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8 votes

Why are statistics textbook questions so frequently totally artificial?

I generally agree with what has already been written in the other answers and comments, so instead of echoing what has been said, here is my hot take (which is too long to be a comment). I recall from ...
6 votes

Why are statistics textbook questions so frequently totally artificial?

A good friend of mine calls this tendency of textbooks to have unrealistic examples 'frictionless statistics'. The phrase comes from high school physics books that start every problem with something ...
10 votes

Why are statistics textbook questions so frequently totally artificial?

I don't think this is unique to statistics. It's common in a variety of areas that make use of mathematical models. One may well learn to solve a problem that begins with "Consider a spherical ...
23 votes

Why are statistics textbook questions so frequently totally artificial?

Textbooks exist to teach complex topics to people who are unfamiliar with them. To help someone grasp a difficult concept, it helps to first introduce it in a simple context. So a question from a ...
1 vote

Intuitive explanation for dividing by $n-1$ when calculating standard deviation?

We can understand Bessel's correction geometrically by moving into $n$-dimensional space! We will start with 3 dimensions and then generalize. Say we have 3 observations $x_1, x_2, x_3$ of a $\mathcal{...
Steven Gubkin's user avatar
2 votes

Bias of an estimator depends on whether you take expectation of the estimator or its inverse

Answered in comments, copied below: It is not the same parameter. Bias is indeed not invariant under re-parametrization, this is a well known property that follows from the fact that $E[f(x)] \ne f(E[...

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