Scientists from the British Geological Survey look at a seismogram readout of Britain's strongest earthquake in twenty years in Edinburgh, Scotland February 27, 2008
Alfred Knopf, the American publisher, once—rather humorously—observed that, “An economist is a man who states the obvious in terms of the incomprehensible."
A statistician, on the other hand, is increasingly someone who expresses overwhelmingly complex phenomena using oversimplified figures and graphics, which often end up serving as the basis of countless business decisions each year.
The per-capita GDP of a particular nation, the likelihood of succumbing to a certain ailment, or the odds of winning an unwise bet are all examples of information regularly displayed in graphic form. But how much truth is there in such quantitative descriptions of real-world phenomena or predictions of how things may unfold in the future?
This question is particularly important because humans seem to set critical thinking aside when they are presented with numbers and charts which seem to be put together by “experts."
We have a soft spot for figures as they have a reassuring quality about them.
Alas, they can also be alarmingly misleading.
Without delving too much into the technicalities of statistics, we are going to have a look at three common pitfalls in numerical and non-numerical analyses common in the world of business.
In averages—or, to be more precise, arithmetic,—means are often used as measures of central tendency: the average life expectancy in Japan or the average salary in Denmark, for example.
However, averages are frequently deceptive for populations which contain outliers or are simply too diverse.
Imagine you are the CEO of a multinational company, and you are deciding on your marketing strategies and pricing policies for the Middle East and North Africa (MENA) region.
Figuring out the average GDP per capita of the MENA region, as a measure of the region's affluence, and setting your regional prices accordingly would not do you any good, because the MENA region includes both countries such as the UAE, whose GDP per capita exceeds USD40,000, and less fortunate nations which have to make do with per capita GDPs in the region of USD500.
In such a heterogeneous sample, ascertaining a certain average figure—say a GDP per capita of USD9,000—for the entire region would reflect the economic strength of a small minority of population in question.
In business statistics, knowing the dispersion and range of the numbers is just as important as knowing their central tendency, and standard deviation (SD) is a good indicator of the amount of variation in your sample.
Simply put, a lower standard deviation means that your sample is more homogeneous, making the mean a more reliable value.
The writer and statistician Nassim Nicholas Taleb perfectly summarized the importance of range in statistical data by saying “never cross a river that is on average four foot deep."
Unlike measures of central tendency which try to provide a description of quantitative phenomena, correlations are used for making inferences regarding potential causal links between variables.
However, as statisticians never get tired of saying, correlation does not necessary imply causation.
Let us imagine that your company's sales jumped by 25% over the past quarter, just as the company started injecting more and more cash into its marketing department.
Would this mean that the company's marketing strategies have been spot-on?
The answer is “no." In all likelihood, both your sales and your spending on advertisement could have gone up due to improvements in general economic conditions.
In order to say, with any confidence, that there is a causal link between two events because one has preceded the other, or because they have fluctuated together, all other possibilities must first be ruled out.
Not all business reports are necessarily numerical, and qualitative studies, which use words instead of figures, are also common in the world of business these days.
One often hears that a group of researchers, after hundreds of hours of detailed interviews with self-made businesspeople, have figured out that all successful entrepreneurs have had three qualities in common: risk-taking, optimism, and passion for their work, for example.
Some may take this to mean that adopting the aforementioned qualities will give them an edge in their entrepreneurial enterprises and increase their chances of success.
However, a rather counter-intuitive but reasonable question to ask could be, “What about those risk-taking, optimistic, and passionate souls who just did not make it?"
Where are they now?
Taleb refers to this philosophical problem as the “invisibility of drowned worshipers."
Taleb recounts the story of a man who has been shown paintings of shipwrecked believers who have been saved because of their sincere prayers during those dark moments of utter helplessness in cold waters.
But the man cannot help but think of those believers who prayed just as sincerely but did not survive the ordeal and have no voice to speak of their experiences for the simple reason that they are dead!
The bottom line is, whether you are dealing with qualitative or quantitative analyses, always critically assess the information at hand.