Statistics for Applications by MIT OpenCourseWare

About this course

Statistics is the language of evidence. Whether you are working on school assignments, interpreting surveys, comparing results in science classes, or trying to make sense of real-world data, this free online course helps you move from guessing to justified conclusions. You will build the core intuition behind statistical thinking, then practice turning observations into reliable estimates, tests, and models that support decision-making.

You start by clarifying what it means to describe data versus infer something about an unseen population. From there, you develop a practical understanding of estimators, including the ideas of bias and consistency, and why large-sample reasoning becomes so powerful. You also learn how uncertainty is quantified, how sampling distributions are used, and how common asymptotic tools support approximations that show up constantly in applications.

As you progress, you connect probability models to real data through parametric inference and maximum likelihood estimation. You learn how estimating parameters works in practice, why likelihood is a natural objective, and how the method of moments provides an alternative route. You also examine how different ways of comparing probability distributions can change how we think about model fit and approximation, building a more mature intuition for what it means for a model to be close to reality.

The course then equips you to make and defend claims using parametric hypothesis testing. You will learn how tests are constructed, how to interpret p-values and error types, and how classic reference distributions such as chi-squared appear in common procedures. Beyond individual parameters, you practice reasoning about functions of parameters and understand how asymptotic normality supports flexible testing in more complex settings, including goodness-of-fit scenarios where parameters may need to be estimated from the data.

To connect inference with prediction, you develop a grounded view of regression: how a best-fit line is chosen, what the coefficient of determination says about explanatory power, and how to test multiple coefficients together when you want to evaluate an entire model rather than a single number. You then broaden your toolkit with Bayesian statistics, learning how priors such as Jeffreys prior are motivated and what they represent in inference. Finally, you explore modern staples of data analysis, including principal component analysis for dimensionality reduction and generalized linear models for extending regression to non-normal outcomes, with an emphasis on how methods like iteratively reweighted least squares make estimation practical.

Throughout, the included exercises are designed to strengthen understanding, not just memorization, so you can explain why methods work and when to use them. By the end, you will be prepared to read statistical results more critically, run your own analyses with clearer assumptions, and communicate conclusions with confidence.