Affiliations: KRUG Life Sciences Inc., Houston, Texas, USA
Note: [1] Reprint address: D.S. Calkins, Ph.D., KRUG Life Sciences, Inc., 1290 Hercules, Suite 120, Houston, TX 77058. Tel: (281) 483-9813; Fax: (281) 483-3058; E-mail: dcalkins@ems.jsc.nasa.gov
Abstract: When the dependent (or response) variable response variable in an experiment has direction and magnitude, one approach that has been used for statistical analysis involves splitting magnitude and direction and applying univariate statistical techniques to the components. However, such treatment of quantities with direction and magnitude is not justifiable mathematically and can lead to incorrect conclusions about relationships among variables and, as a result, to flawed interpretations. This note discusses a problem with that practice and recommends mathematically correct procedures to be used with dependent variables that have direction and magnitude for 1) computation of mean values, 2) statistical contrasts of and confidence intervals for means, and 3) correlation methods.
Keywords: statistical analysis, vector data, data with magnitude and direction, means of vector data, statistical analysis of vector data
