Part 4 of Statistical Sampling by Bruce Truitt | AccountingWEB

Part 4 of Statistical Sampling by Bruce Truitt



Click here to learn more about Bruce.

Posted December 2010 on  newsletter archives

Ah, sweetness!  One more election season has faded to blessed oblivion.  Congratulations on surviving another chance to elect gods then suffer the shenanigans of mere mortals. 

As an alternative, our last episode (more properly epizoodie), thrust Howard the Duck, a/k/a/ “El Pato Vato” or “Duck D-u-u-u-de,” into the political spotlight.  “Hey, why not a duck?” he squawked.  “We’ve had turkeys for over 200 years!” (See our last installment at:

But, recall that exit polls gave our fearless fowl 48% of the vote, plus-or-minus 3%.  These results told him he would win with 51% (48% + 3%) or lose with 45% (48% - 3%).  This less than useless information left our comic-book candidate in suspended animation.  Go ahead and groan, it’s OK.

Following fantastic fits of fulminating frustration, Howard hired a statistics consultant, though ‘twas tough to find one who spoke plain English, much less Mandarin duck.  (BTW, do you know how to recognize an extroverted statistician?  Find the one looking down at your shoes). 

Howard’s numbers nerd said the only way to know if the 48% was dead-on correct was to poll all voters.  “All we have is 95% confidence that your true share of the votes is between 45% and 51%.”  At this, Howard fumed, “Why did I pay for these polls!  I’m in hock up to my bill and still don’t know if I should keep pressing the feathers out there or just fly south!”  Well, our winged warrior has flummoxed his flipper on a fundamental fact of sampling:

  • We must estimate variation to calculate sample size
  • We must sample to estimate this variation

In other words, Howard has to estimate his share of the vote in order to calculate the sample size needed to estimate his share of the vote.  This is a duck and egg sorta thing, at which Howard honked and headed for Florida, thus his absence as a write-in in Alaska.  I did get him to draft Alfred E. Neumann as VP, though.  After all, “What!  Me Worry?” deserves serious consideration as a campaign slogan, n’est-ce pas?

So, how do we estimate the variation needed to calculate sample size via “The Formula:”?

Sample Size = Confidence x Variation

The general answer is simple:

  • Probe
  • History
  • Criteria

That is, we can do a sniff test, like Howard’s exit poll (comprising at least 30 items, the why for which we’ll handle in a later missive), rely on past experience, or look for a “thou shalt” in law, rule, regulation, norm, standard, policy, procedure, professional practice, etc.  We then plug the resulting value into “The Formula,” calculate our sample size, and hope that the variation we find (the duck) is generally akin to the variation we expected (the egg).

Or we can rely on the oldest basis for management assertion – the “Wild A#! Guess,” a/k/a the WAG. 

This sow’s ear sometimes comes in a silk purse called “subjective probability.”   Then, we also have the SWAG, or “Scientific Wild A#! Guess.”  Both of these are windage lacking verifiable substantiating data, but, hey, it’s better than nothing, and we gotta use something to calculate our sample size!  FYI, unrestrained use of the term “windage” guarantees endearment at family reunions, staff meetings, and, most definitely, exit conferences.

OK.  We have an idea of where variation comes from but how much is too much?  Is there a standard for deviation?  Only your oxymoron knows for sure, but Lou Rawls gave us the answer in 1976….”You’ll Never Find.” 

Yet, though no stated norm exists, practical guidelines do:

  • On the Normal Curve (All Hail The Mighty Bell Curve!), the standard deviation is 34% of the mean, “average” for those of us west of the Mississippi.
  • A standard deviation greater than the mean means (Aha!  Spellcheck didn’t snag that redundant repetition) the data are getting really spread out, which tells you to whack before you quack – toss the outliers or group (stratify) the data.  If help is needed, please contact our Ph.D. data experts, Drs. Hacken Whack, Sly Sindice, and Ed Itenfer Getit, or, of course, Tony Soprano, the true Whackmaster.

And, for all you Latin lovers out there, nota bene, (I’ve waited months to use that), the singular of “strata” is “stratum”!  Just like “data” and “datum.”

Well, then, what about standards for “The Formula’s” other two pieces – confidence and precision?

