mathematics

T. A. Bancroft

T. A. Bancroft 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 T. A. Bancroft rather than just read about it. In short: Theodore Alfonso Bancroft (January 2, 1907 – July 26, 1986) was an American statistician. He earned a bachelor's of art degree in mathematics at the University of Florida in 1927, a master's of art degree in mathematics at the University of Michigan in 1934, and a PhD from Iowa State University in 1943.

Key takeaways

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

Reference excerpt

Theodore Alfonso Bancroft (January 2, 1907 – July 26, 1986) was an American statistician. He earned a bachelor's of art degree in mathematics at the University of Florida in 1927, a master's of art degree in mathematics at the University of Michigan in 1934, and a PhD from Iowa State University in 1943. His dissertation, Tests of Significance Considered as an Aid in Statistical Methodology, was supervised by William Gemmell Cochran. He joined the faculty of Iowa State University in 1949 and served as head of the statistics department from 1950 to 1972. He retired in 1977. He was elected a Fellow of the American Statistical Association in 1956 and the Institute of Mathematical Statistics in 1972. He was also a Fellow of the American Association for the Advancement of Science and an Elected Member of the International Statistical Institute. He served as the president of the American Statistical Association in 1970. Bancroft's papers are archived at Iowa State University.

Works

Books Statistical Theory and Inference in Research with R. L. Anderson (1952) Topics in Intermediate Statistical Methods Statistical Theory and Inference in Research with Chien-Pai Han (1981), Marcel Dekker. This textbook, co-authored with Chien-Pai Han, covered fundamental principles of statistical theory and their applications to research problems.

Articles Bancroft, T. A. (June 1944). "On Biases in Estimation Due to the Use of Preliminary Tests of Significance". The Annals of Mathematical Statistics. 15 (2): 190–204. doi:10.1214/aoms/1177731284.

References

Worked examples

Example 1 — a first encounter with T. A. Bancroft

Start with the simplest possible case. Write down what T. A. Bancroft 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 T. A. Bancroft 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 T. A. Bancroft 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 T. A. Bancroft

In research: T. A. Bancroft 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 T. A. Bancroft 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: T. A. Bancroft is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1907 births, 1986 deaths, 20th-century American statisticians, so understanding it makes those chapters shorter.
In everyday life: Look for T. A. Bancroft 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 T. A. Bancroft in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what T. A. Bancroft 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 T. A. Bancroft out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is T. A. Bancroft in simple terms?

Why does T. A. Bancroft 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 T. A. Bancroft?

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 T. A. Bancroft.