Teaching statistics for business: the need for a paradigm shift

Literature review

Managers working in a business environment have to make decisions every day based upon data as Britz et al (1996:3) note 'In the business environment, professional decisions secure the financial health of the company. Goals and objectives are developed to identify areas for improvement initiatives'. The use of statistical applications to business solve and analyse business activities is not a new phenomenon. Its roots can be traced back to Deming where work can be treated as series of interconnected processes (1980) and forms the foundations of his system of profound knowledge 'Appreciation of a system'. The work of Deming has its roots in Shewhart's (1980) classic 'Economic Control of Manufactured Product' and originated as a means for controlling and monitoring process variations as a means to continuous improvement.

However it can be argued that the development of statistical techniques to analyse and monitor organisational behaviour has not been embraced by the wider business community and those who are the custodians of economic success. Statistics is regarded as a mystical black art, and the acceptance of data outputs as a result of any such analysis is rarely questioned. This can be argued is a result of peoples' prior experience with this discipline and the way that statistics was taught. As such it has been argued that ignorance of statistical methods is due to either the lack of teaching expertise in this area or if this does exist it is delivered in isolation of real or practical examples. The emphasis therefore should be focused towards what Britz et al (1996:11) term 'Statistical Thinking' when they advocate that 'When determining course content based on customer needs, Statistical Thinking should be emphasised over statistical methods in an introductory course'.

However, despite this historical context of statistical applications, there would appear to be evidence that the message has still to be taken on board by those who work in business and commercial environments. Snee (1993:149) reports such sentiments when he states that:

'There is a growing feeling in the statistical community that significant changes must be made in statistical education. Statistical education has traditionally focused on developing knowledge and skills and assumed that students create value for the subject in the process. This approach hasn't worked. It is argued that we can help students better learn statistical thinking and methods and create value for its use by focusing both the content and delivery of statistical education how people use statistical thinking and methods to learn, solve problems, and improve processes'.

Thus this might lead us to conclude that traditional statistical education within the academic community has focused upon theory and methods at the expense of real life applications. One might surmise quite rightly that this is the root cause of people's aversion and distancing from the subject and hence its problematic application in real world situations. As Hare et al (1995:53) note:

'There are four major issues that must be addressed if statistics is to become an integral part of management:

• Managers must understand why they need to posses statistical knowledge
• Current and future managers must develop this knowledge
• Measures must be taken to ensure that the knowledge is efficiently applied
• The payoff from the knowledge and its applications must be assessed'

It can be argued this will not be taken on board unless we address the way that statistical education is delivered, and the focus should be upon solving problems, improving processes and predicting process performance (Snee, 1993:153). This is not a new way of thinking as Deming (1986) proclaimed such sentiments when calling for greater emphasis on analytic studies which deal with planning for the future and the prediction for the process which produced the data. This can only be achieved through describes as 'experiential learning is active learning as compared to passive learning via lectures' (Cobb, 1991:182). The notion of statistical value is for Snee (1993:153) a central tenet on which he posits his argument that:

'We must change the content and delivery of statistical education to enable students to experience the use of statistical thinking and methods of dealing with real world problems and issues. These experiences will produce a more favourable attitude toward the discipline and greater desire to put statistical thinking to use'.

This 'new' approach based within old philosophies has to be channelled into a coherent strategy and relevance, and the definition of what statistical thinking applied in a business environment according has to be defined. According to Snee (1990:118) 'If we are to make effective sense of statistical thinking, we must define what we mean by the term. It is my experience that many of us talk about statistical thinking but rarely define it. The result is that there is confusion and lack of agreement over what statistical thinking is'. Snee (1990) then goes on to define statistical thinking under the three categories of Statistical thinking in Quality Improvement, Reducing Variation, and Rugedness of Product and Process Design. Box (1988) also emphasises the need to integrate the organisational functions, and that it will not only help us do a better job of achieving the management leadership and people and teamwork ingredients of Total Quality. This he claims should also enhance our ability to improve product quality and care of customers and achieve constant improvement with innovation.

The case for change

If modern day organisations are to compete effectively they have to have educated employees; this fact was not lost on the industrialisation and rise of the Japanese economy in the latter half of the 20-century. However the facts still not to have been learned by many western organisations that investment in people will enable future prosperity and survival. However it has to be recognised that not all organisations have ignored the well being of their employees, but they reside as a minority rather than the majority. As a recent survey reveals, noting that 'The CBI and TUC agree that the priorities are to tackle the basic skills problems of individuals, increase the proportion of adults with level 2 NVQ qualifications and increase the uptake of Investors in People by small organisations' (Engineering Management, 2001:241).

