Analyzing Collocations and N-grams in R

Introduction

This tutorial introduces collocation and co-occurrence analysis — methods for identifying words that frequently appear together and understanding the semantic relationships between words in text. Collocations are fundamental to understanding natural language patterns, idioms, and the contextual behavior of words (McEnery, Xiao, and Tono 2006; S. Th. Gries 2013).

Prerequisites

Before starting this tutorial, we recommend familiarity with:

• Getting started with R
  
• Loading, saving, and generating data in R
  
• String Processing in R
  
• Regular Expressions in R
  

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The Central Question

Research Question

How can you determine if words occur together more frequently than would be expected by chance?

This tutorial shows how to answer this question using collocation analysis and association measures.

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What Are Collocations?

Collocations are word combinations that appear together significantly more often than random chance would predict.

Examples:

• Merry Christmas — “merry” and “Christmas” co-occur far more than expected
  
• strong coffee — not “powerful coffee”
  
• make a decision — not “do a decision”
  
• take a risk — not “make a risk”

If you randomly shuffled all words in a corpus and tested co-occurrence frequencies, collocations like Merry Christmas would occur significantly less often in the shuffled corpus than in natural text. This statistical evidence of attraction is what defines a collocation.

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Collocations vs. N-grams

We must differentiate between two related but distinct concepts:

Concept	Definition	Example	Adjacency Required?
Collocation	Words significantly attracted to one another (may or may not be adjacent)	black and coffee (can be separated: “black, strong coffee”)	No
N-gram	Sequences of n adjacent words	Bigram: This is Trigram: This is a	Yes

Key Distinction

• N-grams are purely positional: they count adjacent word sequences regardless of whether the combination is meaningful
  
• Collocations are statistical: they identify word pairs (or groups) that are significantly attracted, even across intervening words

Merry Christmas is both a bigram (adjacent) and a collocation (statistically significant). Of the is a bigram but likely not a meaningful collocation (just high-frequency grammatical words).

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Why Collocations Matter

Collocations are crucial for:

1. Language learning: Native-like fluency requires knowing which words “go together”
   
2. Translation: Many collocations don’t translate literally (make a decision ≠ hacer una decisión in Spanish)
   
3. Lexicography: Dictionaries must document typical collocations for each word
   
4. Corpus linguistics: Understanding semantic domains and discourse patterns
   
5. NLP: Training language models, extracting multi-word expressions
   
6. Stylometry: Author profiling, genre classification

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Part I: Conceptual Foundations

Before analyzing collocations in R, we need to understand the statistical foundations.

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The Contingency Table

Collocation analysis is based on co-occurrence frequencies in a 2×2 contingency table. For two words \(w_1\) and \(w_2\):

	\(w_2\) present	\(w_2\) absent	Row totals
\(w_1\) present	\(O_{11}\)	\(O_{12}\)	\(R_1\)
\(w_1\) absent	\(O_{21}\)	\(O_{22}\)	\(R_2\)
Column totals	\(C_1\)	\(C_2\)	\(N\)

Where:

• \(O_{11}\) = Observed frequency of \(w_1\) and \(w_2\) together
  
• \(O_{12}\) = Observed frequency of \(w_1\) without \(w_2\)
  
• \(O_{21}\) = Observed frequency of \(w_2\) without \(w_1\)
  
• \(O_{22}\) = Observed frequency of neither \(w_1\) nor \(w_2\)
  
• \(N\) = Total observations (all words/contexts in the corpus)

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Expected Frequencies

If words were randomly distributed (no attraction/repulsion), we calculate expected frequencies:

	\(w_2\) present	\(w_2\) absent	Row totals
\(w_1\) present	\(E_{11} = \frac{R_1 \times C_1}{N}\)	\(E_{12} = \frac{R_1 \times C_2}{N}\)	\(R_1\)
\(w_1\) absent	\(E_{21} = \frac{R_2 \times C_1}{N}\)	\(E_{22} = \frac{R_2 \times C_2}{N}\)	\(R_2\)
Column totals	\(C_1\)	\(C_2\)	\(N\)

Association measures compare observed (\(O\)) vs. expected (\(E\)) frequencies to quantify attraction/repulsion.

