Vocabulary | What Is a Collocation Association Score? How Word Partnerships Can Mislead or Inform

CHAPTER 01 OF 21 · VOCABULARY

1. Why word partnerships are more than adjacent words

Language contains recurring preferences such as strong evidence or make a decision. These patterns help readers infer meaning and help writers choose natural combinations. A corpus can count which words appear together, but a count alone does not tell us whether the partnership is especially characteristic of either word.

Look at an actual decision

Imagine a school corpus in which strong occurs before coffee, evidence and signal. A high count can arise because both words are common. A striking pairing can arise because a less common word nearly always appears with strong in the collected domain.

The mistake to anticipate

The mistake is to declare any frequent neighbouring words a meaningful collocation. In ordinary sentences, a function word may be adjacent to thousands of different words without constituting a useful lexical partnership.

A stronger method

Define the target pair, the relationship and the kind of corpus evidence you want. Then combine quantitative ranking with the qualitative question: does the expression form a meaningful and reusable pattern in context?

Try it: Is every two-word sequence a collocation?

Explained answer: No. Co-occurrence is an observable event. Collocational strength or lexical conventionality requires interpretation and often comparison with alternative partners.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 02 OF 21 · VOCABULARY

2. Define the node and the collocate

In collocation analysis, the node is the target word or expression; the collocate is a candidate partner within a declared relationship. Defining these roles clarifies whether the project concerns words immediately beside each other, nearby in a window or joined grammatically.

Look at an actual decision

For a study of adjective–noun combinations, strong can be the node and evidence the candidate noun to its right. For a study of verb–object patterns, the relevant link may span intervening words rather than form one adjacent bigram.

The mistake to anticipate

The common failure is to mix right-adjacent nouns with any noun in a five-word window, then rank them as if every observation has the same linguistic meaning.

A stronger method

State the node, candidate category, direction, span and grammatical relation when applicable. A clear query definition is necessary for every observed and expected count.

Try it: Can a candidate word to the left of a node be counted with right-side partners without any note?

Explained answer: Only if the task explicitly pools them and explains why. Direction can affect both grammar and interpretation.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 03 OF 21 · VOCABULARY

3. Choose an observation window

A window defines how close two items must be to count as co-occurring. An immediate right neighbour is one policy; a five-token window is another. Wider windows collect more thematic associations but can also collect words that share a topic without forming a close lexical construction.

Look at an actual decision

In ‘strong evidence supported the claim’, strong and evidence are adjacent. In ‘strong and carefully checked evidence’, they are related across several tokens but not adjacent. Both may be useful for different kinds of analyses.

The mistake to anticipate

An error is to change window size without recording it, then attribute the changed count to a new social trend or improved language use. The counting opportunity has changed.

A stronger method

Fix a suitable span before measuring; compare alternatives as a sensitivity exercise, not a hidden tuning step. Inspect example sentences to see whether a wide-window result still reflects the relationship the project intended.

Try it: Will a wider window always produce a stronger meaningful collocation?

Explained answer: No. It usually permits more observed proximity events, but those may be weaker semantically or grammatically.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 04 OF 21 · VOCABULARY

4. Separate co-occurrence from chance expectation

An association measure often compares observed co-occurrence with how often the pair might occur under a specified independence model. Expected frequency is not a prophecy about English usage; it is a reference calculation based on marginal counts and opportunities.

Look at an actual decision

For 10,000 eligible adjacent positions, if strong appears in the left slot 200 times and coffee appears in the right slot 80 times, independence would imply 200×80/10,000 = 1.6 expected strong–coffee pairs. The constructed observed count might be twelve.

The mistake to anticipate

The tempting interpretation says a score reveals whether a writer intended two words to belong together. Corpus statistics cannot read intent. They describe patterns under the analysis assumptions.

A stronger method

Report all four quantities: total eligible positions, node frequency, candidate frequency and observed pair count. The expected count follows from these and the model; a reader can then audit the association calculation.

Try it: What does an expected count of 1.6 mean here?

