ASA Connect

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, “What is your favorite confidence interval?”

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment—how does one answer such a question? “My favorite confidence interval is (-3.623, 5.783)”?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

Perhaps the question had to do with what kind of procedure would you use to construct a confidence interval in a given situation. Once you step outside of situations where exact confidence interval procedures exist (e.g., for parameters, quantiles, and tail probabilities for a normal or lognormal distribution with complete data), one has to use approximate confidence methods. In mathematical statistics courses, we learn that the Wald, score, and likelihood ratio statistics all have the same chi-square limiting distribution and all of these statistics can be inverted to provide approximate confidence intervals. I recall having the impression that then it did not make much difference which of these three procedures was used to construct a confidence interval. A few years later, when digging into a particular application, I realized that the differences among these interval-procedure methods could be huge and that the score and likelihood-based procedures were, generally, much more trustworthy. In addition to these classical procedures, we also have a variety of bootstrap and objective Bayesian procedures (i.e., Bayesian procedures using diffuse prior information) that are also competitive. For more information on this topic, I can immodestly recommend the recently released Second Edition of Statistical Intervals, published by John Wiley and Sons. Find details at http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471687170.html

 

Bill Meeker

------------------------------
William Meeker
Distinguished Professor of Statistics
Iowa State University
Ames, Iowa
------------------------------

Original Message:
Sent: 05-19-2017 22:50
From: Stephen Smela
Subject: "What is your favorite confidence interval?"

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, "What is your favorite confidence interval?"

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment-how does one answer such a question? "My favorite confidence interval is (-3.623, 5.783)"?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

Original Message------

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, “What is your favorite confidence interval?”

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment—how does one answer such a question? “My favorite confidence interval is (-3.623, 5.783)”?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

Original Message------

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, “What is your favorite confidence interval?”

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment—how does one answer such a question? “My favorite confidence interval is (-3.623, 5.783)”?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

Original Message------

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, “What is your favorite confidence interval?”

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment—how does one answer such a question? “My favorite confidence interval is (-3.623, 5.783)”?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

Given a single observation X from a Normal(mu,sigma^2) distribution, with both parameters unknown, it is possible to construct a valid finite confidence interval for sigma^2.

This surprising confidence interval--which I found in a Russian probability competition--would have to be my favorite.

------------------------------
Jonathan Christensen
------------------------------

Original Message:
Sent: 05-19-2017 22:50
From: Stephen Smela
Subject: "What is your favorite confidence interval?"

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, "What is your favorite confidence interval?"

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment-how does one answer such a question? "My favorite confidence interval is (-3.623, 5.783)"?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

Yes, I can see being dumbfounded by such a question. Having the
advantage of sitting comfortably in my office with time to think it
seems that, if the job is going to be worthwhile, the employers might
respond well to something like:
My favorite CI depends on the context. If I have reason to believe the
data are independently generated, and I have checked that they roughly
follow a Gaussian distribution, I like standard t-distribution CIs.
Otherwise, I am happy to use appropriate transformations or bootstrapped
choices. In those situations where it make sense to do a Bayesian
analysis, I prefer credible intervals.
Note e.g. the last phrasing leaves your opportunities wide open. If
they take a "Bayes only" viewpoint, then Cred Ints always make sense, so
they can hire you. Similarly if they fall into the "never Bayes" they
can also comfortably hire you, because for them they never make sense.
Best,
Steve


Original Message------

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, “What is your favorite confidence interval?”

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment—how does one answer such a question? “My favorite confidence interval is (-3.623, 5.783)”?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

Original Message------

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, “What is your favorite confidence interval?”

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment—how does one answer such a question? “My favorite confidence interval is (-3.623, 5.783)”?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

How about the 100% confidence interval ranging between, and including, +/- infinity? One can never be wrong!

------------------------------
Nestor Rohowsky
President and Principal Consultant
Integrated Data Consultation Services, Inc.
------------------------------

Original Message:
Sent: 05-19-2017 22:50
From: Stephen Smela
Subject: "What is your favorite confidence interval?"