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Association Measures

Association measures quantify the strength of the relationship between words. Here are the most important ones:

Gries’ \(\Delta P_{AM}\) (Recommended)

Gries’ AM (S. T. Gries 2022) is currently the best association measure. It has three critical advantages:

1. Asymmetry-aware: The association from \(w_1 \to w_2\) may differ from \(w_2 \to w_1\)
   
2. Frequency-independent: Unlike χ², MI, and t-score, it’s not inflated by high word frequencies
   
3. Normalized: Accounts for different possible value ranges across word pairs

When to Use Gries’ AM

Use Gries’ AM when:

• You need asymmetric association (directionality matters)
  
• Word frequencies vary widely in your corpus
  
• You want a measure robust to corpus size
  

Delta P (\(\Delta P\))

Delta P (Ellis 2007; S. T. Gries 2013) is based on conditional probabilities:

\[\Delta P_1 = P(w_1 | w_2) - P(w_1 | \neg w_2) = \frac{O_{11}}{C_1} - \frac{O_{12}}{C_2}\]

\[\Delta P_2 = P(w_2 | w_1) - P(w_2 | \neg w_1) = \frac{O_{11}}{R_1} - \frac{O_{21}}{R_2}\]

Interpretation:

• \(\Delta P_1\): How much does seeing \(w_2\) increase the probability of \(w_1\)?
  
• \(\Delta P_2\): How much does seeing \(w_1\) increase the probability of \(w_2\)?
  
• Range: [−1, 1]
  
• Values near 0: no association
  
• Positive: attraction; Negative: repulsion

Asymmetry in \(\Delta P\)

\(\Delta P\) recognizes that association is directional:

• “strong” is highly attracted to “coffee” (high \(\Delta P_{\text{strong} \to \text{coffee}}\))
  
• “coffee” is less exclusively attracted to “strong” (lower \(\Delta P_{\text{coffee} \to \text{strong}}\))

This mirrors how speakers think: strong coffee is a fixed phrase, but coffee can be modified by many adjectives.

Pointwise Mutual Information (PMI)

PMI measures how much more (or less) likely two words are to co-occur compared to independence:

\[\text{PMI}(w_1, w_2) = \log_2 \left( \frac{P(w_1, w_2)}{P(w_1) \cdot P(w_2)} \right) = \log_2 \left( \frac{O_{11}/N}{(R_1/N) \cdot (C_1/N)} \right)\]

Interpretation:

• PMI = 0: Words occur together as often as expected by chance
  
• PMI > 0: Words attract (positive association)
  
• PMI < 0: Words repel (negative association)
  
• Range: (−∞, +∞)

Problems with PMI

1. Rare word bias: PMI is inflated for rare word pairs
   
2. Negative values hard to interpret: What does PMI = −3 mean practically?
   
3. Not normalized: Cannot directly compare PMI values across corpora of different sizes

Solution: Use PPMI (Positive PMI) — set all negative values to 0

Log-Likelihood Ratio (G²)

Log-Likelihood Ratio compares observed vs. expected frequencies using likelihood:

\[G^2 = 2 \sum_{i=1}^{4} O_i \log \left( \frac{O_i}{E_i} \right)\]

\[G^2 = 2 \left( O_{11} \log\frac{O_{11}}{E_{11}} + O_{12} \log\frac{O_{12}}{E_{12}} + O_{21} \log\frac{O_{21}}{E_{21}} + O_{22} \log\frac{O_{22}}{E_{22}} \right)\]

Interpretation:

• G² ≈ χ² but more accurate for small expected frequencies
  
• Higher values = stronger association
  
• Can be tested for significance using χ² distribution with df = 1

Chi-Square (χ²)

\[\chi^2 = \sum_{i=1}^{4} \frac{(O_i - E_i)^2}{E_i} = \frac{(O_{11} - E_{11})^2}{E_{11}} + \frac{(O_{12} - E_{12})^2}{E_{12}} + \frac{(O_{21} - E_{21})^2}{E_{21}} + \frac{(O_{22} - E_{22})^2}{E_{22}}\]

Interpretation:

• χ² = 0: Observed = Expected (no association)
  
• Higher values = stronger association
  
• p-value: Test against χ² distribution with df = 1

Problems with χ²

1. Frequency-dependent: Inflated by high word frequencies
   
2. Unreliable for small expected frequencies (E < 5): violates assumptions
   
3. Symmetric: Cannot distinguish \(w_1 \to w_2\) from \(w_2 \to w_1\)

Better alternative: Use G² instead

t-Score

\[\text{t-score} = \frac{O_{11} - E_{11}}{\sqrt{O_{11}}}\]

Interpretation:

• Measures deviation from expected co-occurrence, normalized by standard deviation
  
• Higher absolute values = stronger association
  
• Range: (−∞, +∞)

t-Score vs. Other Measures

• t-score favors high-frequency collocations (good for finding common phrases)
  
• PMI favors low-frequency collocations (good for finding rare but strong associations)

Choose based on your research goal:

