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Statistics is more than a numbers game – it underpins all sciences

AUSTRALIA 2025: How will science address the challenges of the future? In collaboration with Australia’s chief scientist Ian Chubb, we’re asking how each science discipline will contribute to Australia…

How do we make sense of numbers without stats? Jeffrey/Flickr, CC BY-ND

AUSTRALIA 2025: How will science address the challenges of the future? In collaboration with Australia’s chief scientist Ian Chubb, we’re asking how each science discipline will contribute to Australia now and in the future. Written by luminaries and accompanied by two expert commentaries to ensure a broader perspective, these articles run fortnightly and focus on each of the major scientific areas. Here, we explore the significance of statistics.

We are all familiar with many instances of statistics in everyday life: the statistics of sport, weather, population, the stock market … the sort of thing that might appear in the “number crunch” column in The Age and The Sydney Morning Herald.

The central feature of statistics is data: designing ways to collect, summarise, visualise, present and draw inferences from data.

Fundamental concepts are variability and uncertainty. As a way of making sense of the great variety of ways in which we meet statistics, I’ll give a simple breakdown into three broad categories.

The first category is statistical facts. Such facts are often interesting in themselves, or in comparison with the same fact for different times or places. They might seem like data, but in reality they are summaries of data.

Nathan Rupert/Flickr, CC BY-NC-ND

What was the proportion Australians 15 years of age or older in 2001, who have never married? The answer is 32%.

Behind the 32% figure is the 2001 Australian Census. As a summary of census data, it has no statistical uncertainty.

More complex are data collected in survey sampling of populations based on randomly selected units. Variability enters the equation, as different samples will generally give different results.

Sample survey data is typically summarised as proportions, percentages or averages, and the results are presented as inferences concerning the population. They will be uncertain inferences, because of sampling variability (“error”) and other types of error.

The 2007 National Survey of Mental Health and Wellbeing conducted by the Australian Bureau of Statistics (ABS) found that an estimated 3.2 million Australians (20% of the population aged between 16 and 85) had a mental disorder in the 12 months prior to the survey.

(Presenting the uncertainty in estimates such as this one and explaining how that is interpreted is beyond the scope of this article.)

Let’s call this sample survey statistics – the second category.

Survey results such as those in our example are clearly important if we are to make informed decisions towards realising our aspiration, as outlined by the Chief Scientist in his introductory article.

Now let me turn to my third category: the enormous range of other uses of statistics. It includes the use of statistics by professionals (“statisticians”) and people whose principal activity is something other than statistics.

Statistical subcultures

Sectors of the economy such as agriculture make use of statistics in characteristic ways.

Sergey Melkonov/Flickr, CC BY-NC-SA

Yet when you search the web with key phrases such as “statistics in agriculture”, you will most likely find statistical facts about agriculture, not how statistics can be used to improve agriculture practice. That takes a more directed search, but the uses of statistics in this way are many and varied.

Over a long career in the CSIRO, Helen Newton Turner (1908-1995) applied statistics to animal production and later sheep breeding, and modern versions of her research continue to this day.

Statisticians work on comparative crop variety testing, which is a source of information on variety performance for Australian farmers. Similarly, the mining and manufacturing industries, and even the service industry, make use of statistics.

It is hard to name an area of science, technology, business, industry or government, even the humanities, which does not have its own statistical subculture – its own types of data, collection of questions and models and methods used to answer these questions by analysing the data, alongside a statistical literature.

It seems evident that statistics pervades every field of human endeavour, either through the use of statistical facts, some form of sample-population inference, or other informal or formal methods of addressing questions of interest. As I will explain, this statistical activity need not, and in general will not, be carried out by people calling themselves statisticians.

A role in all aspects of health

We might start with summary facts concerning mortality and morbidity, which show where we are, as a prelude to where we’d like to be. We can move to surveys to elicit more detailed information on particular topics than we have from routine data collections.

The mental health survey mentioned above is one example. Epidemiology works hand in hand with biostatistics in seeking to understand the patterns and causes of disease, and to inform policy decisions by identifying risk factors.

Biostatistics is used in the design, conduct and analysis of clinical trials to assess the efficacy of vaccines, drugs, devices, treatments or interventions.

It is also widely used in pre-clinical biomedical research, where cell lines or model organisms are analysed, in the studies necessary before a drug goes to human clinical trial and beyond.

Industry quality

What about the role of statistics in knowledge-based industries and high value goods and services, aspects of the economy that many (including me) would like to see greatly expanded in Australia in the coming decade?

Statistical methods were first used widely in the manufacturing industry in the 1930s, building on the pioneering 1920s work of Walter Shewhart, who is known as the father of statistical quality control.

Learn more about Walter Shewhart and quality control here.

These activities expanded rapidly following World War II, particularly in Japan, where American engineers and statisticians joined their Japanese counterparts in making important contributions to Japan’s reputation for innovative, high-quality products.