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, "What is your favorite confidence interval?"

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment-how does one answer such a question? "My favorite confidence interval is (-3.623, 5.783)"?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

My current favorite CI is the BC (bias corrected) bootstrap CI, so that's where my mind went when I saw the question. These questions are typically about how you reason through them and not so much about the actual answer.

------------------------------
Elizabeth Grandfield
------------------------------

Original Message:
Sent: 05-19-2017 22:50
From: Stephen Smela
Subject: "What is your favorite confidence interval?"

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, "What is your favorite confidence interval?"

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment-how does one answer such a question? "My favorite confidence interval is (-3.623, 5.783)"?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

A long long time ago, I made some minor edits to the binomial proportion
confidence interval page at Wikipedia. So I would have said something
like the Clopper-Pearson interval or the Wilson score interval and then
explained how you compute it and why it is better than the normal
approximation. But you could have said that asking which is your
favorite confidence interval is like asking which is your favorite child
(for someone with more than one child, of course).

You could have also talked about a data analysis that you are very proud
of and the confidence interval(s) that you calculated as part of that
data analysis.

Or you could have answered a different question, like "I don't have a
favorite confidence interval" but I do have a favorite
test/model/package/... Or start talking about the favorite part of your
dissertation or your favorite class in college.

I'll be honest, though, and admit that if I was blindsided like you were
with a weird question like that, I probably would end up doing what you
did. It's hard to think on your feet.

Steve Simon, blog.pmean.com


Original Message------

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, “What is your favorite confidence interval?”

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment—how does one answer such a question? “My favorite confidence interval is (-3.623, 5.783)”?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

95% conservative confidence interval for proportions (p+/- 1/Sqrt(n)) Simple and often (but not always) useful.

------------------------------
Kenneth Ganning
------------------------------

Original Message:
Sent: 05-19-2017 22:50
From: Stephen Smela
Subject: "What is your favorite confidence interval?"

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, "What is your favorite confidence interval?"

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment-how does one answer such a question? "My favorite confidence interval is (-3.623, 5.783)"?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

I'm in a photography forum and the usual answer to: What is your favorite camera? Is: The one you have with you (including an iPhone) when an interesting opportunity arises. So, my answer for a CI is the one I need at the time. I'll be reporting a CI for an observed proportion of 0 so Bayesian CIs are the most interesting right now.

------------------------------
Chauncey Dayton
------------------------------

Original Message:
Sent: 05-23-2017 07:31
From: Kenneth Ganning
Subject: "What is your favorite confidence interval?"

95% conservative confidence interval for proportions (p+/- 1/Sqrt(n)) Simple and often (but not always) useful.

------------------------------
Kenneth Ganning
------------------------------

Original Message:
Sent: 05-19-2017 22:50
From: Stephen Smela
Subject: "What is your favorite confidence interval?"

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, "What is your favorite confidence interval?"

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment-how does one answer such a question? "My favorite confidence interval is (-3.623, 5.783)"?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

My own (with Yan Liu).  "Speeding up the asymptotics when constructing one-sided coverage intervals with survey data," (Kott and Liu, Metron, 2010).  We use the term "coverage interval" rather than "confidence interval" because it covers on average rather than all the time like a Clopper-Pearson interval for a proportion.

------------------------------
Phillip Kott
RTI International
------------------------------

Original Message:
Sent: 05-23-2017 08:28
From: Chauncey Dayton
Subject: "What is your favorite confidence interval?"

I'm in a photography forum and the usual answer to: What is your favorite camera? Is: The one you have with you (including an iPhone) when an interesting opportunity arises. So, my answer for a CI is the one I need at the time. I'll be reporting a CI for an observed proportion of 0 so Bayesian CIs are the most interesting right now.

------------------------------
Chauncey Dayton
------------------------------

Original Message:
Sent: 05-23-2017 07:31
From: Kenneth Ganning
Subject: "What is your favorite confidence interval?"

95% conservative confidence interval for proportions (p+/- 1/Sqrt(n)) Simple and often (but not always) useful.