Explained answer: Under the independence reference model and the declared eligible positions, the model expects 1.6 co-occurrences; actual counts remain whole numbers.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 05 OF 21 · VOCABULARY

5. Understand raw pair frequency

Raw pair frequency is easy to explain and essential to any ranking. It counts how many eligible times the defined pair was observed. It may favour common expressions and high-frequency words, but it prevents a rare one-hit pair from looking more established than it is.

Look at an actual decision

In the fictional worked table, strong–coffee has twelve observations while strong–signal has five. Raw frequency therefore ranks coffee above signal for observed pair count. That does not settle which pair is more selective relative to individual word frequencies.

The mistake to anticipate

The mistake is to treat twelve matches as evidence that strong–coffee is ‘better English’ or assume five instances are necessarily too few for any meaningful analysis. The counts depend on corpus domain and context.

A stronger method

Keep pair counts beside association scores and inspect several concordance lines. A teacher may privilege frequent useful patterns even when a specialised statistic ranks rarer combinations more highly.

Try it: Does raw frequency alone adjust for how common coffee is everywhere else?

Explained answer: No. It measures the pair count, not the relative selectivity of the two words.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 06 OF 21 · VOCABULARY

6. Calculate a simple observed-to-expected ratio

The ratio O/E divides observed pair count by expected pair count. Values above one indicate more observed co-occurrence than the independence model’s expectation. The number is interpretable only with the same counting rules, denominator and marginal definitions.

Look at an actual decision

For strong–coffee, twelve observed against 1.6 expected gives O/E = 7.5. The pair was observed 7.5 times as often as the simplified independence model would predict for those fictional positions.

The mistake to anticipate

A student might say seven and a half times as many English speakers use the phrase. That conclusion does not follow; the ratio compares observed pairs with a model expectation within one declared corpus.

A stronger method

Label it ‘observed/expected association ratio’ and show O and E. Do not interpret it as an audience percentage, an odds ratio for speaker preference, or a guarantee of grammatical correctness.

Try it: If O=10 and E=2, what is O/E?

Explained answer: Five. Under the model, the observed pair count is five times the expected count; this is not a claim about five times more speakers.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 07 OF 21 · VOCABULARY

7. Learn what mutual information means

Pointwise mutual information, often MI in traditional collocation tools, can be written log2(O/E) when observed and expected counts are defined as a compatible joint and independence model. Positive values indicate observed co-occurrence above expectation; negative values indicate below expectation.

Look at an actual decision

For strong–coffee, O/E=7.5 gives log base two of 7.5, approximately 2.91 bits. For strong–signal, O=5 and E=0.4, so O/E=12.5 and MI is about 3.64; signal ranks higher by this score despite fewer observations.

The mistake to anticipate

The false shortcut treats MI as a probability or as the number of times the phrase occurred. It is neither. It is a logarithmic association measure whose interpretation depends on the model and observed frequencies.

A stronger method

Show the raw pair count, expected count and computed score. Remember that MI is undefined in this simple formula for O=0; decide how zero-count candidates are handled rather than inventing arbitrary values.

Try it: Is 3.64 MI equal to 3.64 observed examples?

Explained answer: No. It is a log-scaled association score. The constructed strong–signal pair has five observed examples.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 08 OF 21 · VOCABULARY

8. Understand rare-pair inflation

A candidate that occurs very rarely overall can have a tiny expected count. Even one or two observed matches may then yield a high observed-to-expected ratio and MI score. Such rankings can surface interesting expressions but may be unstable.

Look at an actual decision

Imagine a candidate occurs once in all eligible right-side positions and happens to follow the node once. Under an independence model the expected count could be very small, so MI can rank it above a reliable expression observed dozens of times.

The mistake to anticipate

The mistake is to present the top MI candidate as the best phrase to teach without checking that it was not a typing error, a proper name, a duplicated quotation or a random accident.

A stronger method

Use minimum frequency floors, source-spread checks and concordance review. The floor is a practical stability choice, not a universal theorem; document it and compare results under nearby thresholds.

Try it: Would a very high MI based on one observed pair justify teaching it as common English?

