOLLINEARITY, LOGARITHMIC TRANSFORMATIONS,OR REGRESSION ANALYSIS*

Using data describing the historical distribution of county seats in the United States, we (1) replicate the traditional ratio-variable test of the size-density law, (2) test a new multivariate, nonratio form of the law, and (3) introduce an alternative method of testing, one which avoids three possible problems in traditional analyses: ratio-variables, multicollinearity, and logarithmic transformation.