mathematics

GRIM test

GRIM test 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 GRIM test rather than just read about it. In short: The granularity-related inconsistency of means (GRIM) test is a simple statistical test used to identify inconsistencies in the analysis of data sets. The test relies on the fact that, given a dataset containing N integer values, the arithmetic mean (commonly called simply the average) is restricted to a few possible values: it must always be expressible as a fraction whose denominator is N and whose numerator is an…

Key takeaways

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

Reference excerpt

The granularity-related inconsistency of means (GRIM) test is a simple statistical test used to identify inconsistencies in the analysis of data sets. The test relies on the fact that, given a dataset containing N integer values, the arithmetic mean (commonly called simply the average) is restricted to a few possible values: it must always be expressible as a fraction whose denominator is N and whose numerator is an integer. If the reported mean does not fit this description, there must be an error somewhere; the preferred term for such errors is "inconsistencies", to emphasise that their origin is, on first discovery, typically unknown. GRIM inconsistencies can result from inadvertent data-entry or typographical errors, or from scientific fraud. The GRIM test is most useful in fields such as psychology where researchers typically use small groups and measurements are often integers. The GRIM test was proposed by Nick Brown and James Heathers in 2016, following increased awareness of the replication crisis in some fields of science.

Procedure The GRIM test is straightforward to perform. For each reported mean in a paper, the sample size (N) is found, and all fractions with denominator N are calculated. The mean is then checked against this list (being aware of the fact that values may be rounded inconsistently: depending on the context, a mean of 1.125 may be reported as 1.12 or 1.13). If the mean is not in this list, it is highlighted as mathematically impossible.

Example Consider an experiment in which a fair die is rolled 20 times. Each roll will produce one whole number between 1 and 6, and the hypothesized mean value is 3.5. The results of the rolls are then averaged together, and the mean is reported as 3.48. This is close to the expected value, and appears to support the hypothesis. However, a GRIM test reveals that the reported mean is mathematically impossible: the result of dividing any whole number by 20, written to 2 decimal places, must be of the form X.X0 or X.X5; it is impossible to divide any integer by 20 and produce a result with an "8" in the second decimal place.

Interpretation and limitations Even if the data fails the GRIM test, this is not automatically a sign of manipulation. Errors in the mean can come about innocently as a result of an error on the part of the tester, typographical errors, calculation and programming mistakes, or improper reporting of the sample size. However, it can be a sign that some data has been improperly excluded or that the mean has been illegitimately fudged in order to make the results appear more significant. The location of failures can be indicative of the underlying cause: an isolated impossible mean may be caused by an error, multiple impossible values in the same row of a table indicate a poor response rate, and multiple impossible values in the same column indicate the given sample size is incorrect. Multiple errors scattered throughout a table can be a sign of deeper problems, and other statistical tests can be used to analyze the suspect data. The GRIM test works best with data sets in which: the sample size is relatively small, the number of subcomponents in composite measures is also small, and the mean is reported to multiple decimal places. In some cases, a valid mean may appear to fail the test if the input data is not discretized as expected – for example, if people are asked how many slices of pizza they ate at a buffet, some people may respond with a fraction such as "three and a half" instead of a whole number as expected.

Applications Brown and Heathers applied the test to 260 articles published in Psychological Science, Journal of Experimental Psychology: General, and Journal of Personality and Social Psychology. Of these articles, 71 were amenable to GRIM test analysis; 36 of these contained at least one impossible value and 16 contained multiple impossible values. GRIM testing also played a significant role in uncovering errors in publications by Cornell University's Food and Brand Lab under Brian Wansink. GRIM testing revealed that a series of articles on the effect of price on consumption at an all-you-can-eat pizza buffet contained many impossible means – deeper analysis of the raw data revealed that in many cases, sample sizes were incorrectly stated and values incorrectly calculated.

References

External links Online GRIM test calculator Lightweight online GRIM test calculator

Worked examples

Example 1 — a first encounter with GRIM test

Start with the simplest possible case. Write down what GRIM test 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 GRIM test 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 GRIM test 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 GRIM test

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

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

Frequently asked questions

What is GRIM test in simple terms?

Why does GRIM test 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 GRIM test?

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 GRIM test.