Confidence Intervals - and how to interpret them correctly?
Hopefully, the correct interpretation was emphasized, again and again, by your instructor is Intro. Stats. 100. Even so, it's alarming to see how many grad. students (and faculty!) still get it wrong.
The concept of a confidence interval was first introduced by Jerzy Neyman and his co-authors. I've posted about some of the history of this here, and noted that even a future Nobel Laureate didn't "get it" when Neyman presented the concept at a seminar!
With this in mind, a really nice post appeared on the Statistical Research blog today. Its title is, When Discussing Confidence Level With Others, and I strongly recommend it.
© 2013, David E. Giles
I agree on the post.
ReplyDeletemost informative for those of us who left uni sometime ago!1
Dave, in discussions about confidence intervals and how to interpret them, one often hears the argument that we all should be Bayesian, because then we can conduct inference in the sense that we can actually generate quantities that correspond to what we would like standard inference quantities to be. For instance, a Bayesian 95% credible interval corresponds exactly to how "we" often (want to) think about confidence intervals, namely as a probability statement. The same argument can be made for p-values. While we often (mis-) use p-values as if they are probability statements about how likely the null is, Bayesian posterior distributions allow us directly to make such assertions.
ReplyDeleteI almost always only read Bayesians discussing this issue, but non-Bayesians (and here I assume you are not a Bayesian) are pretty silent on this. So I wonder, what is your take on this? Would you mind sharing your opinion?
I actually have pretty strong Bayesian "leanings". My PhD was in Bayesian econometrics, most of my statistical training came from Bayesians, and I've published in the area. In this instance I think that the Bayesian viewpoint has a lot to offer. C.I.'s are strange beasts!
DeleteWhen I'm teaching this stuff, and indeed when I'm talking about estimators' properties (unbiasedness, etc) with students, I stress that the concept of a sampling distribution (with its implicit "repeated sampling") on which this is all based, is pretty bizarre. Wouldn't we be more interested in decision rules that are "optimal" in some sense, for the one sample we've been given to work with.
I teach a slab of Bayesian econometrics in one of my elective grad. courses, and students really enjoy the exposure to this different viewpoint.
Thankfully, we're long past the old "if you're not with us, then you're against us" battle between frequentists and Bayesians. I'm one of those who is happy to pick up whatever statistical tool seems to be best suited for the job, as long as I can understand where that tool comes from, and what its strengths and weaknesses are.