------------------------------
Kenneth Ganning
------------------------------

Original Message:
Sent: 05-19-2017 22:50
From: Stephen Smela
Subject: "What is your favorite confidence interval?"

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, "What is your favorite confidence interval?"

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment-how does one answer such a question? "My favorite confidence interval is (-3.623, 5.783)"?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

My favorite statistical interval is that calculable interval that is maximally responsive to the problem at hand--as Bill Meeker, Luis Escobar and I try to say in the new edition of Statistical Intervals: A Guide for Practitioners and Researchers

------------------------------
Gerald Hahn
------------------------------

Original Message:
Sent: 05-24-2017 06:50
From: Phillip Kott
Subject: "What is your favorite confidence interval?"

My own (with Yan Liu).  "Speeding up the asymptotics when constructing one-sided coverage intervals with survey data," (Kott and Liu, Metron, 2010).  We use the term "coverage interval" rather than "confidence interval" because it covers on average rather than all the time like a Clopper-Pearson interval for a proportion.

------------------------------
Phillip Kott
RTI International
------------------------------

Original Message:
Sent: 05-23-2017 08:28
From: Chauncey Dayton
Subject: "What is your favorite confidence interval?"

I'm in a photography forum and the usual answer to: What is your favorite camera? Is: The one you have with you (including an iPhone) when an interesting opportunity arises. So, my answer for a CI is the one I need at the time. I'll be reporting a CI for an observed proportion of 0 so Bayesian CIs are the most interesting right now.

------------------------------
Chauncey Dayton
------------------------------

Original Message:
Sent: 05-23-2017 07:31
From: Kenneth Ganning
Subject: "What is your favorite confidence interval?"

95% conservative confidence interval for proportions (p+/- 1/Sqrt(n)) Simple and often (but not always) useful.

------------------------------
Kenneth Ganning
------------------------------

Original Message:
Sent: 05-19-2017 22:50
From: Stephen Smela
Subject: "What is your favorite confidence interval?"

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, "What is your favorite confidence interval?"

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment-how does one answer such a question? "My favorite confidence interval is (-3.623, 5.783)"?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

Original Message------

95% conservative confidence interval for proportions (p+/- 1/Sqrt(n)) Simple and often (but not always) useful.

------------------------------
Kenneth Ganning
------------------------------

Maybe, they were testing you!
In their minds: "Is he a real person or is he a statistician?" 
They may have expected an answer as this: I enjoy the outdoors, do some photography, play golf, and YES, i adore the 90% confidence interval for the difference of two population means when the underlying populatiuon variances are assumed to be known!


------------------------------
Raid Amin
Professor
University of West Florida
------------------------------

Original Message:
Sent: 05-19-2017 22:50
From: Stephen Smela
Subject: "What is your favorite confidence interval?"

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, "What is your favorite confidence interval?"

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment-how does one answer such a question? "My favorite confidence interval is (-3.623, 5.783)"?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela

I was asked a different one by a hiring manager:  "What's your favorite baseball team?"  I didn't think quickly and the Brooklyn Dodgers bubbled out of my mouth.  He followed up with "You're not that old, are you?"  Fortunately, I didn't really want to experience a whole lot of Chicago winters and got a better job elsewhere.

------------------------------
Emil M Friedman, PhD
emilfriedman@gmail.com
http://www.statisticalconsulting.org
------------------------------

Original Message:
Sent: 05-19-2017 22:50
From: Stephen Smela
Subject: "What is your favorite confidence interval?"

Recently I was interviewing for a job at a marketing firm, and one of the questions I was asked was, "What is your favorite confidence interval?"

The interviewer was a Human Resources person who was just reading a list of questions given to her by the hiring manager, so she was not able to provide clarification.

I was dumbfounded for a moment-how does one answer such a question? "My favorite confidence interval is (-3.623, 5.783)"?

Was I supposed to come down in favor of a 95% interval vs. 90% or 99%?

I replied by talking about how the width of the confidence interval varies with the level of certainty desired, and it really depends on what the application is.

How would you answer such a question?

BTW, I did not get the job.

Steve Smela