• Finding fixed phrases used by everyone? → t-score
  
• Finding specialized terminology? → PMI
  

Dice Coefficient

\[\text{Dice}(w_1, w_2) = \frac{2 \times O_{11}}{\text{freq}(w_1) + \text{freq}(w_2)} = \frac{2 \times O_{11}}{R_1 + C_1}\]

Interpretation:

• Range: [0, 1]
  
• Dice = 1: Perfect overlap (words always co-occur)
  
• Dice = 0: No overlap (words never co-occur)

Minimum Sensitivity (MS)

MS (Pedersen 1998) is the minimum of the two conditional probabilities:

\[\text{MS} = \min \left( P(w_1 | w_2), P(w_2 | w_1) \right) = \min \left( \frac{O_{11}}{C_1}, \frac{O_{11}}{R_1} \right)\]

Interpretation:

• MS = 1: Perfect bidirectional dependence (words always co-occur)
  
• MS = 0: No dependence
  
• Range: [0, 1]

Phi Coefficient

Phi is an effect size measure based on χ²:

\[\phi = \sqrt{\frac{\chi^2}{N}}\]

Interpretation:

• Range: [0, 1] for positive associations
  
• Higher values = stronger effect
  
• Similar to Pearson’s r for 2×2 tables

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Comparing Association Measures

Measure	Range	Frequency-dependent?	Directional?	Best for
Gries’ AM	[0, 1]	No ✓	Yes ✓	General use (robust, asymmetric)
\(\Delta P\)	[−1, 1]	No ✓	Yes ✓	Conditional probabilities
PMI	(−∞, +∞)	Yes ✗	No ✗	Rare but strong associations
G²	[0, +∞)	Yes ✗	No ✗	Significance testing
χ²	[0, +∞)	Yes ✗	No ✗	Large expected frequencies only
t-score	(−∞, +∞)	Yes ✗	No ✗	Common phrases
Dice	[0, 1]	No ✓	No ✗	Fixed expressions
MS	[0, 1]	No ✓	Yes ✓	Mutual dependence
Phi	[0, 1]	No ✓	No ✗	Effect size

Recommendation

For most corpus linguistic research: Use Gries’ AM or \(\Delta P\) (if asymmetry matters) or G² (if you need p-values).

Avoid: χ² (use G² instead), raw PMI (use PPMI), t-score (unless specifically seeking high-frequency collocations).

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Exercises: Association Measures

Q1. Which association measure is MOST appropriate for identifying rare but strongly associated word pairs (e.g., technical jargon)?

Dice coefficient — measures overlap
Chi-square — tests for independence
t-score — measures deviation from expected
PMI (Pointwise Mutual Information) — favors low-frequency pairs

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Q2. A researcher finds that \(\Delta P_{\text{strong} \to \text{coffee}} = 0.45\) but \(\Delta P_{\text{coffee} \to \text{strong}} = 0.12\). What does this asymmetry mean?

The two words have the same association strength in both directions
'Coffee' is more frequent than 'strong' in the corpus
There is an error in the calculation — ΔP should be symmetric
'Strong' strongly predicts 'coffee', but 'coffee' only weakly predicts 'strong' (other modifiers are common)

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Q3. Why should you avoid using raw χ² for collocation analysis?

χ² is too computationally expensive for large corpora
χ² can only be used for bigrams, not longer n-grams
χ² requires normally distributed data
χ² is inflated by word frequency — high-frequency words get high χ² even without strong association

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Q4. A word pair has Dice = 0.95. What does this mean?

The first word strongly predicts the second (but not vice versa)
The pair occurs 95% more than expected by chance
The association is statistically significant at p < .05
The two words almost always appear together — very high mutual overlap

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Part II: Collocation Analysis in R

Now that we understand the theory, let’s extract and analyze collocations using R. We’ll use two proper methods that identify true collocations (non-adjacent word pairs).

Important: Why We Don’t Use quanteda::textstat_collocations()

Although quanteda has a function called textstat_collocations(), it does NOT detect true collocations. Instead, it:

1. Extracts only adjacent n-grams (bigrams, trigrams, etc.)
   
2. Applies statistical tests to these n-grams

This is misleading because true collocations don’t require adjacency. For example, strong and coffee are collocates even in “strong, black coffee” where they’re separated.

We use quanteda::fcm() to create feature co-occurrence matrices (which DO capture non-adjacent co-occurrence), but we avoid textstat_collocations().

