Statistical concepts of false positives / false negatives

Mathematics has multiple areas that help us solve different types of problems.   Sometimes only one area is used to solve a given problem.  More advanced and complicated problems, however, often require combining concepts drawn from multiple disciplinary domains.  See previous article.  These areas – algebra, geometry, trigonometry, calculus, and statistics –provide particular approaches to address different types of “real world” problems.  The ultimate goal is to increase the accuracy and reliability of solutions to those problems by using the most appropriate or relevant mathematical “tool”.

Statistics introduces the important notion of probabilistic error.  There are two types of statistical hypothesis testing errors, Type I (false positives) and Type II (false negatives).  Type I errors occur whenever statistical techniques flag or label a particular instance / event / explanation as representative of some fact / condition when in fact it is not (in actuality).  I’ll explain using an analogy.  Imagine being blindfolded and drawing a ball from a bin containing only balls labeled either “True” or “False”. A Type I error occurs when a given statistical process predicts that the ball drawn will be “True” when in fact the ball drawn is labeled “False”.  This is known as a false positive.  A Type II error occurs when the very same process predicts the ball drawn will be “False” when in fact the ball drawn is labeled “True.”  This is known as a false negative.

We sometimes encounter Type I and Type II statistical errors, but are usually unaware of them.  Mathematicians control the frequency of their occurrence by strengthening the reliability of the underlying statistical tests used.  Generally, we become aware of these problems– and become sufficiently motivated to prevent their reoccurrence (by changing the test reliability) – as the consequences of errors increase.  For example, receiving an inaccurate medical diagnosis due to false lab results.  Or under-planning / over-planning safety measures when models underestimate / overestimate the risks / dangers of a physical structure or mechanical process failing.  Recent design flaws in the Boeing 737 Max jetliner illustrate the potential consequences.

Business valuation errors – Types I and II

Financial decisions made by executives may also suffer from estimation errors.  Corporate finance decisions depend upon accurate estimates of the future worth of particular investments.  The ultimate aim is not to lose money by either overestimating the returns (and investing more than you receive back) or underestimating the returns (and not investing thereby foregoing a profitable opportunity).  The first valuation error is a false positive, a Type I error; the second, a false negative, a Type II error.

Type I valuation errors frequently underlie inflated market valuations caused by investor overconfidence in future returns.  In trader parlance, these are overheated markets.  Civilians call them “financial bubbles.”  Economic history is replete with them, ranging from irrational trading in tulip bulbs, false gold rushes, inflated equity prices  (both before the Great Depression and the “ bubble” of 2000), and inflated real estate values (before the Financial Crisis of 2008).  Some commentators caution that we are currently witnessing a comparable overvaluation of “crypto currency” and “blockchain technology” investments.  See previous article.

Type II valuation errors occur when analysts and investors underestimate the future returns of a company or industry thereby foregoing a profitable investment opportunity or selling a company for less than its worth (based on what the company will actually return in the future).  Counter-cyclical investors hope to capitalize on these opportunities (over the long-term) by buying stocks in companies from sectors that are currently “out of favor” with investors – and therefore sold at lower prices – with the hopes that they will return to be “in favor” in the future when economic / market conditions change (so that these same stocks can be sold at then higher prices).  Value investors similarly hope to buy “out of favor”– and currently undervalued – stocks of companies whose underlying business fundamentals portend future profit opportunities.  Both investment strategies require holding such stocks for longer investment periods against the prevailing market sentiment.

Berkshire Hathaway is frequently referenced as the preeminent example of a company successfully capitalizing on undervalued stocks, i.e. equities of companies reflecting Type II valuation errors.  Berkshire Hathaway exceeds overall market returns using this investment strategy.  China similarly captured 80% of the world’s supply of rare earth elements – essential inputs to most electronic devices – by investing in the sector when the US temporarily exited the market in the 1990s.  China also purchased US-based magnetic and other technology companies (at what are now considered bargain prices) to build electronic components using those rare earth elements.  All patents and intellectual capital were transferred to China after acquisition.  25 years after their investments, Chinese companies control the overwhelming world supply of these vital resources.  A very smart and profitable investment!

Business valuation errors – Extensions and Type X

Some modern mathematicians and logisticians have proposed extending statistical hypothesis testing errors to higher dimensions (e.g. Type III and beyond).  For example, the results of a statistical test may be accurately estimated (i.e., the question correctly answered as either “True” or “False”) but the wrong solution then applied.  Or the question may have been accurately answered, but the prediction was based on a flawed methodology (i.e. the right answer was arrived at but only due to pure luck). Type III errors are not commonly accepted by statisticians, much less understood by civilians!

Business executives, however, do understand using an inappropriate or irrelevant “tool” to fix a particular business problem.  For example, using only communications tools to solve a purely chemical manufacturing process (in a refinery).  Or using just decision science tools to try to optimize a customer’s experience of a service offering (in retail).  Or using inappropriate assumptions / inaccurate financial calculations to weigh investment opportunities (in corporate finance).  See previous article.