Regarding confidence, you’ll be glad to know that neither the Yellow Book, Green Book, Red Book, Grey Book, nor Pink Book (yes, they all really exist) criterionize.  Hey, if “impact” can be a verb, so can “criteria.”  Frankly, I am waiting on the Clear Book, which I hear is due out with the next Kelley Blue Book.

I found some salvation in the “AICPA Sampling Guide” (The Guide), a great example of what happens when statisticians, accountants, and lawyers collide with way too much coffee.  Seriously, though, while its Dostoyevsky-like density mimics that of the “Big Boy” bomb, it is an extremely well-written and valuable volume, despite occasionally high hypnagogics.

In mining “The Guide” I found that, as with my “standard” deviation quest, no criterion confidence exists.  While referencing confidence levels from as low as 50% (!) up to 95% and 99%, it posited no norm.  So, as before, we turn to professional practicality which tells us that, especially if an assertion about the population is sought, auditors do not work at confidence levels below 90%.  Makes sense, right?  After all, “auditor” starts with “A,” and no auditor wants a grade less than an “A.”  That’s good enough for me!

The identical scenario obtains for precision, a/k/a “margin of error,” nee Marge Innoverra of CarTalk fame.  While “The Guide” maxes out precision at 20%, it avoids any stake-in-the-ground standard.  But, again, practice helps out:

  • Auditors rarely use precisions over 10%, especially if a population pronouncement is needed.  And remember that this 10% creates a 20%-wide window since it means “plus-or-minus 10%,” a fact that hobbled Howard’s hopes.
  • As a rule, the more important the audit, the smaller the margin of error.
  • The smaller the margin of error, the more the audit costs.

And, of course, by logical extension:

  • The more the audit costs, the more work you gotta do.
  • The more work you do, the older you get.
  • The older you get, the sooner you retire.
  • The sooner you retire, the happier you are.
  • The happier you are, the longer you live.

Hoohah!  Sampling saves lives!  Sorry ‘bout that.  Got carried away.  Please ignore the last ten seconds of your life.

At any rate:

  • If you are sampling non-critical controls or compliance and/or need to estimate a population error rate, use margin of error of at most 10%.
  • If bad findings mean people die or write big checks, 10% aresn’t gonna cut it.  A five-per cent precision is a useful maximum in such cases.  “Aresn’t” is my contribution to the lexicon and likely the only triple negative in English given its fusion of “aren’t,” “ain’t,” and “isn’t.”
  • The more money on the table, the more you move toward the 3% often used in Harris and Gallup polls and in Medicare and Medicaid work.
  • If you will face God, the Devil, and F. Lee Bailey in court (buena suerte, vato!), you might go to 1%, though this generates ginormously egantic sample sizes.

Hmm.  It looks like your old Audit Manager was right – it all depends on the objective.

OK.  Enough at the firehose fountain.  Let’s wrap it up.  Here is your tchotchke:

Sample Size = Confidence (≥ 90%) x Variation (≤ Mean)
                                          Precision (≤ 10%)

So, in the end, there is nothing standard about deviation, confidence, or precision.  And you thought auditing was a precise profession?!?  Silly goose!  But, hey, our professional sacrament – auditor judgment – remains inviolate.  Yay!

Naturally, this chat aresn’t done.  Tune in next time for more statistical lies, rumors, and half-truths (is that redundant?) when we consider the fundamental lemmas of our honorable profession:

Only Errors Exist


One Man’s Errors Are Another Man’s Data






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.


This blog

Governmental auditors unite! Leita Hart-Fanta, CPA, CGFM, and CGAP is the author of “The Yellow Book Interpreted” and owner of a website devoted to training for governmental auditors. Whether you are an internal auditor or monitor for a government entity or a CPA doing grant audits, you will enjoy Leita’s humorous take on the complexity of auditing in the government environment.

More from this blog

Bloggers crew

Steve Knowles has spent 25 years in business and practice in the UK, but he also worked in the states and the years haven't dulled his way of seeing an alternative view to everyone else, and every day is a new adventure.


Joel M. Ungar, CPA is a lifelong resident of the Detroit area and a graduate of The University of Michigan. He is a principal with Silberstein Ungar, PLLC, a Top 15 auditor of SEC public reporting companies.


Allan Boress, CPA, with over 25 years as a practitioner and consultant to the accounting profession. Mr. Boress is the author of 12 published books in 6 different languages, including a best-seller, The "I-Hate-Selling" Book.