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Preparation and Data Loading

Install Packages

install.packages(c("tidyverse", "flextable", "tokenizers", "quanteda",  
                   "tidytext", "FactoMineR", "factoextra", "GGally",  
                   "ggdendro", "igraph", "Matrix", "cowplot", "checkdown"))  

Load Packages

library(tidyverse)      # data manipulation  
library(flextable)      # tables  
library(tokenizers)     # text tokenization  
library(quanteda)       # ONLY for fcm(), tokens(), and dfm()  
library(tidytext)       # text mining  
library(FactoMineR)     # correspondence analysis  
library(factoextra)     # CA visualization  
library(GGally)         # network plots  
library(ggdendro)       # dendrograms  
library(igraph)         # network analysis  
library(Matrix)         # sparse matrices  
library(cowplot)        # plot arrangements  
library(checkdown)      # interactive exercises  
  
options(stringsAsFactors = FALSE)  
options(scipen = 999)  
options(max.print = 1000)  

Load Example Data

We’ll use Charles Darwin’s On the Origin of Species:

# load Darwin's Origin of Species  
text <- base::readRDS("data/cdo.rda") |>  
  paste0(collapse = " ") |>  
  stringr::str_squish() |>  
  stringr::str_remove_all("- ")  

substr(text, start = 1, stop = 200)
When we look to the individuals of the same variety or sub-variety of our older cultivated plants and animals, one of the first points which strikes us, is, that they generally differ much more from e

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Method 1: Sentence-Based Collocation Detection

This method identifies word pairs that co-occur within the same sentence (regardless of adjacency), then calculates association measures.

Why Sentences as Context Units?

Using sentences as co-occurrence windows has advantages:

• Captures grammatical and semantic relationships within syntactic boundaries
  
• More restrictive than arbitrary word windows (reduces noise)
  
• Linguistically motivated (sentences are meaning units)

Alternative: You could use paragraphs, fixed-size windows (e.g., 10 words), or entire documents depending on your research question.

Step 1: Prepare Sentences

# split text into sentences and clean  
sentences <- text |>  
  # concatenate if text is a vector  
  paste0(collapse = " ") |>  
  # separate possessives (so "Darwin's" becomes "Darwin 's")  
  stringr::str_replace_all(fixed("'"), " '") |>  
  stringr::str_replace_all(fixed("'"), " '") |>  
  # tokenize into sentences  
  tokenizers::tokenize_sentences() |>  
  # unlist to vector  
  unlist() |>  
  # remove non-word characters (punctuation, numbers, etc.)  
  stringr::str_replace_all("\\W", " ") |>  
  stringr::str_replace_all("[^[:alnum:] ]", " ") |>  
  # remove extra spaces  
  stringr::str_squish() |>  
  # convert to lowercase  
  tolower()  

head(sentences, 10)
when we look to the individuals of the same variety or sub variety of our older cultivated plants and animals one of the first points which strikes us is that they generally differ much more from each other than do the individuals of any one species or variety in a state of nature
the variation under nature is clearly seen
natural selection acts exclusively by the preservation and accumulation of variations which are beneficial
the existence of individual variability and of some few well marked varieties though necessary as the foundation for the work helps us but little in understanding how species arise in nature
on the origin of species by means of natural selection or the preservation of favoured races in the struggle for life we may conclude that natural selection has been the main but not exclusive means of modification

Step 2: Create Co-occurrence Matrix

# tokenize sentences using quanteda  
# (we use quanteda ONLY for its fcm() function to create co-occurrence matrices)  
tokens_sent <- quanteda::tokens(sentences)  
  
# create document-feature matrix (words × sentences)  
dfmat <- quanteda::dfm(tokens_sent)  
  
# create feature co-occurrence matrix (FCM)  
# context = "document" means: count co-occurrence within each sentence  
# tri = FALSE means: keep full matrix (not just upper triangle)  
fcmat <- quanteda::fcm(tokens_sent, context = "document",   
                       count = "frequency", tri = FALSE)  
  
# convert to tidy format for easier manipulation  
coll_basic <- fcmat |>  
  tidytext::tidy() |>  
  # rename columns for clarity  
  dplyr::rename(  
    w1 = term,        # word 1  
    w2 = document,    # word 2    
    O11 = count       # observed co-occurrence frequency  
  ) |>  
  # reorder columns  
  dplyr::select(w1, w2, O11)  

w1	w2	O11
when	we	1
when	look	1
when	to	1
when	the	4
when	individuals	2
when	of	5
when	same	1
when	variety	3
when	or	2
when	sub	1

What is O₁₁?

O₁₁ = Number of sentences where w₁ and w₂ both appear.

For example, if “natural” and “selection” appear together in 45 sentences, O₁₁ = 45.

This counts co-occurrence regardless of word order or adjacency within the sentence.

