# Part 3 of Statistical Sampling by Bruce Truitt

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Confessions of a
Recovering Auditor
OR
Does He Win or Lose?
Yes, He Does!

By Bruce Truitt

Posted February 2010 to www.auditskills.com

Confidence – Variation – Precision...

And, welcome back from the Corporate Sector, dear reader.  Missed you, we have.

We trust that the holidaze offered ample opportunity to sink to new heights of non-productivity and rise to new depths of sloth.  The parenthesis between our present and previous offerings confirms my December indolence, though I did succeed in widening my "confidence interval."

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Writing of which, I am 100% confident (more on that later) that all, most, some, a few, one, or none of you did, as counseled, mantra, dream, share, speak, and think "The Formula" since our last sermon on the mound-shaped distribution.  So, I hereby proclaim it anew:

Sample Size = Confidence x Variation
Precision

In the end, these three elements—confidence, variation, and precision—work like an air bubble in a waterbed.  Ha!  Made you squint and say "Huh!" didn’t we?

No, really.  Ever try to get an air bubble out of a waterbed?  It’s harder than summoning children to dinner.  If you depress the bubble or its environs, it merely migrates.  In exactly the same way, altering any part of the right side of "The Formula" causes the other parts to change.  For now, we will save "Variation" for a future missive and focus here on "Confidence" and "Precision."

So "The Formula" says, "To be more confident or more precise when you open your pie hole to make an assertion, you gotta do more work."  Sample size has to go up.  Makes perfect sense, doesn’t it?  (This is where you blindly nod agreement.)  But, what’s this "Confidence" all about, Alfie?

"Confidence" is nothing more than repeatability, and I am not referring to the number of times with the emphasis on "numb," you repeated the word "confidence" in your statistics class.  Rather, to be 90% confident is to say that if we sample the same population in the same way 100 times (boring!), we will get statistically the same result 90 times, i.e., 90% of the time.  Similarly, if we are 95% confident, repeated sampling in the same way produces statistically the same result 95 times out of 100.

The "statistically" part relates to the other bubble—"Precision."  Remember from our second installment, "Ye Shall Know The Formula, And The Formula Shall Set Ye Free," that precision is also called "margin of error."  If we combine the "sample statistic" that is, what we get from the sample—sample error rate or sample mean—with the margin of error, we build the so-called "Confidence Interval."

(Sample Statistic) Minus (Margin Of Error) = Lower Confidence Limit

And

(Sample Statistic) Plus (Margin Of Error) = Upper Confidence Limit

So let’s say that we conducted an exit poll after a Presidential Election and discovered that 48% of the voters voted for Howard The Duck, plus or minus three percent.  The "plus or minus three percent" means there is a three percent margin of error.  Our confidence interval for this election would be, therefore:

48%                –              3%              =             45%
(Sample Statistic) Minus (Margin Of Error) = Lower Confidence Limit

And

48%            +            3%             =           51%
(Sample Statistic) Plus (Margin Of Error) = Upper Confidence Limit

If we abbreviate "Lower Confidence Limit" as "LCL" and "Upper Confidence Limit" as "UCL," we get the General Confidence Interval—you’d better salute!

45%                   48%                51%
LCL           Sample Statistic         UCL

Here, "statistically the same result" would be any percentage between 45% and 51%.  If we did 100 exit polls at 95% confidence, 95% of the time the exit poll percentage would be between 45% and 51%.  Sometimes, the exit poll percentage would be closer to 45% and sometimes closer to 51%.

So, we would end up being 95% confident that 45% to 51% of the voters would quack for Howard.  Mmmm, we could not say if Howard will win or not.  See?  You can get opposing right answers from one statistician!  But, hey, if Howard wins, we get a duck in the White House.  If not, we get a turkey.  Either way, the bird brains continue. Man, I love history!

OK.  We’ve laid enough eggs for one day.  Is this election battle over!?!  Or will the feathers keep flying?  Tune in next time for:

"Dancing The Pennsylvania Avenue Poultry Polka"

Or

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Bruce Truitt has 25+ years' experience in applied statistics and government auditing, with particular focus on quantitative methods and reporting in health and human services fraud, waste, and abuse. His tools and methods are used by public and private sector entities in all 50 states and 33 foreign countries and have been recognized by the National State Auditors Association for Excellence in Accountability.

He also teaches the US Government Auditor's Training Institute's "Practical Statistical Sampling for Auditors" course, is on the National Medicaid Integrity Institute's faculty, and taught Quantitative Methods in Saint Edward's University's Graduate School of Business.

Bruce holds a Master of Public Affairs from the LBJ School of Public Affairs, as well as Masters' degrees in Foreign Language Education and Russian and East European Studies from The University of Texas at Austin.

www.auditskills.com