However the use of statistical tools and techniques are more often than not subsumed in a plethora of subject modules and is not afforded the status of its own stand alone course, or taught as a pure mathematical subject. Thus the dilution of statistical thinking and application becomes common practice in many undergraduate and postgraduate degree programmes. A common reaction to the word statistics brings on revulsion and angst amongst many students studying business and management degrees, and this unfortunately extends to those who also study the natural sciences and engineering disciplines as well. How often have we heard comments such as this from students:

"Why do we have do learn this stuff when we have computers to do the calculations?"

A vital fact has been lost within this comment, and that is the one that ignores the understanding of how we arrive at the final value i.e. the very answer lies in the use of the word calculations. The feeding into a computer will not give us this 'learning experience' or a 'feel for the data'. This is often borne out by students who are supposedly well educated and hold responsible positions in their organisations. When asked to calculate a mode or a median for a frequency distribution many do not even recognise these terms, never mind trying to find their values. The sad fact of the matter is that some of these have in their possession first degrees, and leaves one to ask how they interpret data on a day to day basis in their normal day job.

However what we also find is a lack of any simple mathematical manipulation skills when undertaking statistical calculations. A recent comment received by a final year BSc Engineering Management student is quite a concern. When asked to manipulate a formula with square roots, and to transpose, he complained that this was beyond him. Challenged why this was beyond him he relied:

"It's seven years since I did this in my HND, and in any case I don't use it in my job"

This is disturbing on two counts. The first is that his HND was in an Engineering discipline, and secondly he worked for a large national organisation where paradoxically the analysis of data is part of his job. What this tells us about the general level of the mathematical and statistical education of modern day graduates is all too evident, but this is not an uncommon reaction.

The aversion to statistical methods is one not confined only to management students, where they might be forgiven for their lack of 'specialist knowledge' within a general degree. Those studying professional examinations in quality management also display a lack of knowledge of statistical skills. The notion of process variation is a concept many struggle with (a central theme of Shewhart's and Deming's work), even though they may be dealing with this on a day to day as quality professionals. The extension to process capability and the related indices baffles only but the few.

It is no coincidence that the Institute of Quality Assurance (IQA) has now disbanded their B2 Statistics paper which covered such topics as probability distributions, SPC, significance testing, and design of experiments, because many educational centres offering their examinations cannot provide the expertise to teach this subject. As a consequence the number of candidates that entered for this examination dwindled to only a handful of entrants before its demise in 2000. Their B5 Reliability paper was also disbanded for the same reason. And yet, when these students finally achieve professional membership of the IQA many are bereft of any real knowledge of statistical methods and their application. It must be remembered that process variation and an understanding of its concept are central to the continuous improvement journey, and it leaves one to wonder how this can be achieved without a critical appreciation rather that a passing awareness of statistical methods.

The trend of not using statistical analysis is also evinced in both undergraduate and postgraduate projects and dissertations. Although we are not arguing that statistics should appear in every such document, it must be acknowledged that even those undertaking elementary data analysis struggle with such a task. The analysis of questionnaires is such an example. Here many students use Likert scales to record data, which in essence is a valid way to collect data. What they then to proceed to do is attach a weight against each of the responses for example 1 to 5, and then calculate averages. What they fail to realise is that this is not the correct way to proceed. First they are treating the Likert scale in the same way as a ratio scale, the values between 1 to 5 do not have equal distance between them. Secondly the use of the modal value would be appropriate in this situation, as the Likert scale is essentially a scale to rank perceived preferences. When this is pointed out to students a sense of bewilderment is to be witnessed, and the reasoning behind this latter approach has to be given. Again this is not 'difficult stuff', but it does reveal a lack of statistical understanding and the consequences of applying the wrong approach and/or methods.

The use of simple measures of central tendency and the lack of understanding between the mean, mode and median of frequency distribution cause a great deal of disenchantment with students. Many (not all) have difficulty with these and their relative positions when a frequency distribution becomes skewed. Again this is straightforward if the basics are well understood. This can also be easily explained if they are presented diagrammatically. However the number of students who struggle with this seemingly easy task fails to dismay. This is a result again of not being able to think critically as to how the statistics work, and yet this is an important aspect of exploratory data analysis. One student doing his final year BSc Engineering Management degree was heard to say:

"Why do we have to know about this stuff [mean, mode and median] anyway? I manage people not numbers. If a problem goes wrong with any of my processes we just fiddle with it until it comes back into specification"

When asked how he measured his process variation and how it was behaving he replied:

"We stick in the computer and it gives us the answer"

And when asked about process ownership and understanding:

"I can't be bothered learning statistics, it has no relevance to my situation"

These latter comments should provoke us to re-think the way we deliver and apply statistics, and again should cause concern as this student holds down a managerial position as a supplier to a well-known automobile company in the UK. This has important implications as a lack of understanding of process behaviour can lead to the misunderstanding of the answers that we arrive at.