Explained answer: No. A high score on tiny counts is a reason to investigate, not proof of widespread conventionality.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 09 OF 21 · VOCABULARY

9. Meet the traditional t-score

A common approximate collocation t-score is (O−E)/sqrt(O) for positive observed count O. It often favours frequent pairs relative to MI. Despite its name, a reported collocation t-score should not be casually treated as a conventional Student t-test result or an automatic p-value.

Look at an actual decision

For strong–coffee, O=12 and E=1.6: (12−1.6)/sqrt(12) is approximately 3.00. For strong–signal, O=5 and E=0.4, the corresponding value is about 2.06. Coffee ranks above signal by this score.

The mistake to anticipate

A careless comparison calls the pair with the largest t-score ‘statistically significant’ under a scientific threshold without specifying the measure’s assumptions. The ranking has not alone established such a claim.

A stronger method

Explain what formula the tool uses and treat the score as one ranking aid. If the project requires formal inference, design and report a suitable statistical analysis separately.

Try it: Why might t-score and MI rank the same candidates differently?

Explained answer: MI highlights departure from expectation, including rare combinations; the traditional t-score gives substantial influence to observed pair frequency.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 10 OF 21 · VOCABULARY

10. Learn why a single magic threshold fails

Collocation measures serve ranking and exploration. A cut-off such as MI above three may be useful in one project but cannot universally decide whether an expression is natural, teachable or accepted across all English genres.

Look at an actual decision

A technical discipline may have strong low-frequency combinations, while common conversational collocations behave differently. A threshold chosen for a large edited corpus may give poor results on a small student-writing dataset.

The mistake to anticipate

The error is to print ‘valid collocation’ beside every score above one preset number and ‘invalid’ below it, ignoring context and variation between target words.

A stronger method

State a task-specific threshold if you use one, test how sensitive the list is to it, and verify candidates with authentic examples and relevant dictionaries or teacher judgement.

Try it: Does MI greater than three prove a phrase is idiomatic?

Explained answer: No. It indicates a level of statistical association under a specified measure and dataset; idiomaticity and naturalness are different questions.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 11 OF 21 · VOCABULARY

11. Distinguish grammatical partnership from topical proximity

Words can occur near each other because they share a topic, even when they do not form a conventional phrase. ‘Doctor’ and ‘hospital’ may co-occur in medical texts without being a fixed two-word expression.

Look at an actual decision

A five-word window around ‘exam’ might frequently contain ‘school’, ‘student’ and ‘revision’. This describes a topical field, not necessarily a reusable phrase that can be inserted intact into a sentence.

The mistake to anticipate

A collocation list becomes misleading when its items are taught as ready-made expressions despite being only semantic neighbours within an extended window.

A stronger method

Separate grammatical relations and adjacent phrases from looser thematic association. For writing lessons, ask whether the words form a useful and grammatical construction in the examples.

Try it: Is a thematic association automatically a two-word expression?

Explained answer: No. The relationship can be semantic or contextual without forming a fixed grammatical sequence.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 12 OF 21 · VOCABULARY

12. Use a complete observed-and-expected table

A compact worked table makes an association score interpretable. It should show candidate word, pair count, candidate marginal, expected count, and any chosen measure. The node frequency and total eligible opportunities belong above the table.

Look at an actual decision

Our constructed calculation fixes N at 10,000 eligible immediate-right word positions and strong as the left element in 200 positions. Candidate marginal counts vary. With these assumptions, expected E for each right candidate is 200×candidate count/10,000.

The mistake to anticipate

The common shortcut extracts only the ranked score column from a tool and hides the counts. Readers then cannot tell whether a top item is supported by one token, five or five hundred.

A stronger method

Make a table that a learner could recompute with a calculator. Include at least one pair where a rarer candidate receives a higher MI than a more frequent pair, then explain the reversal.

Try it: What is the first piece of evidence to inspect before praising a high association score?

Explained answer: The observed pair count, alongside the expected count and the search definition. A high score without them can be misleading.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 13 OF 21 · VOCABULARY

13. Check the direction of association

Association can be directional in how it is interpreted even when a symmetric score is used. The proportion of a node’s contexts containing a candidate differs from the proportion of candidate contexts containing the node.

