Welcome to the Statistics guide
Have you ever found data confusing?
Ever suspected that some statistics might be misleading?
Do terms like standard deviation or confidence interval make you hesitate?
Or maybe you need to conduct your own data analysis and aren’t sure how to proceed?
This guide is here to help you with both:
Throughout the guide, you’ll find entertaining short videos, lessons from our numeracy adviser, interactive activities, online courses, and practical tools, all designed to help you build confidence and skill in studying statistics.
Statistics is “the practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample” (Oxford Languages). In practice, statistics means working with data, usually numbers, to describe patterns in society and the natural world, so that we can better understand, interpret, and take action. It is a wide-reaching discipline that underpins much of science and social life. You will often see statistics in the news, for example:
For university students, statistics is especially important. You need to understand statistics in order to interpret data critically and spot misleading claims. You may also need to apply statistics in your own work, particularly if you are conducting quantitative analysis or research.
Reflect on the following provocative assertions about statistics: what do you think?
This memorable line, attributed to Benjamin Disraeli, a statesman, and popularised by Mark Twain, a writer, reminds us that numbers can be used to persuade, mislead, or confuse.
We’ve all seen headlines, charts, or infographics that look convincing but hide crucial details. Statistics can create an illusion of certainty – numbers make a claim feel authoritative even when the underlying evidence is shaky.
Learning the foundations of statistics helps you question data critically and see beyond the façade.
Astrophysicist Neil deGrasse Tyson reminds us in the next short video how unnatural it is for us to understand probability and statistics:
👉 Watch this short video: Why statistics are hard for humans
If you use the expression “It’s a small world” sarcastically, you already have a good grasp on probability!
The irony is that, although humans have only recently developed formal statistical methods, we have arguably always been prone to making crude statistical inferences – seeing patterns where none exist, overestimating rare events, and misjudging risks. In his classic (and highly recommended) Thinking, Fast and Slow, psychologist Daniel Kahneman explores how our minds trip up when faced with uncertainty, probabilities, and numbers. That’s why learning the basics properly is essential to interpret data and experience more accurately.
Kahneman, D. (2012) Thinking, fast and slow. London: Penguin Books.
Attributed to physicist and chemist Ernest Rutherford, this quote highlights the idea that researchers should aim to design their experiments with as little uncertainty or error as possible, rather than relying on averaging or statistical analysis to compensate for poor design.
However, since natural variation and measurement error are inevitable (at least for now, and given available resources and technology) statistical tools (including large samples and repeated measurements) are invaluable for distinguishing meaningful patterns from random fluctuations and for reducing the impact of error.
Rutherford’s comment remains a useful reminder: while researchers should always strive to design studies that minimise error and maximise accuracy, statistics are essential for revealing and interpreting patterns within the unavoidable uncertainty of complex systems.
With this famous remark, theoretical physicist Albert Einstein expressed his discomfort with the idea that phenomena in the universe could be fundamentally random, as suggested by some interpretations of quantum mechanics (the theory describing the behaviour of tiny particles). Instead, Einstein was a determinist, believing that the universe is governed by precise laws and that every event has a cause.
Whether some events, especially at the quantum level, are truly random, or simply appear random due to our limited knowledge, remains a matter of debate. Even in the quantum world, however, patterns emerge. For example, in radioactive decay or particle spin, individual events appear unpredictable, but large numbers of events reveal clear patterns, and probability provides the best description of their overall behaviour.
Similarly, in everyday life, many phenomena that seem random at first reveal striking patterns when considered in large numbers. Each flip of a coin is independent and unpredictable, yet after many throws, outcomes form a predictable uniform distribution (half heads, half tails) (for an advanced explanation linking this to the concept of entropy, see this video). Seemingly unrelated phenomena like human heights, measurement errors, or even crime rates often form predictable distributions, such as the Gaussian (bell curve, illustrated on the right). These are "statistical regularities": patterns emerging from many independent events.
Beyond the philosophical debate between determinism, probabilism, and randomness, the key idea is this: probability and statistics let us recognise patterns and regularities in nature, society, and science. They help us see trends and make sense of complexity, even when they cannot explain and predict individual events.
While a close study of the dice may ultimately be needed to understand every outcome, throwing the dice and collecting results can be a more practical, if limited, approach. Think of longitudinal studies tracking health habits or the effects of medications: it’s often too difficult to determine the exact mechanism in each individual, but patterns in populations reveal clear effects.
With these ideas in mind, this guide aims to equip you with a solid understanding of statistics and to help you use statistics effectively and responsibly.