Conclusions

The evidence cited in this paper represents but a snapshot of experiences from a variety of sources. However what is clear is the need to re-look at the way statistically based disciplined are delivered and applied to real organisational problems. It is perhaps of little comfort to know that as organisations, and we as individuals, have to deal with an increasing amount of data, and accept that society's understanding and general education in this area is perhaps lacking.

Much of our statistical education is based upon standard methods that have little or no direct application to problem analysis and solutions. What is needed is a methodology that teaches organisations and individuals to think critically in order to build models of real life problems. This latter point needs to be headed. It requires us to think 'systems' not 'local' when solving problems. This is exemplified by Goldratt and Cox (1984) where their fictional character Alex Roggo has to think outside the box to solve his bottleneck problem and finds solace within the context of a weekend hike with a group of boy scouts. As the fictional Roggo notes:

'It's starting to make sense. Our hike is a set of dependent events...in combination with statistical fluctuations. Each of us fluctuates in speed, faster and slower. But the ability to go faster than the average is restricted. It depends upon all the others ahead of me in the line. So even if I could go at five miles per hour, I couldn't do it if the kid in front of me could only walk five miles per hour'.

And that:

'What's happening isn't an averaging out of the fluctuations our various speeds, but an accumulation of the fluctuations'

(Goldratt and Cox, 1984:99-100)

It is at this point that Roggo realises that his bottleneck problem in the line of scouts on the hike has deeper implications in its solution. Once the principles of the line model are understood, their transferability to the context of an industrial plant to solve his real life resource constraints becomes a reality. We must therefore follow such an example and think laterally. What therefore emerges is the need to formulate principles in the way we educate and deliver statistical disciplines. It has also to be recognised that those who receive such education have to be engaged on their terms and environment. The Chinese proverb perhaps sums up this:

I hear, I forget
I see, I remember
I do, I understand

This perhaps encapsulates the very essence of what statistical education should be about i.e. making sense of personal experience. As Rowntree (2000:14) states 'It is by making sense of our experiences that we human beings grow wiser and gain greater control over the environment we live in.'

Therefore if we are to be more educated and more confident in handling statistics in the business environment the prevalence of supportive organisational cultures has to be a pre-requisite for developing the following principles if we are to operate more effectively within ever increasing competitive business environments:

• Think big, think systems
• All work is a series of interconnected processes and activities
• Identify statistical variation and fluctuation and use these as a means to instigate organisational improvements
• Resources must be in place to educate the workforce
• Managers: Don't blame and shame
• Colleges and Universities must adopt a novel approach when delivering modules/subjects that require statistical techniques

References

Box, G.E.P. (1988) Statistical Tolls for Engineers, Scientists and Production Workers: The Opportunity and the Challenge, unpublished paper at the American Statistical Association annual meeting, August

Britz, G., Emerling, D., Hare, L., Hoerl, R., Shade, J. (1996) Statistical Thinking, ASQC, Milwaukee

Cobb, G. (1990) Teaching Statistics: More data, Less Lecturing, Amstat News, Vol.1, and No.4

Deming, W.E. (1986) Out of the Crisis, Cambridge, Massachusetts Institute of Technology

Engineering Management (2001) December, Vol.11, No.2

Goldratt, E.M. and Cox, J.F. (1984) The Goal, Gower publications, Aldershot

Hare, L.B, Hoerl, R.W, Hromi, J.D, Snee, R.D. (1995) The Role of Statistical Thinking in Management, Quality Progress, February

Rowntree, D. (2000) Statistics without tears, Penguin Books, London

Shewhart, D. (1980) Economic Control of Quality of Manufactured Product, ASQC, Milwaukee

Snee, R.D. (1990) Statistical Thinking and Its Contribution to Total Quality, The American Statistician, May, Vol.44, No.2

Snee, R.D. (1993) What's Missing in Statistical Education?, The American Statistician, May, Vol.47, No.2