mathematics

Statistical thinking

Statistical thinking is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Statistical thinking rather than just read about it. In short: Statistical thinking is a tool for process analysis of phenomena in relatively simple terms, while also providing a level of uncertainty surrounding it. It is worth nothing that "statistical thinking" is not the same as "quantitative literacy", although there is overlap in interpreting numbers and data visualizations.

Key takeaways

Statistical thinking belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Statistical thinking to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Statistical thinking from memory before moving on to harder problems.

Reference excerpt

Statistical thinking is a tool for process analysis of phenomena in relatively simple terms, while also providing a level of uncertainty surrounding it. It is worth nothing that "statistical thinking" is not the same as "quantitative literacy", although there is overlap in interpreting numbers and data visualizations. Statistical thinking relates processes and statistics, and is based on the following principles:

All work occurs in a system of interconnected processes. Variation exists in all processes Understanding and reducing variation are keys to success.

History

W. Edwards Deming promoted the concepts of statistical thinking, using two powerful experiments:

The Red Bead experiment, in which workers are tasked with running a more or less random procedure, yet the lowest "performing" workers are fired. The experiment demonstrates how the natural variability in a process can dwarf the contribution of individual workers' talent. The Funnel experiment, again demonstrating that natural variability in a process can loom larger than it ought to. The take home message from the experiments is that before management adjusts a process—such as by firing seemingly underperforming employees, or by making physical changes to an apparatus—they should consider all sources of variation in the process that led to the performance outcome. Nigel Marriott breaks down the evolution of statistical thinking.

Benchmarks Statistical thinking is thought to help in different contexts, such as the courtroom, biology labs, and children growing up surrounded by data. The American Statistical Association (ASA) describes the "statistically educated" as understanding the following:

data beat anecdotes data is natural, predictable, and quantifiable random sampling allows results of surveys and experiments to be extrapolated to the population random assignment in comparative experiments allows cause-and-effect conclusions to be drawn to know association is not causation significance does not necessarily imply practical importance, especially for studies with large sample sizes no statistically significant difference or relationship does not necessarily mean there is no difference or no relationship in the population, especially for studies with small sample sizes Statistical thinking is a recognized method used as part of Six Sigma methodologies.

See also Systems thinking Evidence-based practice Analytical thinking Critical thinking Computational thinking Data thinking

References

Worked examples

Example 1 — a first encounter with Statistical thinking

Start with the simplest possible case. Write down what Statistical thinking claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Statistical thinking before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Statistical thinking ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Statistical thinking

In research: Statistical thinking appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Statistical thinking in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Statistical thinking is common in secondary-school and first-year university syllabi. It links to neighbouring topics Data science, Six Sigma, Statistical process control, so understanding it makes those chapters shorter.
In everyday life: Look for Statistical thinking outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Statistical thinking in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Statistical thinking means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Statistical thinking out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Statistical thinking in simple terms?

Why does Statistical thinking matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Statistical thinking?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Statistical thinking.