Look at an actual decision

In the toy example, strong occurs as left word 200 times and coffee as right word 80 times; twelve are the target pair. Twelve of 200 strong contexts contain coffee, while twelve of eighty coffee right-positions follow strong. Those fractions are 6% and 15%.

The mistake to anticipate

The error is to treat a symmetric MI score as proof that both words depend equally on each other in ordinary speech. Conditional probabilities have different denominators.

A stronger method

When asking which word predicts the other more strongly, show the appropriate directional conditional rate and inspect semantic context. Do not replace two directional questions with one vague term ‘association’.

Try it: Does 12 out of 200 equal 12 out of 80?

Explained answer: No. The numerators are the same but the conditional denominators differ: 6% versus 15% in the constructed example.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 14 OF 21 · VOCABULARY

14. Inspect how genres change rankings

A collocate can be prominent because a corpus concentrates on a particular subject. A science report, sports commentary and family email may have very different partner distributions for the same node.

Look at an actual decision

Strong evidence may be typical in research prose, while strong coffee may be useful in everyday descriptions. A school corpus dominated by science explanations will favour one and underrepresent the other.

The mistake to anticipate

The overclaim says the top collocate of strong in one institutional corpus must be its strongest partner in the language as a whole.

A stronger method

Identify genre, register and sampling frame. Compare like with like or label genre-specific patterns. Check whether a high association depends on one writer, document or duplicated line.

Try it: Which is the more defensible claim: ‘strong evidence is prominent in this research corpus’ or ‘everyone prefers strong evidence’?

Explained answer: The first, assuming the table and examples support it. The second generalises beyond the domain.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 15 OF 21 · VOCABULARY

15. Keep lemma and surface form policies consistent

Association scores can be built from exact surface forms or aggregated lemmas. The choice affects marginals and pair counts. A verb lemma that includes wrote and written does not behave like a single exact spelling.

Look at an actual decision

A collocation study of take a decision versus took a decision would obtain different results if it groups TAKE forms in one query or searches only the exact word take. The choice may be useful but must be explicit.

The mistake to anticipate

The mistake is to mix lemma counts in one half of the calculation with exact-form counts in another, creating an expected value that does not match the observation definition.

A stronger method

Use a single compatible representation for the node and candidate. Preserve surface examples for reading and label the association score as lemma-based or form-based as appropriate.

Try it: Can the score change after lemmatisation without the underlying text changing?

Explained answer: Yes. Aggregating inflections changes node and pair frequencies, which changes the derived statistics.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 16 OF 21 · VOCABULARY

16. Handle documents that repeat a phrase

A phrase may appear frequently because one source repeats it in a title, template or instruction. High pair frequency from a single document is not the same as broad adoption across texts or speakers.

Look at an actual decision

Suppose a school worksheet repeats ‘strong evidence’ fifteen times in rubric instructions. A corpus can record those fifteen events, but the spread across independent texts is limited.

The mistake to anticipate

The shortcut reports the observed pair count as if fifteen separate writers independently preferred the phrase. A token-based count cannot establish the number of independent users.

A stronger method

Show the pair’s distribution across documents and consider deduplication or sampling-unit design. Choose counting rules according to whether the question concerns exposure, unique phrasing or writer preference.

Try it: How would repeated boilerplate affect an association ranking?

Explained answer: It can increase observed pair frequency and perhaps the score without adding independent evidence of usage across writers.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 17 OF 21 · VOCABULARY

17. Recognise the difference between score and significance

Statistical association, effect size, ranking, uncertainty and formal hypothesis testing are related but different. A collocation tool may output several columns whose labels sound scientific. Each column requires its own interpretation.

Look at an actual decision

One tool reports MI and t-score; another offers logDice and likelihood measures. A top-ranked item under one method need not be top under another because the formulas weight observed frequency and expected behaviour differently.

The mistake to anticipate

The mistake is to compare an MI value directly with a logDice value or treat a ranking score as a p-value. Different scales and models invalidate that comparison.

A stronger method

Read the tool’s definition for the exact statistic, list methodological settings and, where appropriate, conduct separate inferential analysis. Use scores primarily to prioritise inspectable language examples.