Step 3: Calculate Contingency Table Values

To compute association measures, we need all four cells of the 2×2 contingency table plus marginal totals:

# calculate row totals (R1, R2), column totals (C1, C2), and grand total (N)  
colldf <- coll_basic |>  
  # calculate total observations (sum of all co-occurrences)  
  dplyr::mutate(N = sum(O11)) |>  
  # group by w1 to calculate R1 (total for word 1)  
  dplyr::group_by(w1) |>  
  dplyr::mutate(  
    R1 = sum(O11),           # how often w1 appears (with any word)  
    O12 = R1 - O11,          # w1 without w2  
    R2 = N - R1              # everything except w1  
  ) |>  
  dplyr::ungroup() |>  
  # group by w2 to calculate C1 (total for word 2)  
  dplyr::group_by(w2) |>  
  dplyr::mutate(  
    C1 = sum(O11),           # how often w2 appears (with any word)  
    O21 = C1 - O11,          # w2 without w1  
    C2 = N - C1,             # everything except w2  
    O22 = R2 - O21           # neither w1 nor w2  
  ) |>  
  dplyr::ungroup()  

w1	w2	O11	N	R1	O12	R2	C1	O21	C2	O22
when	we	1	5,200	52	51	5,148	88	87	5,112	5,061
when	look	1	5,200	52	51	5,148	52	51	5,148	5,097
when	to	1	5,200	52	51	5,148	52	51	5,148	5,097
when	the	4	5,200	52	48	5,148	446	442	4,754	4,706
when	individuals	2	5,200	52	50	5,148	103	101	5,097	5,047
when	of	5	5,200	52	47	5,148	460	455	4,740	4,693
when	same	1	5,200	52	51	5,148	52	51	5,148	5,097
when	variety	3	5,200	52	49	5,148	153	150	5,047	4,998
when	or	2	5,200	52	50	5,148	139	137	5,061	5,011
when	sub	1	5,200	52	51	5,148	52	51	5,148	5,097

Contingency Table Recap:

	w2 present	w2 absent	Row totals
w1 present	O11	O12	R1
w1 absent	O21	O22	R2
Column totals	C1	C2	N

Step 4: Focus on a Target Word

For demonstration, we’ll find collocates of “selection”:

# filter for collocates of "selection"  
colldf_redux <- colldf |>  
  dplyr::filter(  
    w1 == "selection",  
    # minimum frequency of w2 (reduces noise from rare words)  
    (O11 + O21) > 2,  
    # minimum co-occurrence frequency  
    O11 > 2  
  ) |>  
  # calculate expected frequencies (under independence assumption)  
  dplyr::rowwise() |>  
  dplyr::mutate(  
    E11 = (R1 * C1) / N,  
    E12 = (R1 * C2) / N,  
    E21 = (R2 * C1) / N,  
    E22 = (R2 * C2) / N  
  ) |>  
  dplyr::ungroup()  

w1	w2	O11	N	R1	O12	R2	C1	O21	C2	O22	E11	E12	E21	E22
selection	the	9	5,200	84	75	5,116	446	437	4,754	4,679	7.204615	76.79538	438.7954	4,677.205
selection	of	9	5,200	84	75	5,116	460	451	4,740	4,665	7.430769	76.56923	452.5692	4,663.431

Step 5: Calculate Association Measures

Now we calculate all the association measures discussed in Part I. The code below implements the formulas from the theoretical section:

assoc_tb <- colldf_redux |>  
  # count number of rows (for Bonferroni correction)  
  dplyr::mutate(Rws = n()) |>  
  dplyr::rowwise() |>  
    
  # Fisher's Exact Test (p-value for significance)  
  # Tests null hypothesis: w1 and w2 are independent  
  dplyr::mutate(  
    p = as.vector(unlist(  
      fisher.test(matrix(c(O11, O12, O21, O22), ncol = 2, byrow = TRUE))[1]  
    ))  
  ) |>  
    
  # Gries' AM (Association Measure)  
  # Step 1: Calculate "bias towards top-left" (maximum possible co-occurrence)  
  # This represents the upper bound if w1 and w2 always co-occurred  
  dplyr::mutate(  
    btl_O12 = ifelse(C1 > R1, 0, R1 - C1),  
    btl_O11 = ifelse(C1 > R1, R1, R1 - btl_O12),  
    btl_O21 = ifelse(C1 > R1, C1 - R1, C1 - btl_O11),  
    btl_O22 = ifelse(C1 > R1, C2, C2 - btl_O12),  
      
    # Step 2: Calculate "bias towards top-right" (minimum co-occurrence)  
    # This represents the lower bound if w1 and w2 never co-occurred  
    btr_O11 = 0,  
    btr_O21 = R1,  
    btr_O12 = C1,  
    btr_O22 = C2 - R1,  
      