These developments broadened the role of statistics, moving it beyond the realm of statisticians. Statistical thinking entered the minds of both management and workers, through concepts such as quality circles. Problem identification, data collection and basic statistical analyses became important aspects of the job.

In the decades since the 1950s and 1960s, the value of statistical thinking in industries of all kinds has become widely acknowledged.

Developments such as Total Quality Management, Six Sigma and the series of standards from the International Organisation for Standardisation (ISO) known as ISO 9000 have all contributed to the near-universal awareness of the value of statistics in helping “define, establish, and maintain an effective quality assurance system for manufacturing and service industries” and in improving the quality of products and services.

It was understood from the earliest days that methods from manufacturing industries were also effective, with appropriate modifications, in the service industry, but uptake in that area has definitely been slower.

One thing is certain

Statistics, in one or more of the modes that I have described, has entered almost every aspect of human endeavour. We can use it for better planning, more efficient delivery of services, and increased productivity.

The value of statistics is only limited by a lack of awareness and the severe shortage of adequately trained statisticians. This can be remedied.

Just as it is difficult to quantify the benefit of having a workforce with an adequate knowledge of written and spoken language, so it is difficult to quantify the benefit of having a workforce who can adequately communicate about variability and uncertainty.


John Henstridge, Professor at the University of Western Australia

Jim Pennucci/Flickr, CC BY

Terry has illustrated the way in which statistics pervades almost any area where science, industry and government work to improve Australia. I must agree with this – even though I have spent decades working as a statistician, I remain surprised at just how useful this set of tools is and how widely it can be applied.

It really is a mathematical Swiss Army penknife.

Terry presents good reasons to be optimistic about statistics and what it can contribute to our aspirations for Australia. With such a track record, it is difficult to imagine anything else. But statistics is facing challenges in Australia.

With notable exceptions, statistics, like all the mathematical sciences, is in decline in Australian universities. This is partly due to declining standards of mathematics in secondary schools. Statistics is also challenged by a lack of clear recognition, in part due to the all-pervasive nature of its application as Terry highlights.

People in many areas do not realise that statisticians have developed tools that they need and often view statistics through the somewhat dated way it used to be taught. Statisticians share some of the responsibility for what is frequently poor teaching of their subject.

Despite these concerns, I have to be optimistic like Terry. One of the reasons is that statisticians form a passionate community who want to understand our world through data. That is exactly what Australia needs to make the right decisions.


David Warton, Associate Professor at the University of New South Wales

At university I planned to specialise in ecology, but turned to a subject I found more interesting – statistics! An ecologist might spend his or her whole career studying only plants, seals, invertebrates, frogs, birds or microbes, but I have studied all of these and more (although mostly from a computer screen).

Samuel Sharpe/Flickr, CC BY

Statistical research has a key role helping ecologists find structure in the face of so much uncertainty. It has a similar role as an enabling science in all disciplines in focus in this series.

While statistics is a rewarding career choice, a challenge is to ensure that sufficient students make this choice – so that the discipline continues to have the capacity and expertise to meet the demands of science and industry, and challenges of the digital age such as big data and the study of networks.

But recent budget decisions are an immediate threat, with risks that the path to a postgraduate degree in statistics will become financially out-of-reach for many, and with cuts to graduate destinations such as CSIRO and the ABS.

A second challenge is improving standards of statistical literacy among scientists, journalists, doctors, patients and the community at large, so all can make informed decisions in the face of uncertainty.

The increased role of statistics in the national mathematics curriculum can help improve statistical literacy, provided that teachers have sufficient resources and support to implement curriculum changes effectively.

Universities can also help by ensuring full-time staffing of statistical consulting services, invaluable resources for their research communities.



This article is part of the Australia 2025: smart science series, co-published with the Office of the Chief Scientist. Further reading:

Australia’s future depends on a strong science focus today
Physics: a fundamental force for future security
Proteins to plastics: chemistry as a dynamic discipline
Optimising the future with mathematics
Australia can nurture growth and prosperity through biology
A healthy future? Let’s put medical science under the microscope
Groundbreaking earth sciences for a smart – and lucky – country
To reach for the stars, Australia must focus on astronomy
Marine science: challenges for a growing ‘blue economy’
Building the nation will be impossible without engineers
Australia’s got ICT talent – so how do we make the most of it?
Agriculture in Australia: growing more than our farming future

Join the conversation

11 Comments sorted by

    1. Erich Heinzle

      logged in via email @internode.on.net

      In reply to Dr Graham Lovell

      On account of persistent agitation from scientific types (of the sort not into rugger or boxing I warrant) regarding the heat balance of the planet, I suspect that the current government will find it simplest to just repeal the laws of thermodynamics in the near future.
      Let's face it, the so-called "laws" of thermodynamics never made it into the all time top ten did they?
      The widespread use of the entropy maximising normal distribution in the field of statistics may find its usefulness somewhat diminished thereafter.
      Here's hoping that the goverment might finally be able to put all this climate concern based on the statistical analysis of mountains of cold, hard consilient data to rest, once and for all.....

