This paper extends the scaled and adjusted corrections to goodness-of-fit test statistics developed by Satorra and Bentler (1988a,b) to score, Wald, and difference test statistics in the context of multi-sample analysis of moment structures. The theory is framed under general conditions on the distribution of observable variables. The paper discusses computational issues and the relationship between the scaled and corrected statistics and asymptotic robust ones. A Monte Carlo study illustrates the comparative performance of corrected score test statistics in finite samples. The study uses a simple regression model with measurement errors and non-normal data to evaluate the performance of various test statistics, including the scaled and adjusted score statistic, robust score statistic, and difference statistic. The results show that the scaled and adjusted score statistic performs well in small samples, while the robust score statistic outperforms other alternatives in large samples. The adjusted test statistic shows acceptable performance across various sample sizes.This paper extends the scaled and adjusted corrections to goodness-of-fit test statistics developed by Satorra and Bentler (1988a,b) to score, Wald, and difference test statistics in the context of multi-sample analysis of moment structures. The theory is framed under general conditions on the distribution of observable variables. The paper discusses computational issues and the relationship between the scaled and corrected statistics and asymptotic robust ones. A Monte Carlo study illustrates the comparative performance of corrected score test statistics in finite samples. The study uses a simple regression model with measurement errors and non-normal data to evaluate the performance of various test statistics, including the scaled and adjusted score statistic, robust score statistic, and difference statistic. The results show that the scaled and adjusted score statistic performs well in small samples, while the robust score statistic outperforms other alternatives in large samples. The adjusted test statistic shows acceptable performance across various sample sizes.