    # Step 3: Calculate observed proportion relative to bounds  
    upp = btl_O11 / R1,    # upper bound proportion  
    low = btr_O11 / R1,    # lower bound proportion (= 0)  
    op = O11 / R1,         # observed proportion  
      
    # AM = observed relative to maximum possible  
    # Ranges from 0 (no association) to 1 (perfect association)  
    AM = op / upp  
  ) |>  
    
  # Remove temporary columns used for AM calculation  
  dplyr::select(-starts_with("btr_"), -starts_with("btl_"),   
                -upp, -low, -op) |>  
    
  # Chi-Square (χ²)  
  # Sum of squared deviations (observed - expected) / expected  
  dplyr::mutate(  
    X2 = (O11 - E11)^2 / E11 + (O12 - E12)^2 / E12 +   
         (O21 - E21)^2 / E21 + (O22 - E22)^2 / E22  
  ) |>  
    
  # All other association measures  
  dplyr::mutate(  
    # Phi coefficient (effect size based on χ²)  
    # Normalized χ² value, ranges 0-1 for positive associations  
    phi = sqrt(X2 / N),  
      
    # Dice coefficient  
    # Measures overlap: how much of w1+w2's total frequency is co-occurrence?  
    Dice = (2 * O11) / (R1 + C1),  
    LogDice = log((2 * O11) / (R1 + C1)),  
      
    # Mutual Information  
    # Log ratio of observed to expected co-occurrence  
    MI = log2(O11 / E11),  
      
    # Minimum Sensitivity  
    # Minimum of the two conditional probabilities  
    MS = min(O11 / C1, O11 / R1),  
      
    # t-score  
    # Deviation from expected, normalized by sqrt(observed)  
    # Favors high-frequency collocations  
    t.score = (O11 - E11) / sqrt(O11),  
      
    # z-score  
    # Deviation from expected, normalized by sqrt(expected)  
    z.score = (O11 - E11) / sqrt(E11),  
      
    # Pointwise Mutual Information  
    # Log of ratio: P(w1,w2) / (P(w1) * P(w2))  
    PMI = log2((O11 / N) / ((C1 / N) * (R1 / N))),  
      
    # Delta P (two directions)  
    # DeltaP12: How much does w2 increase probability of w1?  
    # DeltaP21: How much does w1 increase probability of w2?  
    DeltaP12 = (O11 / (O11 + O12)) - (O21 / (O21 + O22)),  
    DeltaP21 = (O11 / (O11 + O21)) - (O12 / (O12 + O22)),  
      
    # Simple DP  
    DP = (O11 / R1) - (O21 / R2),  
      
    # Log Odds Ratio  
    # Log of (O11*O22) / (O12*O21), with +0.5 smoothing to avoid zeros  
    LogOddsRatio = log(((O11 + 0.5) * (O22 + 0.5)) /   
                       ((O12 + 0.5) * (O21 + 0.5))),  
      
    # Log-Likelihood (G²)  
    # More robust than χ² for small expected frequencies  
    G2 = 2 * (O11 * log(O11 / E11) + O12 * log(O12 / E12) +   
              O21 * log(O21 / E21) + O22 * log(O22 / E22))  
  ) |>  
    
  # Bonferroni-corrected significance levels  
  # Adjusts for multiple comparisons: threshold = α / number of tests  
  dplyr::mutate(  
    Sig_corrected = dplyr::case_when(  
      p / Rws > .05 ~ "n.s.",  
      p / Rws > .01 ~ "p < .05*",  
      p / Rws > .001 ~ "p < .01**",  
      p / Rws <= .001 ~ "p < .001***",  
      TRUE ~ "N.A."  
    ),  
    p = round(p, 5)  
  ) |>  
    
  # Filter: keep only significant, attractive collocations  
  dplyr::filter(  
    Sig_corrected != "n.s.",    # must be significant after Bonferroni  
    E11 < O11  # observed > expected (attraction, not repulsion)  
  ) |>  
    
  # Sort by DeltaP12 (or choose another measure for ranking)  
  dplyr::arrange(desc(DeltaP12)) |>  
    
  # Remove temporary/redundant columns for cleaner output  
  dplyr::select(-O12, -O21, -O22, -R1, -R2, -C1, -C2,   
                -E11, -E12, -E21, -E22, -Rws) |>  
  dplyr::ungroup()  

w1	w2	O11	N	p	AM	X2	phi	Dice	LogDice	MI	MS	t.score	z.score	PMI	DeltaP12	DeltaP21	DP	LogOddsRatio	G2	Sig_corrected

Interpreting the Results

Each row shows a word that significantly collocates with “selection”. Key columns:

• w2: The collocate word
  
• O11: Number of sentences containing both “selection” and this word
  
• N: Total observations (all word pairs)
  
• AM: Gries’ association measure (0–1, higher = stronger)
  
• DeltaP12: Conditional probability measure (directional)
  
• phi: Effect size based on χ²
  
• Dice: Overlap coefficient
  
• PMI: Pointwise Mutual Information
  
• G2: Log-likelihood ratio
  
• p: Fisher’s exact test p-value
  
• Sig_corrected: Significance after Bonferroni correction

Compare different measures to see which words rank highest by each criterion!

