Lecture 13. Confidence Intervals, Hypothesis Testing, and Power Calculations

This is a systematic lecture from the MIT course 14.310x "Data Analysis for Social Scientists," taught by Professor Sara Ellison, focusing on the three core tools of statistics: confidence intervals, hypothesis testing, and power calculations. The content is tailored to common scenarios encountered by social science researchers—how to infer the population from a sample, how to determine if observed differences are real, and how to estimate the required sample size in the research design phase to avoid "ineffective experiments" or "over-sampling." The key highlights are Professor Ellison's integration of abstract statistical concepts with empirical research, not only explaining formulas and logic but also emphasizing misuse and pitfalls in practical applications. For example, how to interpret the true meaning of confidence intervals, why p-values cannot be simply equated to "probability of error," and how power analysis affects the reliability of experimental conclusions. The course structure is clear, progressing from interval estimation to testing principles and then to power calculations, building a complete inferential statistics thinking framework for learners. Target audience: Individuals with basic knowledge of statistics, students and researchers studying or working in social science quantitative research, and professionals who wish to systematically review inferential statistics. Viewing suggestions: It is recommended to review the concepts of normal distribution and standard error before watching, take notes while watching, and try to replicate the post-class cases using statistical software. If time is limited, focus on the power calculation section, which is the most easily overlooked key aspect in research design.