If you don’t understand your statistics, they can become a liability

Written by Matthew Barsalou on . Posted in Features

The science writer Michael Shermer, has previously written about something he calls 'Darwin’s dictum'. It's based on a letter Charles Darwin sent to his friend Henry Fawcett in which he stated - 'How odd it is that anyone should not see that all observation must be for or against some view if it is to be of any service!' Shermer applies this to science, but it applies equally well to statistics, hence I propose a 'statistics dictum': all statistics must be for or against some view to be of any service and the underlying statistical concepts must be understood.

Somebody recently said to me, 'I am surprised that you are interested in statistics. I did not expect you to like maths.' Actually, I found maths classes to be pure drudgery. What is there to like about being forced to memorise formulas simply to get a good grade? I have nothing against pure maths - only something against teaching maths as a rote memorisation activity. Statistics, like math, can be taught as merely a collection of formulas one must memorise under penalty of a failing grade, or it can be taught as useful formulas one must understand to accomplish things.

A consultant once told me 'don’t bother learning statistics, there are programs that can do it for you.' That sounded to me like 'don’t bother learning how to write, there are programs that can do that for you.' I would not expect an illiterate person to type a letter and I would not want a statistically illiterate person to analyse my data, even if a program does it for them.

A different consultant assisted in the investigation of a failed manufactured product and he was convinced he had identified the root cause because he found a statistically significant difference in sets of measurement data. Unfortunately, the data was from factors that had absolutely no relevance to the problem under investigation. It does not matter if the difference is statistically significant, the area measured could have been removed from the components and this would not have made a difference to the issue under consideration.

Statistics must be used for drawing a conclusion to be of any use. George Box reminds us that 'statistics is, or should be, about scientific investigation and how to do it better, but many statisticians believe it is a branch of mathematics.'1 I believe statistics is a tool that engineers should apply to understand data, but many engineers think it has something to do with maths.

An engineer investigating changes in a manufacturing process does not perform a statistical analysis merely to determine if the mean yield of process one is greater than the mean yield of process two with p > 0.05. The objective is to determine if there is a difference in the mean yields so that actions can be taken.

Many, if not most, engineering and business degrees require at least one course on statistics and anybody certified as an ASQ Certified Quality Engineer or Six Sigma Black Belt must have some knowledge of statistics. Knowledge of statistics alone will not accomplish anything, only the proper application of statistics with the intent to understand the data will accomplish anything.

In today’s industry, statistics are easily assessable to engineers and managers due to the rise in easy to use statistical software packages. This does not mean just anybody can open a statistical software program and crunch numbers, an understanding of statistics is still needed.  Conclusions reached through statistical test when the test’s assumptions have been violated are worse than no data at all. Changing a manufacturing process due to the results of a Student’s t test when the data did not represent the population or a Z test when the population was not normal could mean a large investment in a machine that lowers quality.

Successful professionals in industry can apply the 'statistics dictum' by using statistical thinking, which is a 'philosophy of learning' consisting of understanding that 'all work occurs in a system of interconnected processes', 'variation exists in all processes' and 'understanding and reducing variation are keys to success.'2

To apply statistical thinking, engineers, technicians and managers must understand the statistical tests they use, as well as the assumptions and limitations of these tests. This requires more than just memorising the formulas behind the tests. It requires an understanding and an appreciation for statistics. With statistical thinking, statistics can be for or against a view and therefore of service to us. Statistics may for example be of the view that the new process, under the given test conditions, is better than the old process with a specific degree of certainty.

This is not to say that there is no room for studying statistics merely to work with statistics. New statistical methods must be developed and new applications for statistics should be identified. However, even new methods and uses must be for or against some view when they are applied in the real world, or they would serve no purpose.

Statistics is not just a field for statisticians. Engineers and managers in industry must be able to understand and correctly apply statistical concepts as well as evaluate and interpret statistical data. Statistics is too important a topic to be left only to the experts.

 

References

  • 1. George E.P. Box. (1990), 'Commentary on Communications Between Statisticians and Engineers/Physical Scientists,' Technometrics, 32, 251-252.
  • 2. Roger W. Hoerl and Ronald D. Snee, 'Redesigning the Introductory Statistics Course', Center for Quality and Productivity. Technical Report No. 130, 1995.

The views expressed in the Opinion section of StatsLife are solely those of the original authors and other contributors. These views and opinions do not necessarily represent those of The Royal Statistical Society.

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