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  1. Mark Harrigan

    PhD Physicist

    The "trouble" with statistics is that, to some degree, it is "hard".

    I don't mean by that that some of the maths is complex (though it can be).

    I mean that it takes effortful thinking (lots of system 2 in Kahneman terms) to appreciate and understand the statistical nature of what goes on the world. It is not (often) "intuitive" - indeed more often that not it is counter intuitive (meaning that proper application of statistical thinking often reveals a surprising and opposite conclusion to most…

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    1. David Menere

      part-time contractor

      In reply to Mark Harrigan

      Another area of statistics that doesn't receive sufficient attention is risk analysis, or more specifically, perception of risk vs the reality of risk. Certain tabloid publications play regularly with this, leading to beat-ups such as campaigns on violence in the community.

      Another critical area of risk analysis is consideration of climate change. Misunderstanding (intentional or otherwise) of the risks arising from climate change seriously hamper society's ability to make prudent and rationally-based preparations for highly probable events in future decades.

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    2. Mark Harrigan

      PhD Physicist

      In reply to David Menere

      Yes - good point. It would help a lot if when we taught "statistics" we also taught the basics of the various cognitive biases that mislead us.

      In this instance the availability heuristic, the availability cascade and the observation selection bias. Because they very much impact the distortion of perception of risk vs reality of risk to which you refer.

      I suspect most journalists have no idea about these but that certain "wily" (or should I say "Foxy"?) proprietors understand them and use them to manipulate the public all too well.

      Some years ago, precisely because of this, I cancelled my subscription to The Australian and will no longer provide News Ltd media with any of my consumer sponsorship.

      You may have heard the joke? Do you want your news limited or do you want to know what is going on? Alas I do not think there is any mainstream media that is very much better.

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  2. Richard Hockey

    logged in via Facebook

    "What was the proportion Australians 15 years of age or older in 2001, who have never married? The answer is 32%."
    This should read "What was the proportion of persons who stated in the 2001 census that they were 15 years of age or older and who also stated they were never married? "
    Its incorrect to say the census is a statistical fact, its just the best guess we've got.
    R

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  3. Robert Tony Brklje
    Robert Tony Brklje is a Friend of The Conversation.

    retired

    The biggest problem with statistics has always been people tend to look to hard at the numbers and the conclusions drawn from those outputs and not hard enough at the inputs, their basis and their representative values.
    One current day example being schizophrenics and cannabis use. So the same statistics can be twisted two ways, cannabis causes schizophrenia or existing schizophrenics self medicate with cannabis.
    So statistics is a really 'FUZZY' science because it is very much tied to the specific…

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  4. garybass

    Education IT Physics

    Herein lies the the main issue with preparing the next generation...(you) cannot put old head on new bodies!

    While we may say it is important, the up coming generation need to be convinced. just because digital devices are more common than..TV/taps/toilets..whatever..does not mean they understand how to use them efficiently (properly)..similarly the current generation can see statistics, but..to use them properly!? not likely.
    even this week a quote in theAustralian stated'..global temperatures…

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  5. John Phillip
    John Phillip is a Friend of The Conversation.

    Grumpy Old Man

    Great article! Thank you. As a secondary maths/physics teacher, I agree that it is vital that we improve statistical literacy in our population. This is one of the most important ways for hem to understand the truth of what is happening in their world. Cheers.

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    1. Robyn Williams

      multitasker

      In reply to John Phillip

      Agree. But the more of us that remain numerically and statistically illiterate, the easier it is for those in politics, the media and advertising to bamboozle and pull the wool over our eyes. They rely on it.
      I do despair at the widespread ignorant or deliberate misuse of numbers. Journalists are hopeless, and politicians constantly demonstrate ignorance of relevant use of statistics.
      Unfortunately, the federal government does not understand the importance of quality data collection and statistical analysis. What you don't know doesn't matter. Cuts to Bureau of Stats.and many others is because stats is a waste of time, "red tape", and for environmental and scientific assessment, just unnecessary "green tape".

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  6. rory robertson

    logged in via email @gmail.com

    Terry, David and John,

    Given the importance of maths and statistics in credible science, I've been amused to find that influential scientists at the University of Sydney's Charles Perkins Centre do not appear talented at (even) school-level maths. That became a problem after they made various basic errors in maths, confused up with down, and then self-published a spectacularly faulty paper in a formal "peer reviewed" journal: http://www.mdpi.com/2072-6643/6/2/663/htm ; http://www.australianparadox.com/pdf/quickquizresearch.pdf ; http://www.australianparadox.com/pdf/CPCscientistsresponse.pdf

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