ABSTRACT
This chapter provides formal testing of linear association between ordered groups and mean group responses. Some groups can be ordered, at least in a qualitative fashion. This ordering may be based on the level of a factor determining groups or on another measurement which characterizes those groups. Path diagrams can provide a very convenient visual representation of relationships among factors and multiple responses. A linear relationship between group level and mean response may be adequate in many experiments. The scientist may wish to investigate whether there is an association between the ordering and the measured responses. If the association is linear, the problem reduces to simple linear regression. The nonlinear sum of squares represents the difference in explained variation between the group mean model and the regression model.