I label these Type X errors.  Not properly diagnosing the underlying business problem, not knowing which disciplinary theory is appropriate for / relevant to solving the problem, not understanding the details of a particular methodology (and its limitations), or some combination of the preceding.  Type X errors occur more often in business than executives care to admit.  The consequences of these errors can be catastrophic.  Consider the Financial Crisis of 2008.  Financial institutions held mispriced portfolios of complex derivative securities (Mortgage-Backed Securities, Collateralized Debt Obligations, Credit Default Swaps, etc.) whose inter-relationships and risk were poorly understood by corporate leaders.  Or the overextension of consumer and corporate debt whose repayment cannot be supported by the earnings of borrowers.  Or not properly understanding the time horizons of future returns – and the sources of those returns – for emerging technologies, resulting in the wrong cost-of-capital used to discount cash flows.  All of these Type X errors require understanding business value on multiple levels: conceptual, theoretical, methodological and managerial!

Increase business valuation accuracy by understanding value

At The University of Chicago Booth School of Business, I studied Accounting and Finance.  One of the assigned texts for the introductory accounting course was entitled Accounting: The Language of Business.   Accounting is indeed the language of business.  It provides a type of Esperanto so shareholders, investors, financiers, managers, regulators, creditors, auditors, suppliers, lawyers, and credit rating companies can communicate and understand the financial “workings” of a company.

While accounting is the language of business, value is the essence of business.  Value is key to strategy. Value is the foundation of the value chain, i.e. the interconnected value activities within the firm. Value activities are the physically and technologically distinct activities the firm performs. They are the building blocks by which the firm creates a product / service valuable to its buyers, i.e. the firm’s value proposition.  Value touches every area of business.

Unlike accounting, however, which is based on Generally Accepted Accounting Principles (GAAP in the US) to express financial value, there is no equivalent – no generally accepted definition of business value — across business functions.  Marketing focuses on customer value, value chain management on the ultimate customer’s value, purchasing on the cost of the firm’s supplied inputs, manufacturing on production costs, logistics on transportation / warehousing costs, finance on shareholder returns, economics on industry margins, strategy on competitive advantage, innovation on product development, IT on information flows, etc.  These alternative “lenses” on business value, particularly those used by front-line workers, often lead to mistranslation / misinterpretation / misalignment as employees attempt to monetize their respective value contributions.  In other words, a company’s workers wear different eyeglasses!

For example, most production line workers cannot “see” the worth of their work in shareholder value terms.  Even marketing struggles to monetize buyers’ insights or “customer experiences.”  Since corporate finance uses accounting figures to evaluate investment decisions; since GAAP doesn’t reflect current market prices, actual company costs, and / or the “worth” of intangibles; since future cash flows depend on industry / customer / operations estimates; and since no accepted “rules” exist to monetize all these assumptions, financial valuation errors are likely.  How then does an executive maximize shareholder value?

Use Integrated Value Process (IVP) to improve financial decisions

In order to understand value deeply, one needs a robust theory of value (conceptual intelligence), a way of properly specifying value (encoded intelligence), an effective way to communicate value (socio-emotional intelligence), and a way to decide which actions / activities to undertake (experiential intelligence).  One needs to integrate or synthesize all four areas to be effective.   Moreover, individuals across the organization need to do so simultaneously.

Value is multi-dimensional.  See earlier article.  Understanding value is like solving a Rubik’s Cube.   A Rubik’s Cube has multiple colors.  To truly understand and manage value on multiple levels, I developed the Integrated Value Process (IVP) framework in An Empirical Framework for Evaluating, Implementing and Managing a Value-based Supply Chain Strategy (my PhD thesis accepted by the University of Bath School of Management — ProQuest publication number 3121355).  IVP consists of (1) a conceptual framework explaining how value is managed across an organization, (2) a methodology to detect any ‘value gaps’ in that process, (3) five value ‘first principles’ on which value chain activities are based, and (4) a ‘meta’ definition of value to communicate effectively across functions within the firm.

IVP promotes an integrative and holistic approach to value management.  A “new way of thinking” about value — one that is interdisciplinary, multifunctional, and systems-based – that can improve the monetization and financial translation of business value from all value perspectives.     The framework provides a way to translate between the essence of business (value) and the language of business (accounting).  Don’t force your employees to work using the same set of eyeglasses!   They won’t be able to “see” their work and your overall organization will stumble.  Use IVP to increase business valuation accuracy and avoid the accounting distortion – and bad financial decisions — caused by the multiple value lenses used by your organization.

About the Author

Andrew Swan, PhD is a multidisciplinary and cross-functional integrator of strategy, processes, and information technology. His focus and expertise center on helping executives increase value creation and optimize value flows in business. Dr. Swan holds four degrees in Management, Accounting & Finance, Information & Knowledge Strategy, and Computer Science from the University of Chicago Booth School of Business,  the University of Bath School of Management, and Columbia University.

He frequently publishes articles on value chains, value streams / flows, and Integrative Value Management on his website Dr. Swan created the Integrated Value Process (IVP) Framework to help companies optimize the flow of goods & services, funds, and information across their respective value chains for multiple stakeholders. He can be reached at or at +1.773.633.7186.  He lives in Chicago.

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