Chapter 5, exercise 5.8 p.77

[williamlai2]

Hi. this might be an error, though also might not. It is in the exercises for Chapter 5 (p.77)

In the first bit, we are working with standard error, but in (a) it is standard deviation.

5.8 Coverage of confidence intervals: On page 15 there is a discussion of an experimental study of an education-related intervention in Jamaica, in which the point estimate of the treatment effect, on the log scale, was 0.35 with a standard error of 0.17. Suppose the true effect is 0.10—this seems more realistic than the point estimate of 0.35—so that the treatment on average would increase earnings by 0.10 on the log scale. Use simulation to study the statistical properties of this experiment, assuming the standard error is 0.17. (a) Simulate 1000 independent replications of the experiment assuming that the point estimate is normally distributed with mean 0.10 and standard deviation 0.17.

[andrewgelman]

"Standard error" is statistics jargon for "estimated standard deviation of an estimate" or "uncertainty of an estimate." Thus, we use the term "standard error" in the first paragraph above because we are referring to an estimate, and we use the term "standard deviation" in the second paragraph because we are referring to a probability distribution.

We could have simply used the term "standard deviation" throughout, but then this could perhaps have led to confusion if people thought that 0.17 was the standard deviation of the measurements. The term "standard error" is used to make it clear that we're talking about the standard deviation of an estimate.

[williamlai2]

Thanks for the explanation.