Larry Perry, CPA, CPA Firm Support Services, LLC, is the author of accounting and auditing manuals, author and presenter of live staff training seminars, and author of webcast and self-study CPE programs. He blogs about small audits, reviews, and compilations.

Sandra Wiley, COO and Shareholder, is ranked by Accounting Today as one of the 100 Most Influential People in Accounting as a result of her prominent role as an industry expert on HR and training as well as influence as a management and planning consultant. She is also a founding member of The CPA Consultant's Alliance. Sandra is a certified Kolbe™ trainer who advises firms on building balanced teams, managing employee conflict and hiring staff.

Maria Calabrese, CIR, Human Resources manager for Fazio, Mannuzza, Roche, Tankel, LaPilusa, LLC in Cranford, New Jersey, Maria's topics revolve around the world of: Mentoring, Performance management, and The "Y Generation," a.k.a. "The whY generation".


William Brighenti is a CPA, Certified QuickBooks ProAdvisor, and Certified [Business] Valuation Analyst, operating an accounting, tax, and QuickBooks consulting firm in Hartford, Connecticut, Accountants CPA Hartford.


Ken Garen, CPA, is the co-founder and President of Universal Business Computing Company (, a software development firm of high-volume, high-productivity accounting and payroll technology.


Eva Rosenberg, MBA, EA, is the publisher of, and author of the weekly syndicated Ask TaxMama column. She provides answers to tax questions from taxpayers and tax professionals worldwide.


Amy Vetter, CPA, CITP is the CPA Programs Leader for Intacct Corporation responsible for leading the CPA/BPO Partners nationally.

Brian Strahle is the owner of LEVERAGE SALT, LLC where he provides state and local tax technical services to accounting firms, law firms and tax research organizations across the United States. He also writes a weekly column in Tax Analysts State tax Notes entitled, "The SALT Effect." For more info, visit his website:
Scott H. Cytron, ABC, is president of Cytron and Company, known for helping companies and organizations improve their bottom line through a hybrid of strategic public relations, communications, marketing programs and top-notch client service. An accredited consultant, Scott works with companies, organizations and individuals in professional services (accounting, finance, medical, legal, engineering), high-tech and B2B/B2C product/service sales.

Rita Keller is a nationally known CPA firm management consultant, speaker, author, mentor and blogger. She has over 30 years hands-on experience in CPA firm management, marketing, technology and administrative operations.

Stacy Kildal is the mom of two fantastic kids, an Advanced Certified QuickBooks ProAdvisor, Certified Enterprise Solutions ProAdvisor, Sleeter Group Certified Consultant, a nationally recognized member of the Intuit Trainer and Writer Network, and co-host of RadioFree QuickBooks.
Michael Alter's blog specializes in providing practical advice to those who seek greater profitability and practice management tactics that enhance deeper client relationships.

Sally Glick, CMO, Principal, Marketer of the Year in 2003 and AAM Hall of Famer in 2007, leads a lively discussion of the constantly expanding roles of marketing and the professional marketers that drive this initiative in accounting firms of all sizes.


The IMA Young Professionals Blog features the insights of IMA’s Young Professionals Committee. Committee members share advice and experiences on careers, continuing education, work/life balance, and other issues affecting young accounting and finance professionals.


FEI Financial Reporting Blog provides highlights from SEC, PCAOB, FASB, IASB, and other regulatory news, including reporting under Sarbanes-Oxley Sect 404. It is written by Edith Orenstein, Director of Technical Policy Analysis at FEI.


Sue Anderson has 30 years of experience in continuing education for accountants. Currently she is the program director for online CPE provider CPE Link.


Jim Fahey is COO of Apple Growth Partners, a regional CPA firm in Ohio. His focus is on the effective and efficient use of technology within the firm by all team members.

Caleb Newquist is the Editor-in-Chief of Sift Media US, overseeing content for both AccountingWEB and Going Concern.

Leita Hart-Fanta, CPA, CGFM, and CGAP is the author of "The Yellow Book Interpreted" and owner of a website devoted to training for governmental auditors.


AccountingWEB is more than just a U.S. team of journalists and financial and technology experts - we have an international side, too! Members of our British team who publish share their ideas, insights, and perspectives from across the pond.