this study did the comparison between the proposed statistic and previous indices for model data fit in confirmatory factor analysis. The new statistic scales the mean and adjusts the degrees of freedom to match the skewness of the reference chi-square variate. The simulation study exhibited that Type I error of the new statistic was closer to the optimal value than the other statistics at a very small sample size (n= 25). Although the result of this new statistic was a little conservative when the sample size is large, the statistic with adjusted the degrees of freedom is valuable because they could perform well under the small and medium sample size. However, the cost of the lower power was came at a small sample size.
1) Sample size indeed affects Type I error rate and Power in model data fit issue. However in rationale of fit between observed data and theoretical model, the optimal index shouldn't be affected by sample size. Therefore to develop the effect size of model data fit deserves to be investigated more rather than to adjust the statistic test.