This paper examines several issues related to the goodness of fit in structural equation models (SEM) with unobservable variables and measurement error. The authors critique the convergence and differentiation criteria proposed by Bagozzi, arguing that these criteria are not relevant to the properties of the chi-square statistic and are unreliable from a statistical perspective. They demonstrate that structural consistency, rather than convergence and differentiation, is the key factor in determining the degree of fit. The paper also addresses the choice of interpretative statistics, suggesting that they should be chosen based on the research objective. The authors propose an Fornell-Larcker Testing System that is internally consistent and aligns with the rules of correspondence for relating data to abstract variables. They further discuss the handling of systematic measurement error in SEM, showing that high and uniform measurements can decrease the estimated correlation between unobservables, while poor and uneven measurements can increase it. The paper concludes by addressing Bagozzi's criticisms of their testing system, emphasizing the importance of understanding the research objective in determining the nature and scope of analysis.This paper examines several issues related to the goodness of fit in structural equation models (SEM) with unobservable variables and measurement error. The authors critique the convergence and differentiation criteria proposed by Bagozzi, arguing that these criteria are not relevant to the properties of the chi-square statistic and are unreliable from a statistical perspective. They demonstrate that structural consistency, rather than convergence and differentiation, is the key factor in determining the degree of fit. The paper also addresses the choice of interpretative statistics, suggesting that they should be chosen based on the research objective. The authors propose an Fornell-Larcker Testing System that is internally consistent and aligns with the rules of correspondence for relating data to abstract variables. They further discuss the handling of systematic measurement error in SEM, showing that high and uniform measurements can decrease the estimated correlation between unobservables, while poor and uneven measurements can increase it. The paper concludes by addressing Bagozzi's criticisms of their testing system, emphasizing the importance of understanding the research objective in determining the nature and scope of analysis.