Step 6: Visualize Top Collocates

# Visualize top 20 collocates by ΔP  
assoc_tb |>  
  top_n(20, DeltaP12) |>  
  mutate(w2 = reorder(w2, DeltaP12)) |>  
  ggplot(aes(x = DeltaP12, y = w2)) +  
  geom_col(fill = "steelblue", alpha = 0.8) +  
  theme_bw() +  
  labs(  
    title = "Top 20 Collocates of 'selection' (Sentence-Based Method)",  
    subtitle = "Ranked by ΔP (directional conditional probability)",  
    x = "ΔP (selection → collocate)",  
    y = ""  
  ) +  
  theme(panel.grid.minor = element_blank())  

---

Method 2: KWIC-Based Collocation Detection

This method uses KeyWord In Context (KWIC) to find words that appear near a target word within a fixed window (e.g., ±5 words).

KWIC vs. Sentence-Based

• Sentence-based: Broader context (entire sentence), captures long-range dependencies
  
• KWIC: Narrower context (fixed window), captures immediate collocates

KWIC is better for finding grammatical collocates (adjectives, verbs directly modifying/complementing the target). Sentence-based is better for semantic collocates (thematic associates that may be distant).

Step 1: Prepare Corpus

We’ll split the text into chapters (to mimic a corpus with multiple documents):

# Clean and split corpus into chapters  
texts <- text |>  
  paste0(collapse = " ") |>  
  # Separate possessives  
  stringr::str_replace_all(fixed("'"), " '") |>  
  stringr::str_replace_all(fixed("'"), " '") |>  
  # Split by chapter markers (if present; otherwise creates single chunk)  
  stringr::str_split("CHAPTER [IVX]{1,4}") |>  
  unlist() |>  
  # Remove non-word characters  
  stringr::str_replace_all("\\W", " ") |>  
  stringr::str_replace_all("[^[:alpha:] ]", " ") |>  
  # Clean spaces  
  stringr::str_squish() |>  
  # Lowercase  
  tolower()  

head(substr(texts, 1, 100), 3)
when we look to the individuals of the same variety or sub variety of our older cultivated plants an

Why Split Into Chunks?

Splitting the corpus into chapters (or other units) mirrors real-world corpora, which typically consist of multiple texts/documents. This allows tokens_select() to extract KWIC contexts across different document boundaries.

Step 2: Extract KWIC Context

We use quanteda::tokens_select() to extract words within a window around our keyword:

# Define keyword  
keyword <- "selection"  
  
# Extract words within ±5 word window of "selection"  
# tokens_select() finds all instances of the pattern and extracts surrounding context  
kwic_words <- quanteda::tokens_select(  
  quanteda::tokens(texts),  
  pattern = keyword,  
  window = 5,          # 5 words before and 5 words after  
  selection = "keep",  # keep the keyword itself in results  
  case_insensitive = TRUE  
) |>  
  unlist() |>  
  # Tabulate frequencies of words in KWIC contexts  
  table() |>  
  as.data.frame() |>  
  # Rename columns  
  dplyr::rename(token = 1, n = 2) |>  
  # Mark as 'kwic' type  
  dplyr::mutate(type = "kwic")  

token	n	type
natural	3	kwic
selection	3	kwic
the	3	kwic
by	2	kwic
of	2	kwic
preservation	2	kwic
acts	1	kwic
been	1	kwic
but	1	kwic
clearly	1	kwic
conclude	1	kwic
exclusively	1	kwic
favoured	1	kwic
has	1	kwic
is	1	kwic

Understanding the KWIC Table

Each row shows:

• token: A word that appears within ±5 words of “selection”
  
• n: How many times it appears in those contexts
  
• type: “kwic” (from KWIC contexts)

High-frequency words here are collocate candidates — they appear near “selection” frequently.