Try it: Can ‘MI 3.2’ be compared numerically with ‘logDice 8.1’ as if larger means stronger?

Explained answer: No. These are different statistics with different scales and interpretations.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 18 OF 21 · VOCABULARY

18. Understand what logDice contributes

LogDice is an alternative association measure widely used in word sketches. It considers pair frequency relative to each member’s overall frequency and is intended as a practical ranking of typical collocates. Its scale and assumptions differ from MI and the traditional t-score.

Look at an actual decision

For a word-sketch query, the tool may rank adjective–noun or verb–object relations by logDice rather than by simple adjacent bigrams. This gives writers a structured view of common grammatical partners.

The mistake to anticipate

The failure is to assume logDice numbers can be directly substituted into the worked MI formula or that a single universal logDice cut-off identifies every meaningful collocation.

A stronger method

Use the source tool’s documented statistic and grammatical-relation policy. Link back from rankings to authentic concordance lines and inspect the observed counts and genre.

Try it: Is logDice just another name for MI?

Explained answer: No. It is a different association measure; compare rankings as alternative lenses rather than treating values as the same unit.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 19 OF 21 · VOCABULARY

19. Turn scores into better vocabulary teaching

For learners, the final goal is not a ranking number. It is the ability to recognise a natural word partner, understand its meaning and produce it appropriately. A score is helpful when it directs attention to useful patterns supported by good examples.

Look at an actual decision

A class might contrast strong evidence, convincing evidence and compelling evidence, then explore whether strong coffee fits the same sense. Students learn that partners can shape meaning, argument strength and register.

The mistake to anticipate

The weak activity asks students to memorise scores without reading sentences. This teaches a technical label while neglecting actual word choice and grammatical constraints.

A stronger method

Choose a few candidates with sufficient occurrences and clear contexts. Use sentence-completion, error correction and retrieval tasks; invite learners to explain why a near-synonym sometimes changes tone or idiomaticity.

Try it: Would a student improve writing by memorising that one pair has MI 3.64?

Explained answer: Not by that fact alone. The learner needs contextual examples, meaning distinctions and practice using the expression.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 20 OF 21 · VOCABULARY

20. Design a small and honest investigation

A classroom inquiry can begin with two texts, an agreed node and a list of adjacent neighbours. The activity should be transparent about its tiny sample and distinguish simple counts from formal association statistics when the dataset is too small.

Look at an actual decision

Choose a permitted public instructional text and highlight every use of ‘clear’. Record the noun or adjective that follows under a precise rule, then compare the counts and examine which pairings read naturally.

The mistake to anticipate

The shortcut is to calculate elaborate scores from two or three matches and claim to have found the most idiomatic phrase in English. The evidence supports a local observation and a question worth checking elsewhere.

A stronger method

Begin with close reading and counts. When appropriate, consult a larger, properly documented corpus and tool; inspect raw frequency, score, concordance and domain before choosing teaching targets.

Try it: What can a tiny class exercise legitimately demonstrate?

Explained answer: How to define co-occurrence, organise examples, spot a potential pattern and state evidence limits, not an authoritative global ranking of English collocations.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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CHAPTER 21 OF 21 · VOCABULARY

21. Audit every impressive collocation claim

Before sharing a ranked list, ask: what corpus, what node, what candidate, what window or grammatical relation, what observed count, what expected model, which association measure and what source distribution? Also ask whether sample sentences support the language conclusion.

Look at an actual decision

A defensible report might say ‘Under this constructed immediate-right bigram model, strong–signal receives a higher MI than strong–coffee despite fewer occurrences.’ It is specific, arithmetically checkable and limited to the fictitious dataset.

The mistake to anticipate

The misleading version says ‘signal is universally the most natural noun after strong’ without examining genre, frequency or authentic examples. A mathematical score cannot make that generalisation true.

A stronger method

Use the audit on one candidate ranked by MI and one ranked by t-score. Explain how each measure changes the selection, then choose a writing example based on meaning and context as well as frequency.

Try it: What is the strongest end product of collocation analysis for students?

