The Hardest Part of Learning Statistics

Spoiler: It isn't the math

You signed up for this newsletter because, in one way or another, you want statistics to be part of your life. That is not a small thing. Most people never make a deliberate commitment to study anything after school ends. But wanting to learn is one thing, and knowing how to go about it is another.

Over the years, I have found that learning statistics breaks down into four distinct subtasks. They are not the ones most people expect, and the first one is the most personal and the most underestimated.

Learning on your own

Learning independently is a very different experience from learning under the guidance of a teacher. In a classroom, a good instructor will not only point out your mistakes, but also suggest exactly how to fix them. This allows you to focus entirely on the learning itself.

When you are your own teacher, there is a second layer of work that must happen in the background. You are not just trying to work on problem sets. You are also trying to figure out whether you are learning the right things, whether your understanding is correct, and how to fix it if it is not. That is an extra layer of thinking about your own thinking, a skill psychologists call metacognition.

This “thinking about thinking” adds what is known as metacognitive load. It is the mental equivalent of carrying your own ladder while trying to climb it. In a guided setting, the teacher supplies the ladder and holds it for you, freeing you to focus solely on the climbing itself. Alone, you have to build the ladder, inspect it, and climb it all at once. That extra burden is why self-teaching is slower and much more exhausting, even for bright and motivated learners.

When I applied to Harvard’s PhD program in statistics, I had an interview with the chair of the department. She was warm and friendly, and I enjoyed talking with her. (Later, I learned she had won what many consider to be the “Nobel Prize” of statistics.) During the interview, she asked about my past experience, and I described the various projects I had taken on. She listened closely, and at one point she laughed and said, “Do you always do everything on your own!?”

I had not realized it until she said it, but nearly everything I had done in statistics up to that point had been self-driven, pulling myself up by my own bootstraps. It struck me as strange that, on the threshold of graduate study at one of the best institutions in the country, I had never once considered the simple insight that doing things on your own is also doing things the hard way. I felt like such a dummy.

So even as you continue your self-learning, don't be like I was. Remember that you have me and you have the others on this mailing list. Whenever possible, avoid learning in isolation. And once you have given yourself permission to seek help, the next step is to choose carefully where that help will come from.

Finding Resources

The resources available today are overwhelming: textbooks, online lecture series, YouTube videos, free and paid online courses, blog posts, and possibly AI systems like ChatGPT. Each has its strengths and weaknesses. Some explain concepts beautifully but lack practical exercises. Others bombard you with exercises without explaining why the methods work. The hard part is not finding resources, but finding resources that you can trust, and that fit your level of expertise and style of learning.

Many self-learners either cling to the first book or course they find, even if it is a poor match, or jump endlessly from one resource to another without ever finishing anything. Both can completely derail the learning process. Choosing well means thinking about your goals, your background, and how you prefer to engage with material, whether you learn best from worked examples, from mathematical proofs, from visual demonstrations, or from building things yourself.

Finding the right materials is a start, but they will not teach you much unless you can carve out the space to use them. That brings us to the third subtask.

Protecting Time

Learning statistics requires more than good books or courses. Without regular, distraction-free time to think, progress is almost impossible. This is the hardest part for most professionals and adult learners, whose days are filled with urgent demands that always seem more pressing than the slow, steady work of self-study.

Statistics, like any skill, builds gradually. It needs repeated exposure, spaced practice, and quiet moments to reflect on what you have learned. That cannot happen if study time is squeezed into the scraps left over at the end of the day. Protecting time means making learning a fixed part of your schedule, not an afterthought.

This newsletter is meant to help with that. Even if you do not read every email the moment it arrives, simply seeing it appear in your inbox can act as a gentle reminder of the role you want statistics to play in your life. It is a small signal from your past self to your present self, a prompt to remember what you aspire to be. Over time, those reminders can help you hold space for statistics in the middle of everything else competing for your attention.

Learning the content itself

This is what people usually imagine when they think of “learning statistics,” but it is only the fourth step. In my view, real skill in statistics rests on five interconnected competencies:

Data sense. The ability to tell when data “looks right” or “looks wrong” after a transformation or analysis. You develop an eye for the patterns that should be there, and a nose for the ones that signal trouble.

Mathematical statistics. The capacity to reason rigorously about statistical relationships, to follow a chain of logic from assumptions to conclusions, and to see where a method’s limitations come from.

Coding. The practical ability to automate analyses and handle real-world datasets, which are often too large, messy, or complex to handle by hand. Without this, the statisticians of today would be severely limited.

Probabilistic intuition. The instinct to gauge what is likely or unlikely in systems with randomness. This is not the same as traditional logic, which proceeds step by step through a single scenario. Probability demands that you hold many scenarios in mind at once, including those that contradict each other, and reason about them collectively.

Statistical communication. The ability to convey statistical insights clearly and persuasively. Most statisticians analyze information in order to influence others, which means the work is wasted if you cannot explain it in a way that others can understand and act on.

The awkward thing about these skills is that they involve very different modes of learning. Acquiring data sense is often visual work, involving extensive plotting and experimentation. Mathematical statistics and the development of probabilistic intuition require long periods of focused reasoning with pencil and paper. Coding happens at the computer. Statistical communication demands yet another skill set: writing and thinking about how others will receive your message.

Switching between these modes of learning adds to the metacognitive burden. You are not only learning new ideas, but also shifting between entirely different ways of working, each with its own pace, tools, and challenges. That complexity is one reason why learning statistics can feel harder than learning most other things.

Summary

Each of these foundational aspects of learning statistics takes time to build. And here is the hard truth: many people try to jump straight to the last step, skipping over the first three. I have seen this especially on Twitter, where people are eager to dive into details of statistical ideas without having the structure in their life to study them deeply. They skip over the “softer” but equally essential prerequisites like learning how to learn, choosing the right materials, and carving out time for regular practice.

By joining this newsletter, you have already solved part of that first problem. You have committed to keeping statistics in your life, and you have connected yourself to a community of people with the same goal. It is not the same as joining a class, but it is a start, and from here we can tackle the rest together.

Each of these topics could be an essay in itself. I could recommend a dozen books and other resources for every idea we’ve touched, but that will come later. This is day one of a long and rewarding journey. We will learn about statistics, and we will learn about ourselves. To be a self-learner is to master the art of seeing yourself exactly as you are, in full context, so you can take the precise next step to improve. That is the work ahead of us, and it is a glorious endeavor.