Introductory physics lab instruction is undergoing a transformation, with increasing emphasis on developing experimentation and critical thinking skills. These changes present a need for standardized assessment instruments to determine the degree to which students develop these skills through instructional labs. In the first part of this thesis, we present the development of the Physics Lab Inventory of Critical thinking (PLIC), an instrument that probes students' critical thinking skills in the context of physics experimentation. We define critical thinking here as the ability to use data and evidence to decide what to trust and what to do. Using interviews and data from 11,206 students from 52 institutions, we demonstrate, through qualitative and quantitative means, the validity and reliability of the instrument at measuring students' critical thinking skills. In the second part of this thesis, we examine existing quantitative methods in Physics Education Research (PER) and discuss new techniques that may be useful to the field. We develop a novel quantitative method for evaluating assessment instruments, such as the PLIC, by applying information theory concepts to evaluate the utility of response choices. We use the PLIC as an example to illustrate how developers can use this method when developing their own instruments. We also examine existing methods for conducting explanatory modeling using data from assessment instruments. In one study, we synthesize ongoing conversations surrounding the use of quantitative methods in PER by focusing on how results can be interpreted through an equity lens, and what questions can and cannot be answered using different methods. In another study, we examine the role of omitted variable bias in explanatory modeling. Our results underscore the importance of carefully considering why or why not to include variables in a model, informed by both data and theory. In the third part of this thesis, we examine three outcomes of introductory physics labs: students' attitudes about experimental physics, their critical thinking skills in the context of experimental physics, and students' interactions with each other in labs. In one study, we used the PLIC and the Colorado Learning Attitudes about Science Survey for Experimental Physics (E-CLASS) to examine what features of lab curricula promote the development of students attitudes about experimental physics and critical thinking skills. The data for this study came from surveys administered to more than 20,000 students from over 100 institutions in the United States and internationally. Our results from this study indicate that labs designed explicitly to develop lab skills are most effective for improving students' attitudes about experimental physics and critical thinking skills. We further find that this effect is consistent across various sub-populations of students (i.e., gender, race/ethnicity) and can be partially explained by the increased opportunities for decision-making and communication in labs designed to develop experimentation skills. In another study, we explore the effectiveness of using video to capture information about students' social networks in a physics lab setting. Students' positions within the social network of a physics classroom has been shown to correlate with students' sense of belonging, performance, and persistence in physics. Our preliminary work here indicate that students' generally interact more with each other over time. This work also lays the foundation for future studies to examine how students' positions in the lab social network correlate with other outcome measures such as attitudes about experimental physics and critical thinking skills. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]