Explained answer: An evidence-based explanation of which combinations are appropriate in specific sentences, supported by counts, context and honest limits rather than a detached score.

Transfer challenge: Take a sentence from a different school subject or a permitted public text and identify what would change if the writer, genre, context or counting rule changed. Write the exact observation first, then a conclusion no broader than the evidence. The same discipline should govern both familiar words and technical vocabulary.

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Worked evidence: audit every example

We create a tiny, fictional counting universe of N = 10,000 eligible ordered adjacent word positions. The adjective strong occupies the left slot in 200 positions. Right-slot marginal totals are: coffee 80, tea 100, evidence 60, possibility 40 and signal 20. Each observed pair count is a subset of the relevant marginals. We use E = (200 × right marginal) / 10,000, MI = log2(O/E), and the traditional collocation t-score approximation (O−E)/sqrt(O). These are constructed calculations, not observations of real English.

Strong + noun	Observed O	Expected E	MI (approx.)	t-score (approx.)
coffee	12	1.60	2.91	3.00
tea	8	2.00	2.00	2.12
evidence	10	1.20	3.06	2.78
possibility	2	0.80	1.32	0.85
signal	5	0.40	3.64	2.06

Strong–coffee: the candidate marginal is 80, giving E = 200×80/10,000 = 1.6. Its observed/expected ratio is 12/1.6 = 7.5, so MI ≈ log2(7.5) ≈ 2.91. Its conventional t-score approximation is (12−1.6)/sqrt(12) ≈ 3.00. Every arithmetic step is visible.

Strong–signal: E = 200×20/10,000 = 0.4. With O=5, O/E=12.5 and MI ≈ 3.64. Its t-score is (5−0.4)/sqrt(5) ≈ 2.06. It outranks coffee by MI but not by the illustrative t-score. This reversal is the central lesson: the score’s definition determines which property receives emphasis.

Strong–evidence: E = 200×60/10,000 = 1.2; O/E ≈ 8.33, MI ≈ 3.06 and t-score ≈ 2.78. These model calculations do not demonstrate that the adjective–noun pair is correct or suitable in every context. A concordance or dictionary check still matters.

The model treats the pair universe as immediate left-to-right positions. A five-token window, lemmatised noun list or dependency-based grammar would produce other marginal totals and observations. Scores from those different analyses should not be pasted into the same comparison without describing the changed method.

If an actual research report used this method, it would also examine source distribution, data-cleaning rules, small counts, independent texts and the qualitative role of each phrase. The fictional table teaches calculation and interpretation, not real prevalence.

Twelve applications: identify the trap, then choose the repair

These situations are original fictional tasks, not empirical claims about particular people or systems. Answer the transfer question by specifying both the observed evidence and the boundary of the permitted conclusion.

1. MI reversal

Situation. A score list ranks a pair with five examples over one with twelve.

What goes wrong. A reader assumes the top pair must be more common.

Repair. Check both observed frequency and expected frequency; MI can favour greater selectivity.

Next question. Which pair will a frequency-first teacher inspect first?

2. One rare partner

Situation. A phrase appears once with a word that is otherwise extremely rare.

What goes wrong. A high MI may be unstable or accidental.

Repair. Apply a declared frequency floor and inspect source and context.

Next question. What could explain a single surprising pair?

3. Wide window

Situation. A node and candidate appear within five tokens but not as a phrase.

What goes wrong. Topical relatedness is mistaken for idiomatic partnership.

Repair. Label the relation as proximity and consider a grammar-specific query.

Next question. Which sentence shows direct grammatical linkage?

4. Repeated template

Situation. A school form repeats the same pair fifty times.

What goes wrong. A document template masquerades as independent linguistic preference.

Repair. Audit document spread and duplicates.

Next question. How many independent sources support the result?

5. Changing corpus

Situation. The node is analysed in sports reports and research articles.

What goes wrong. Genre changes ranking without a rule change.

Repair. Report genre-specific statistics and scope.

Next question. Would both genres support the same writing lesson?

6. Case-sensitive form

Situation. The node is a word identical in letters to a name.

What goes wrong. A query combines different lexical items.

Repair. Review case, POS and entity context; separate when relevant.

