(The views expressed here are those of the author, the founder of FridsonVision High Yield Strategy.)

One person you wouldn’t expect to hear tout a statistical fallacy is Warren Buffett, but the legendary investor appeared to do just that at the recent Berkshire Hathaway annual meeting, a reminder of just how easy it is to fall into statistical traps.

While speaking at the annual meeting – otherwise known as “Woodstock for Capitalists” – in early May, Buffett made the following rather odd comment while holding up a can of sugar-laden soda:

“For 94 years I’ve been able to drink whatever I want to drink. They predict all kinds of terrible things for me, but it hasn’t happened yet ... Charlie (Munger) and I never really exercised that much or did anything – we were carefully preserving ourselves for these years.”

Buffett has a deep knowledge of the insurance business. So we can be confident that he understands actuarial methods and probability theory better than his remarks suggest.

But that might not be the case for everyone in the conference audience.

While plenty of investors have prospered over long periods without the benefit of formal training in statistics, an inability to think probabilistically can lead to serious errors. Understanding a few of the field’s basic principles can help everyone avoid the most common financial pitfalls.

STATISTICAL FALLACY

Assuming that Buffett’s longevity somehow negates the long-proven health benefits of diet and exercise is a clear statistical fallacy. It’s like pointing to a 90-year-old who smokes three packs of cigarettes a day to disprove the correlation between tobacco use and longevity. In reality, both cases merely show that some people have exceptionally good genes.

Correlations between health and bad habits predict the percentage of individuals within a population who are likely to have adverse consequences from engaging in these behaviors. Those correlations predict nothing about the outcome for a particular individual within the population.

It’s much the same with investing. Just because one company’s stock defies a trend – like Amazon after the bursting of the 1990s tech bubble – that does not mean other seemingly overvalued firms will eventually become corporate superstars.

Another common statistical mistake among investors is blindly accepting a bearish prediction by a reputed genius who successfully forecast a previous market decline.

If stocks suffer an especially large drop – proving the supposed oracle “right” – the forecaster is apt to run video clips of the dire warnings he flooded the airwaves with before the down year. No mention will be made, of course, of the wrong calls the “genius” made in prior years.

The fact is that the S&P 500 has fallen in 32% of the past 97 years. That means a forecaster can warn of an impending selloff at the start of every year and pretty much expect to be right one out of three times.

Of course, the one-out-of-three odds are based on averages over a significant period of time, but the point remains that inevitability, rather than insight, is a key contributor to the fame of many forecasters.

STATISTICAL SIGNIFICANCE

Another way that unfamiliarity with statistical concepts can lead to unwise investment choices is the failure to properly understand statistical significance.

Let’s say the stock of a fictitious company – call it XYZ Corporation – generated the following annual total returns in the 10 years after its initial public offering.

Comparing these results with the S&P 500’s total return over the same period, a broker might make a pitch like this:

“XYZ has outperformed the market for an entire decade, posting an average return of 16.09% versus 14.15% for the index. An advantage of nearly two full percentage points over the next 20 or 30 years would give your portfolio a gigantic boost over the long term, thanks to the magic of compounding. These returns suggest that XYZ’s management team knows how to create superior results for shareholders.”

Kudos if your reflexive response is “Past performance is not indicative of future results.” But the problem with the broker’s sales pitch goes deeper. It asserts that XYZ’s C-suite executives have demonstrated managerial skill by engineering an index-beating stock return. Missing from the discussion is the critically important concept of statistical significance.

In non-technical terms, no genuine evidence exists that XYZ’s stock’s performance edge was anything more than chance.

Confirming statistical significance would require an understanding of several other quantitative tools, including standard deviation, t-statistics, confidence intervals, and p-values, as well as the use of a difference-of-means calculator.

You’ll be forgiven if you decide not to wander that far into the weeds of empirically based financial analysis, but this four-minute read on statistical significance would be well worth your while.

In attending to your physical health, it’s hazardous to fall prey to statistical fallacies such as, “People who don’t exercise can expect to live as long – or longer – on average than people who do. Just look at Warren Buffett.”

Your financial health could be similarly jeopardized if you fail to recognize that numbers presented in misleading ways can lead incautious investors to make terrible decisions.

(The views expressed here are those of Marty Fridson, the founder of FridsonVision High Yield Strategy. He is a past governor of the CFA Institute, consultant to the Federal Reserve Board of Governors, and Special Assistant to the Director for Deferred Compensation, Office of Management and the Budget, The City of New York.).

(Writing by Marty Fridson; Editing by Anna Szymanski and Stephen Coates)