This paper by Satorra and Bentler proposes a scaled difference chi-square test statistic for moment structure analysis, particularly useful in small samples, large models, and nonnormal data. The authors address the issue of testing the restrictions imposed by a null model ($\mathcal{M}_0$) on a less restricted model ($\mathcal{M}_1$) using the difference test statistic $T_d = T_0 - T_1$, where $T_0$ and $T_1$ are the goodness-of-fit test statistics for $\mathcal{M}_0$ and $\mathcal{M}_1$, respectively. They show that the difference between two Satorra-Bentler (SB) scaled test statistics does not yield the correct SB scaled difference test statistic. The paper provides a simple formula to compute the SB scaled difference test statistic from the scaled goodness-of-fit test statistics of the two models. This formula is practical and can be easily implemented using standard computer software. A Monte Carlo study is conducted to illustrate the performance of the proposed statistic compared to other competing statistics, such as the robust test statistic and the difference of scaled chi-square statistics. The results suggest that the proposed statistic performs well, especially in small samples and nonnormal data.This paper by Satorra and Bentler proposes a scaled difference chi-square test statistic for moment structure analysis, particularly useful in small samples, large models, and nonnormal data. The authors address the issue of testing the restrictions imposed by a null model ($\mathcal{M}_0$) on a less restricted model ($\mathcal{M}_1$) using the difference test statistic $T_d = T_0 - T_1$, where $T_0$ and $T_1$ are the goodness-of-fit test statistics for $\mathcal{M}_0$ and $\mathcal{M}_1$, respectively. They show that the difference between two Satorra-Bentler (SB) scaled test statistics does not yield the correct SB scaled difference test statistic. The paper provides a simple formula to compute the SB scaled difference test statistic from the scaled goodness-of-fit test statistics of the two models. This formula is practical and can be easily implemented using standard computer software. A Monte Carlo study is conducted to illustrate the performance of the proposed statistic compared to other competing statistics, such as the robust test statistic and the difference of scaled chi-square statistics. The results suggest that the proposed statistic performs well, especially in small samples and nonnormal data.