by256's comments

In the book, Freedman states that two assumptions of the standard error of the difference are violated by the way subjects are assigned to control and treatment groups in randomized controlled trials (RCTs).

The standard error of the difference assumes that a) samples are drawn independently, i.e., with replacement; and b) that the two groups are independent of each other. By samples being drawn, I mean a subject being assigned to a group in a RCT here.

If you derive the standard error of the difference, there are two covariance terms that are zero when these assumptions are true. When they're violated, like in RCTs, the covariances are non-zero and should in theory be accounted for. However, Freedman implies that it doesn't actually matter because they effectively cancel each other out, as one inflates the standard error and the other deflates it.

I read/worked through Freedman's Statistics a couple of years ago and I walked away from it a different person. I always recommend it when someone asks for a good book to learn statistics from. However, it did leave me craving some of the maths that the authors intentionally left out to make the material more accessible. Freedman's more advanced book, Statistical Models, has you derive many of the results from the first book right at the start, then focuses mainly on linear models. It was a great follow-up which provided the mathematical substance that I felt was missing from the first book.

It depends how comfortable you are with mathematics. Statistics by David Freedman is a great starting point and does an excellent job of developing intuition without delving deep into the mathematical aspects. Although it may leave you wanting more details on the math side. Another great book for beginners is Statistics: The Art and Science of Learning from Data by Agresti and Franklin.

In any case, I would recommend skimming a lot of books and finding one that contains enough practice questions (with solutions) and is suitable for your level.

Anki + practice.

1. Find a good textbook on the topic that is around the right level for you, and that also has many practice questions in it. 'Good' is determined by a combination of reviews plus an initial skim of the book.

2. Read and work through the textbook. Use Anki to memorize the key points/equations and do the practice questions as you work through each chapter.

3. Continue to use Anki for several months/years to review the things that you learned. This only takes a few minutes a day, but the benefits are astounding.

Location: London, UK or remote.

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Technologies: Python, MATLAB, Pandas, Pytorch, Git + the usual machine learning stack.

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Email: see Résumé/CV.