~ Contributed by Mike Gilliland ~
Theoretical mathematics has beauty and elegance, along with logical rigor. Mathematical conjectures – or even real-life conjectures that can be formulated as such – can often be proven or disproven with certainty.
And then there is Statistics
Statistics provide a mathematical foundation for the descriptive and inferential judgments we make in business, and life in general.
We often use statistics descriptively, by citing a specific statistic like the sum (“SAS 2010 revenue was $2.43 billion”) or the mean (“My GPA was 1.89”).
However, the really interesting use of statistics, and the most relevant for business decision making, is inferentially – i.e., to draw conclusions and make decisions based on available data.
Examples Please?
We use statistics to make inferences in situations where we lack mathematical certainty, to answer questions like:
• Will this new drug cure the common cold?
• Does this batch of products meet design specifications?
• How much must I cut my price to increase sales by 25%?
• What is the ROI on the proposed project?
In many situations, such as determining the safety and efficacy of a new drug, statisticians utilize design of experiments to create efficient testing procedures.
Sampling methods are well recognized for their use in opinion polls. But they are also used in quality control, where examination of every item would be unnecessary, destructive (e.g. crash testing a car), or otherwise prohibitively expensive.
Fact Sheets for software like SAS/STAT, SAS/IML, and SAS/QC describe many more specific types of analyses that are available, and the kinds of business problems for which they would be used. A rapidly expanding area is data visualization, where highly interactive statistical graphics assist with exploratory data analysis.
Learnings and Warnings
The attribution of cause and effect is the desired outcome of many statistical analyses, but here we tread into dangerous territory. Statistics may identify a relationship between two variables (hemlines and the stock market, election winners and Super Bowl champs), but whether one causes the other is a much more difficult question.
It is probably safe to assume that most of the cause and effect attributions in business literature are unsubstantiated. It is easy to cherry-pick results that are favorable to our point of view, ignoring any contrary evidence, and not conduct a proper experiment (or in other ways) determine what is correct.
We are happy to claim positive ROI for our efforts when company results (added revenue, increasing stock price, etc.) turn favorable. But did our efforts really cause the results? What about the things we did through mid-2008? Would we admit they caused our revenues to fall and stock price to collapse as the world fell into recession?
It is also possible to draw elaborate conclusions from what may well be a random or chance result.
Considering all the organizations and individuals who provide hurricane predictions for the year, is it really surprising that somebody gets it exactly right? And just because they do in one year, is their weather model really superior, or was this pure luck? One data point is not going to give us the answer – and we need to be skeptical of all such claims. Statistics can help us distinguish what is likely real from what is likely just chance.
Parting Thoughts
Statistics can be of great assistance to decision making – especially in areas where we lack certainty. However, we must be very careful in its application, and the application of analytics in general, to avoid making assertions that are unsubstantiated by solid data or sound reason.
Statistics should be used to take the high road – to provide the truth or at least our best understanding of reality – but not to twist the data in support of a personal agenda or political point.
The tools available in statistical software provide the means for reaching this high road.
