特殊教育研究常透過跨群組的比較來增進研究者們對特定群體的理解，不同群體在心理測驗上的結果可否互相比較，和該構念測量是否具有測量恆等性（measurement invariance, MI）的心理計量特質密切相關。倘若忽略測驗的MI性質可能導致虛假的顯著結果，或降低統計分析正確檢測出組間差異的機率。回顧近10年發表於國內特教期刊的實徵研究，我們發現許多研究者們在進行跨群比較時仍經常忽略MI的檢測。故本研究旨在說明MI在特殊教育研究的重要性，並以某篇針對新住民家庭與非新住民家庭背景跨群組比較之文章為例，將此文章所使用的資料進行實徵分析與模擬，藉此提出相關建議與實徵範例供相關研究者參考。具體而言，本研究首先重新檢視近10年在2本臺灣社會科學引文索引資料庫(TSSCI)級特殊教育期刊所發表之跨群組構念比較之研究，展示特教領域研究對MI檢驗的重視性仍然不足。其次，本研究以一篇針對新住民家庭背景跨群組比較之文章為例，透過實徵分析和模擬研究顯示MI檢驗對特教研究結果可解釋性和可複製性的影響。最後，我們亦提供範例和詳細的說明，協助研究者理解如何利用手邊的資料逐步完成MI的檢定。

Objectives

Special education researchers often increase their understanding of specific groups through intergroup comparisons. From the psychometrics perspective, whether the psychological testing results of different groups are comparable is linked to the measured construct’s measurement invariance (MI) properties. Methodological research has shown that inattention to a measure’s MI properties might lead to false significant findings or lower the probability of a statistical analysis accurately estimating intergroup differences. However, our review of one hundred and ninety-two empirical studies published in two Taiwan Social Sciences Core indexed (TSSCI) special education journals over the past ten years revealed that out of the 64 studies conducting cross-group comparisons based on construct measure results, only six mentioned or examined MI. We believe such a lack of attention to MI is due to the absence of empirical examples in special education demonstrating its impact on the interpretability and replicability of study results. Therefore, the present research aimed to fill this gap in the literature and enhance special education researchers’ understanding of the importance of MI and its testing procedures.

Methods

We conducted a secondary analysis of data from a published article to show how MI analyses can increase the alignment between significant statistical results and theory-based hypotheses about the differences between children with disability from immigrant and non-immigrant families. The original article reported that in the three-factor (family status, living skill, and communication skill), 14-item construct measure it used, one subscale’s composite scores (living skills) and four items’ observed scores did not show the expected intergroup differences in t-tests. The authors did not provide a consistent explanation for these unexpected results in the article. Since MI was not addressed in the article, we first examined the measure’s MI properties by identifying the non-invariant parameters and developing a partial invariance model. Next, we compared the latent mean difference and non-invariant parameter estimates in the partial invariance model with the t-test results from the original paper to see if MI testing improved the interpretability of the unexpected results in the original article. In addition, using the final partial invariance model as the population model, we performed simulations to quantify the impact of MI by manipulating the latent mean differences of each factor across groups. Specifically, there are two conditions in our simulation: condition 1: latent mean differences from the final partial invariance model = 0.210, 0.282, and 0.410, and condition 2: no latent mean difference for all subscales. One thousand replications were generated per condition. For each replication, we conducted an intergroup mean comparison with the partial invariance model that adjusted for the detected non-invariance parameters and traditional independent t-tests based on the composite scores of the three subscales. The power and type I error rates of these two methods were calculated to quantify the impact of MI on replicability and interpretability.

Results

By using the Chi-square difference tests and modification indices within the framework of multiple group factor analyses (MG-CFA), we found that five items in the construct measure have non-invariant intercepts across immigrant and non-immigrant groups. We released the equality constraints to build the corresponding partial scalar invariance model. In this model, the latent mean differences of all factors, including living skills, become significant (p < 0.05). Furthermore, by cross-referencing the items in the original paper where the unexpected results occurred with the non-invariant items identified in the partial invariance model, we found substantial overlap. Specifically, among the four items that did not show the expected difference in the original paper, three are also identified as non-invariant items. In addition, for all of these non-invariant items, their intercepts are higher in immigrant groups. This suggests that even though the latent scores of non-immigrant families are higher than those of immigrant families in the latent factors, their latent level differences may not manifest in the observed scores of these items, due to the cancel-out effect of higher non-invariant intercepts in the immigrant group. The follow-up simulations further showed that the difference in significance between the latent mean differences detected in the partial invariance model and the traditional non-significant t-tests based on observed composite scores was not merely a coincidence. Specifically, in the condition with latent mean differences, using the partial invariance model that accounts for non-invariance can almost double the power of detecting intergroup differences in comparison to the traditional t-tests (e.g., 0.712 vs. 0.326, for the living skills factor). On the other hand, in the condition with no latent mean difference, the partial invariance model approach can maintain the type I error rate around the nominal level (α = 0.053). In contrast, the type I error rate of the raw independent t-test was highly inflated (α = 0.514).

Conclusion and Suggestion

In the current study, we demonstrated that MI testing procedures can help researchers find statistically significant results that better align with theory-based hypotheses. Specifically, after considering MI, most of the unexpected non-significant intergroup comparisons in the original article become significant or can be explained by the pattern of non-invariant parameters across groups. In addition, the follow-up simulations further showed that considering MI can almost double the replication rate (power). Similarly, in the condition with no intergroup difference, our simulations reveal that considering MI can maintain the type I error rate at the nominal level. In contrast, ignoring MI and directly conducting intergroup comparisons based on observed scores may have more than a 50% chance of yielding spurious differences. Both statistical properties (i.e., high power and low type error rates) can enhance the interpretability of the results. As a result, we suggest researchers in the area of special education check the MI properties of the construct measures used in the studies before conducting intergroup comparisons based on the results of construct measures. We also provide detailed examples and explanations in the online appendix to guide researchers to complete MI testing step by step with the data they have on hand (https://osf.io/amswb/?view_only=fe30f285ca9a47108f2c7170381f792a). Readers who are interested in the topic can refer to the online resources and conduct the MI by themselves. We hope this article can be helpful for researchers in the area of special education.