Next question. What would the ambiguous concordance lines reveal?

7. MI versus t-score

Situation. Two measures yield different top-ten lists.

What goes wrong. Users assume one must be wrong.

Repair. Explain each formula’s emphasis and assess task suitability.

Next question. Which measure rewards frequent observed pairs more?

8. Different software

Situation. Tool A uses adjacent bigrams; Tool B a dependency grammar.

What goes wrong. Their association scores describe different events.

Repair. Record tool settings and compare only compatible analyses.

Next question. What metadata must accompany the exported list?

9. One word two senses

Situation. A candidate occurs with a target in unrelated senses.

What goes wrong. The association merges distinct semantic contexts.

Repair. Inspect KWIC lines and, if useful, stratify by sense.

Next question. Would the pair aid writing in both senses?

10. Direction matters

Situation. The pair strong–coffee appears twelve times, with unequal node and candidate totals.

What goes wrong. A reader assumes conditional rates are symmetric.

Repair. Compare 12/200 and 12/80 as separate descriptive questions.

Next question. Which word is more predictive in the example?

11. A writing correction

Situation. A student writes ‘powerful rain’ instead of ‘heavy rain’.

What goes wrong. A high score for a different word may not fix the sentence.

Repair. Use actual expression evidence and grammar-sensitive examples to teach a suitable collocation.

Next question. How does the partner change the adjective choice?

12. Statistics in a headline

Situation. A page says ‘MI above three proves correctness’.

What goes wrong. Statistical rank is confused with grammatical acceptance.

Repair. Use measure-specific explanation, frequency, context and authoritative usage checks.

Next question. What claim can the score itself support?

Eight practice problems with worked solutions

Complete the question independently first. Then check the reasoning, not only the final label or number. A good vocabulary explanation tells the reader why the answer is appropriate in this exact context.

Exercise 1: Expected count

Task. N=10,000 positions; node left frequency 200; candidate right frequency 80. Calculate E.

Model solution. E = 200×80/10,000 = 1.6 expected pair events under the stated independence model.

False shortcut. Dividing only by node frequency changes the expected event model.

Exercise 2: Association ratio

Task. The constructed pair appears twelve times with E=1.6. Calculate O/E.

Model solution. 12/1.6 = 7.5. Observed is 7.5 times the independence expectation in this example.

False shortcut. The ratio does not measure the proportion of speakers choosing the pair.

Exercise 3: MI from ratio

Task. If O/E=8, find MI in base two.

Model solution. MI = log2(8) = 3 bits under this model.

False shortcut. MI is not the count of eight occurrences.

Exercise 4: Rare versus common

Task. Pair A has O=5 and E=0.4; B has O=12 and E=1.6. Which has larger MI?

Model solution. A: log2(12.5)≈3.64; B: log2(7.5)≈2.91. Pair A ranks higher by MI although B has more matches.

False shortcut. Ranking by observed pair count alone answers a different question.

Exercise 5: Traditional t-score

Task. For O=12 and E=1.6 compute the conventional approximate t-score.

Model solution. (12−1.6)/sqrt(12) = 10.4/3.464 ≈ 3.00.

False shortcut. Do not interpret the ranking number as an automatic Student t-test p-value.

Exercise 6: Change the window

Task. A researcher increases the co-occurrence window from one right neighbour to five either-side neighbours. Can the old scores be reused?

Model solution. No. Observation opportunities, pair counts and expected model may change. Recompute and label settings.

False shortcut. The corpus text can stay identical while the measurement changes.

Exercise 7: Interpret a one-off

Task. A pair occurs once and receives a high MI because E is tiny. What should the learner do?

Model solution. Show the raw count, inspect context, check whether the phrase is real and set a documented minimum-frequency policy for robust ranking.

False shortcut. The highest association score is not guaranteed to be the best phrase for learners.

Exercise 8: Teach a word partner

Task. Two expressions are ranked differently under MI and t-score. How should a teacher choose?

Model solution. Inspect authentic examples, meaningful grammatical relations, learner goals, register and adequate frequency before selecting an expression for practice.

False shortcut. A measure optimises a specific numerical property, not the complete educational value of a phrase.

