Stance detection in social media data has received attention in recent years as an approach to determine the standpoint of users toward a target of interest, such as a person or a topic included in Twitter data. Although interviewing, surveying, and polling representative populations have long proven reliable methods for analyzing public opinion, these methods suffer from various limitations, including high costs and an inability to be collected retrospectively. On the other hand, detecting and analyzing social media trends through natural language processing approaches, such as text classification, offers a valuable alternative or complementary approach to gathering, analyzing, monitoring, and understanding public opinion on emerging issues. Existing stance detection and analysis studies use multiple methodologies and strategies to determine and analyze the standpoint of Twitter users towards a target. These techniques feature strengths and weaknesses, and the literature lacks studies investigating the broad implications of using such methods for public stance measurements. Understanding these implications is crucial to the validity, interpretation, and replicability of research findings. In this dissertation, we first introduce the concept of user-based stance analysis and highlight the difference between user-based and tweet-based stance analyses. We describe the relevance of user-based stance analysis to the measurement of public opinion. We suggest that the stance of Twitter users, instead of the stance presented in a tweet's content, must be the core aspect of stance analysis for measuring public opinion. Therefore, we claim that a user-based stance analysis is more aligned with the concept of public opinion than a tweet-based stance analysis. Second, we compare the results of measuring public opinion with tweet-based and user-based stance analyses from Twitter data and demonstrate that each produces statistically different results. Third, we present findings that, while a tweet-based stance analysis is sensitive to the presence of social bots, a user-based stance analysis provides a more robust measure of public opinion with minimal impact from social bots. Fourth, we describe the design and evaluation of StanceDash, a web-based dashboard that assists end users measure, analyze, and monitor public opinion through a user-based stance analysis of Twitter data.