Differential test functioning, or DTF, occurs when one or more items in a test demonstrate differential item functioning (DIF) and the aggregate of these effects are witnessed at the test level. In many applications, DTF can be more important than DIF when the overall effects of DIF at the test level can be quantified. However, optimal statistical methodology for detecting and understanding DTF has not been developed. This article proposes improved DTF statistics that properly account for sampling variability in item parameter estimates while avoiding the necessity of predicting provisional latent trait estimates to create two-step approximations. The properties of the DTF statistics were examined with two Monte Carlo simulation studies using dichotomous and polytomous IRT models. The simulation results revealed that the improved DTF statistics obtained optimal and consistent statistical properties, such as obtaining consistent Type I error rates. Next, an empirical analysis demonstrated the application of the proposed methodology. Applied settings where the DTF statistics can be beneficial are suggested and future DTF research areas are proposed.

Measurement Invariance (MI) is often concluded from a nonsignificant chi-square difference test. Researchers have also proposed using change in goodness-of-fit indices ( $\Delta$GOFs) instead. Both of these commonly used methods for testing MI have important limitations. To combat these issues, To combat these issues, it was proposed using an equivalence test (EQ) to replace the chi-square difference test commonly used to test MI. Due to concerns with the EQ's power, and adjusted version (EQ-A) was created, but provides little evaluation of either procedure. The current study evaluated the Type I error and power of both the EQ and EQ-A, and compared their performance to that of the traditional chi-square difference test and $\Delta$GOFs. The EQ was the only procedure that maintained empirical error rates below the nominal alpha level. Results also highlight that the EQ requires larger sample sizes than traditional difference-based approaches or using equivalence bounds based on larger than conventional RMSEA values (e.g., > .05) to ensure adequate power rates. We do not recommend the proposed adjustment (EQ-A) over the EQ.

Quantitative methods (QM) dominate empirical research in psychology. Unfortunately most researchers in psychology receive inadequate training in QM. This creates a challenge for researchers who require advanced statistical methods to appropriately analyze their data. Many of the recent concerns about research quality, replicability, and reporting practices are directly tied to the problematic use of QM. As such, improving quantitative literacy in psychology is an important step towards eliminating these concerns. The current paper will include two main sections that discuss quantitative challenges and opportunities. The first section discusses training and resources for students and presents descriptive results on the number of quantitative courses required and available to graduate students in Canadian psychology departments. In the second section, we discuss ways of improving quantitative literacy for faculty, researchers, and clinicians. This includes a strong focus on the importance of collaboration. The paper concludes with practical recommendations for improving quantitative skills and literacy for students and researchers in Canada.