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\begin{array}{rcl} H_{1} : & One-factor model with parallel tests \\ ρ = 1 \\ β_{W} = β_{X} and Var (E_{W}) = Var (E_{X}) \\ β_{Y} = β_{Z} and Var (E_{Y}) = Var (E_{Z}) \\ H_{2} : & Two-factor model with parallel tests \\ β_{W} = β_{X} and Var (E_{W}) = Var (E_{X}) \\ β_{Y} = β_{Z} and Var (E_{Y}) = Var (E_{Z}) \\ H_{3} : & Congeneric model: One factor without assuming parallel tests \\ ρ = 1 \\ H_{4} : & Full model: Two factors without assuming parallel tests \end{array}

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\begin{eqnarray*} H_{1}\colon & & \mbox{One-factor model with parallel tests} \\ & & \rho = 1 \\ & & \beta _ W = \beta _ X \phantom{X}\mbox{and}\phantom{X}\mbox{Var}(E_ W) = \mbox{Var}(E_ X) \\ & & \beta _ Y = \beta _ Z \phantom{X}\mbox{and}\phantom{X}\mbox{Var}(E_ Y) = \mbox{Var}(E_ Z) \\[0.05in] H_{2}\colon & & \mbox{Two-factor model with parallel tests} \\ & & \beta _ W = \beta _ X \phantom{X}\mbox{and}\phantom{X}\mbox{Var}(E_ W) = \mbox{Var}(E_ X) \\ & & \beta _ Y = \beta _ Z \phantom{X}\mbox{and}\phantom{X}\mbox{Var}(E_ Y) = \mbox{Var}(E_ Z) \\[0.05in] H_{3}\colon & & \mbox{Congeneric model: One factor without assuming parallel tests} \\ & & \rho = 1 \\[0.05in] H_{4}\colon & & \mbox{Full model: Two factors without assuming parallel tests } \end{eqnarray*}