mathematics

Unmatched count

Unmatched count 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 Unmatched count rather than just read about it. In short: In psychology and social research, unmatched count, or item count, is a technique to improve, through anonymity, the number of true answers to possibly embarrassing or self-incriminating questions. It is very simple to use but yields only the number of people bearing the property of interest and leads to a larger sampling error than direct questions.

Key takeaways

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

Reference excerpt

In psychology and social research, unmatched count, or item count, is a technique to improve, through anonymity, the number of true answers to possibly embarrassing or self-incriminating questions. It is very simple to use but yields only the number of people bearing the property of interest and leads to a larger sampling error than direct questions. It was introduced by D. Raghavarao and Walter T. Federer in 1979.

Method The participants of the survey are divided into two groups at random. One group, the control group, is given a few harmless questions, while the other group gets an additional question regarding the property of interest. The respondents are to reveal only the number of "yes" answers they have given. Since the interviewer does not know how they arrived at that number, it is safe to answer the awkward question truthfully. Due to the unmatched count of items, the number of people who answered "yes" to the awkward question can be mathematically deduced. [1]

Example The control group is asked how many of the following statements apply:

I have changed my place of residence. I own a pet. I like to go to the theatre. I have never been in a traffic accident. Let the total number of "yes" answers from this group be 410. The second group additionally gets a question concerning the point of interest:

I have cheated on an examination. Let the total number of "yes" answers from this group be 460.

Evaluation The number of "yes" answers in the control group is called the baseline. It is assumed that the second group would have given the same number, were it not for the critical question. Thus, their additional "yes" answers (50 in the example) are due to the critical question. This is used to estimate the percentage of cheaters in the population. Let the number of participants in each group be 300. As expectation value, 50 of them answered "yes" to the critical question, meaning that approximately 17% of the population have cheated on examinations.

See also Bogus pipeline Randomized response

References

Further reading Elisabeth Coutts, Ben Jann (2009). Sensitive Questions in Online Surveys: Experimental Results for the Randomized Response Technique (RRT) and the Unmatched Count Technique (UCT), General Online Research Conference in Vienna Dan R. Dalton, James C. Wimbush, Catherine M. Daily (1994). Using the Unmatched Count Technique (UCT) to estimate base rates for sensitive behavior. Personnel Psychology 47, pp. 817–829 Allison M. Ahart, Paul R. Sackett (2004). A New Method of Examining Relationships between Individual Difference Measures and Sensitive Behavior Criteria: Evaluating the Unmatched Count Technique. Organizational Research Methods, Vol. 7, No. 1, pp. 101–114 Joseph LaBrie, Mitchell Earleywine E. (2000). Sexual risk behavior and alcohol: Higher base rates revealed using the unmatched-count technique. The Journal of Sex Research, 37, 321–326 doi:10.1080/00224490009552054 T. Tsuchiya, Y. Hirai, S. Ono (2007). A study of the properties of the item count technique. Public Opinion Quarterly doi:10.1093/poq/nfm012

Worked examples

Example 1 — a first encounter with Unmatched count

Start with the simplest possible case. Write down what Unmatched count 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 Unmatched count 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 Unmatched count 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 Unmatched count

In research: Unmatched count 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 Unmatched count 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: Unmatched count is common in secondary-school and first-year university syllabi. It links to neighbouring topics Data anonymization techniques, Sampling (statistics), Survey methodology, so understanding it makes those chapters shorter.
In everyday life: Look for Unmatched count 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 Unmatched count in 20 minutes

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

Frequently asked questions

What is Unmatched count in simple terms?

Why does Unmatched count 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 Unmatched count?

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 Unmatched count.