Numerical fata morgana
Many years ago an article was published in the UK lamenting the dismal state of primary education in Great Britain. The key premise of the article: half of the students had below average reading skills.
Apparently the article was promoted as highlighting a serious problem, conveniently ignoring an important fact in favour of selling more newspapers – in any typical statistical sample, the number of values below and above average will be similar.
As a consequence, the natural phenomenon was portrayed as a disaster. If policy decisions had been made based on such statistics, this would have created a real problem.
Similar misuse of data can often be found in the world of business, where the consequences can also be severe, making it crucial for executives to know how to present and use data correctly.
The simple example below illustrates one of the common mistakes made by retail executives when presenting and analysing data.
Many retail executives would argue that the right-hand diagram provides more useful sales data as it shows fluctuations. On the surface, they would be well within their rights to question the figures in weeks 2, 7 or 8.
Yet, according to Total Quality Management (TQM), which dictates a methodical approach to interpreting data, not all such revenue changes should attract management attention. Furthermore, intervention to address some of the fluctuations could be inappropriate.
To determine if the graph warrants any action we first need to calculate the average sale and then its standard deviation:
- The average sales across the eight weeks = $4.18 million
- The standard deviation = $0.02 million
- Therefore, the normal, statistically expected fluctuation sits between $4.12 and $4.25 million.
Since none of the weeks deviate outside of this control band, the sales should be considered stable, requiring no action by management. The fluctuations observed can be explained as noise inherent in the system. This means that the first graph offers more value, as it suppresses the noise.
The diagram on the left-hand side carries some other useful information. It shows no trend (static figures), which confirms that the situation calls for no immediate intervention. However, if revenue remained static over a longer period, the business would need to take action – a flat sales graph spells long-term trouble.
Like all new skills, adopting such a method of thinking takes practice. Executives need to focus on process capability and variation rather than on reacting to normal fluctuations. Only real emergencies, caused by special causes (e.g. sales drop due to flooding in a store) need specific intervention.
We all know that using the right tool for the job can make a substantial difference to the results. When it comes to information, adopting a statistical toolset will help in distinguishing superficial appearances from facts. This can save your business from all kinds of unnecessary pain, and make it more effective and efficient.
Just like a desert mirage can draw a thirsty traveller off the road and into an uncertain wilderness, when viewed without sound statistical understanding, a numerical Fata Morgana can be just as deceiving. One should act only when truly necessary.