mathematics

Repeatability

Repeatability 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 Repeatability rather than just read about it. In short: Repeatability or test–retest reliability is the closeness of the agreement between the results of successive measurements of the same measure, when carried out under the same conditions of measurement. In other words, the measurements are taken by a single person or instrument on the same item, under the same conditions, and in a short period of time.

Key takeaways

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

Reference excerpt

Repeatability or test–retest reliability is the closeness of the agreement between the results of successive measurements of the same measure, when carried out under the same conditions of measurement. In other words, the measurements are taken by a single person or instrument on the same item, under the same conditions, and in a short period of time. A less-than-perfect test–retest reliability causes test–retest variability. Such variability can be caused by, for example, intra-individual variability and inter-observer variability. A measurement may be said to be repeatable when this variation is smaller than a predetermined acceptance criterion. Test–retest variability is practically used, for example, in medical monitoring of conditions. In these situations, there is often a predetermined "critical difference", and for differences in monitored values that are smaller than this critical difference, the possibility of variability as a sole cause of the difference may be considered in addition to, for example, changes in diseases or treatments.

Conditions The following conditions need to be fulfilled in the establishment of repeatability:

the same experimental tools the same observer the same measuring instrument, used under the same conditions the same location repetition over a short period of time. same objectives Repeatability methods were developed by Bland and Altman (1986). If the correlation between separate administrations of the test is high (e.g. 0.7 or higher as in this Cronbach's alpha-internal consistency-table), then it has good test–retest reliability. The repeatability coefficient is a precision measure which represents the value below which the absolute difference between two repeated test results may be expected to lie with a probability of 95%. The standard deviation under repeatability conditions is part of precision and accuracy.

Attribute agreement analysis for defect databases An attribute agreement analysis is designed to simultaneously evaluate the impact of repeatability and reproducibility on accuracy. It allows the analyst to examine the responses from multiple reviewers as they look at several scenarios multiple times. It produces statistics that evaluate the ability of the appraisers to agree with themselves (repeatability), with each other (reproducibility), and with a known master or correct value (overall accuracy) for each characteristic – over and over again.

Psychological testing Because the same test is administered twice and every test is parallel with itself, differences between scores on the test and scores on the retest should be due solely to measurement error. This sort of argument is quite probably true for many physical measurements. However, this argument is often inappropriate for psychological measurement, because it is often impossible to consider the second administration of a test a parallel measure to the first. The second administration of a psychological test might yield systematically different scores than the first administration due to the following reasons:

The attribute that is being measured may change between the first test and the retest. For example, a reading test that is administered in September to a third grade class may yield different results when retaken in June. One would expect some change in children's reading ability over that span of time, a low test–retest correlation might reflect real changes in the attribute itself. The experience of taking the test itself can change a person's true score. For example, completing an anxiety inventory could serve to increase a person's level of anxiety. Carryover effect, particularly if the interval between test and retest is short. When retested, people may remember their original answer, which could affect answers on the second administration.

See also Accuracy and precision Monitoring (medicine) Reliability (statistics) Reproducibility

References

External links Practical explanation of repeatability and reproducibility in terms of how data can be different between samples. - oil industry example Archived 2017-09-22 at the Wayback Machine

Worked examples

Example 1 — a first encounter with Repeatability

Start with the simplest possible case. Write down what Repeatability 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 Repeatability 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 Repeatability 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 Repeatability

In research: Repeatability 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 Repeatability 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: Repeatability is common in secondary-school and first-year university syllabi. It links to neighbouring topics Metrology, Statistical reliability, so understanding it makes those chapters shorter.
In everyday life: Look for Repeatability 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 Repeatability in 20 minutes

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

Frequently asked questions

What is Repeatability in simple terms?

Why does Repeatability 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 Repeatability?

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 Repeatability.