Frequently asked questions about a collocation association score

What is a collocation?

A recurrent or preferred combination of linguistic items, considered in context rather than as any arbitrary adjacent sequence.

What does an association score measure?

It summarises a relation between observed pair counts and a declared statistical model or scoring scheme.

Is the most frequent pair always the strongest collocation?

Not by every association measure. Selectivity relative to the marginal frequencies can reorder candidates.

How is MI calculated in a simple model?

Pointwise MI can be written log2(observed/expected) where observed and expected are compatible co-occurrence counts.

Why can MI overvalue rare phrases?

A very small expected count can yield a high ratio and log score from only a few observed tokens.

What does the traditional collocation t-score emphasise?

It commonly gives more influence to observed pair frequency, so frequent expressions may rank strongly.

Is a t-score a p-value?

No. It is a score under a specified calculation and should not be reported as a conventional hypothesis-test p-value without appropriate separate analysis.

What is logDice?

A different association measure used in word-sketch tools for comparing typicality from pair and marginal frequencies.

Does the search window matter?

Yes. Adjacency, wider proximity and grammatical relations define different co-occurrence events and can change the scores.

Do scores prove a phrase is grammatical?

No. Corpus counts and scores are evidence of observed patterns; close reading and linguistic analysis are still required.

Can collocation strength vary by genre?

Yes. Text domains and communicative tasks can substantially affect pair distribution and rankings.

What does a student need to learn from a collocation table?

How to examine candidate partners in context and use natural phrases for a specific reading or writing task, not merely how to memorise one score.

Should a published ranking disclose raw counts?

Yes. A measure without observed frequencies, corpus scope and counting settings can conceal rare-event or methodological problems.

Practical glossary

• Node: The target item around which collocates are found.
• Collocate: A candidate partner near or grammatically connected to a node.
• Co-occurrence: Two items meeting a stated positional or grammatical condition in the corpus.
• Span/window: The declared distance permitted between items.
• Marginal count: A count of an individual item in the eligible positions of a co-occurrence analysis.
• Expected frequency: The co-occurrence predicted by a specified reference model, often independence.
• Mutual information: A logarithmic measure of observed co-occurrence relative to expectation.
• T-score: A traditional collocation association ranking statistic influenced by observed frequency.
• logDice: A distinct practical measure of collocation typicality used by some word-sketch systems.
• Concordance: A display of example contexts for a searched item.
• Genre: A recurring communication type influencing typical word choices.
• Frequency floor: A minimum observed count used to limit fragile rare-event rankings.

An evidence-first learning routine

Choose one recurring difficulty from the article rather than attempting to memorise every heading. First, explain the word or measure in a sentence. Next, locate three examples that genuinely fit the definition and one that looks similar but falls outside it. Discuss the exceptional example before revealing the solution. This is where a terminology lesson becomes a reading skill.

Then complete a short retrieval cycle. Close the article and reconstruct the key distinction without looking. Reopen it to check the unit, condition and limit. A day later, use the idea on a different text. If a learner cannot apply the method to a changed case, that is a signal to return to a worked example rather than add further jargon.

Finally, keep a brief record of decisions: the original question, the evidence used, the precise count or label, what remains uncertain, and the revised conclusion. This record lets a teacher offer feedback on reasoning. It also protects a researcher against accidentally presenting an attractive number as a universal statement.

Methodological sources and tools

• University of Zurich: n-grams and comparison of collocation statistics
• Sketch Engine: word sketches, grammatical relations and association strength
• Sketch Engine: logDice explained
• Sketch Engine: t-score and its limitations
• AntConc documentation: choosing collocate measures and windows

The linked sources support the general methods. The numerical datasets and classroom records above were constructed for learning and should not be cited as published findings.

Continue into the related vocabulary evidence guides

• Corpus sampling frame: learn which texts were eligible
• Normalised word frequency: compare equal-sized rates
• Corpus metadata: inspect dates, authorship and source context
• Concordance lines: inspect real sentence context
• Gold-standard corpus: understand checked language reference answers
• Vocabulary Learning Hub
• Vocabulary article library

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