Step 3: Create Corpus Frequency List

We need overall corpus frequencies for comparison (to calculate expected frequencies):

# Create frequency table for entire corpus  
corpus_words <- texts |>  
  quanteda::tokens() |>  
  unlist() |>  
  as.data.frame() |>  
  dplyr::rename(token = 1) |>  
  dplyr::group_by(token) |>  
  dplyr::summarise(n = n(), .groups = "drop") |>  
  dplyr::mutate(type = "corpus")  

token	n	type
the	13	corpus
of	12	corpus
in	4	corpus
and	3	corpus
natural	3	corpus
nature	3	corpus
or	3	corpus
selection	3	corpus
species	3	corpus
variety	3	corpus
but	2	corpus
by	2	corpus
for	2	corpus
individuals	2	corpus
is	2	corpus

Step 4: Combine and Calculate Contingency Table

# Join KWIC and corpus frequencies  
freq_df <- dplyr::left_join(corpus_words, kwic_words, by = "token") |>  
  dplyr::rename(corpus = n.x, kwic = n.y) |>  
  dplyr::select(-type.x, -type.y) |>  
  # Replace NA with 0 (words not in KWIC contexts)  
  tidyr::replace_na(list(corpus = 0, kwic = 0)) |>  
  # Filter out words that don't appear in corpus  
  dplyr::filter(corpus > 0) |>  
  # Adjust corpus count: subtract KWIC instances to avoid double-counting  
  # (corpus should represent "outside KWIC" contexts)  
  dplyr::mutate(corpus = corpus - kwic)  
  
# Calculate contingency table values  
stats_tb <- freq_df |>  
  dplyr::mutate(  
    corpus = as.numeric(corpus),  
    kwic = as.numeric(kwic),  
    # Column totals  
    C1 = sum(kwic),      # total words in all KWIC contexts  
    C2 = sum(corpus),    # total words outside KWIC contexts  
    N = C1 + C2          # grand total  
  ) |>  
  dplyr::rowwise() |>  
  dplyr::mutate(  
    # Row totals and observed frequencies  
    R1 = corpus + kwic,  # total frequency of this word  
    R2 = N - R1,         # all other words  
    O11 = kwic,          # word appears in KWIC  
    O12 = R1 - O11,      # word appears outside KWIC  
    O21 = C1 - O11,      # other words in KWIC  
    O22 = C2 - O12,      # other words outside KWIC  
    # Expected frequencies  
    E11 = (R1 * C1) / N,  
    E12 = (R1 * C2) / N,  
    E21 = (R2 * C1) / N,  
    E22 = (R2 * C2) / N  
  ) |>  
  dplyr::select(-corpus, -kwic) |>  
  dplyr::ungroup()  

token	C1	C2	N	R1	R2	O11	O12	O21	O22	E11	E12	E21	E22
a	33	109	142	1	141	0	1	33	108	0.2323944	0.7676056	32.76761	108.2324
accumulation	33	109	142	1	141	0	1	33	108	0.2323944	0.7676056	32.76761	108.2324
acts	33	109	142	1	141	1	0	32	109	0.2323944	0.7676056	32.76761	108.2324
and	33	109	142	3	139	0	3	33	106	0.6971831	2.3028169	32.30282	106.6972
animals	33	109	142	1	141	0	1	33	108	0.2323944	0.7676056	32.76761	108.2324
any	33	109	142	1	141	0	1	33	108	0.2323944	0.7676056	32.76761	108.2324
are	33	109	142	1	141	0	1	33	108	0.2323944	0.7676056	32.76761	108.2324
arise	33	109	142	1	141	0	1	33	108	0.2323944	0.7676056	32.76761	108.2324
as	33	109	142	1	141	0	1	33	108	0.2323944	0.7676056	32.76761	108.2324
been	33	109	142	1	141	1	0	32	109	0.2323944	0.7676056	32.76761	108.2324

Contingency Table for KWIC:

	KWIC context	Outside KWIC	Row totals
Token	O11	O12	R1
Other tokens	O21	O22	R2
Column totals	C1	C2	N

Step 5: Calculate Association Measures (KWIC)

We apply the same association measure formulas, but now comparing KWIC vs. non-KWIC contexts:

assoc_tb2 <- stats_tb |>  
  dplyr::mutate(Rws = n()) |>  
  dplyr::rowwise() |>  
    
  # Fisher's exact test  
  dplyr::mutate(  
    p = as.vector(unlist(  
      fisher.test(matrix(c(O11, O12, O21, O22), ncol = 2, byrow = TRUE))[1]  
    ))  
  ) |>  
    
  # Gries' AM  
  dplyr::mutate(  
    btl_O12 = ifelse(C1 > R1, 0, R1 - C1),  
    btl_O11 = ifelse(C1 > R1, R1, R1 - btl_O12),  
    btl_O21 = ifelse(C1 > R1, C1 - R1, C1 - btl_O11),  
    btl_O22 = ifelse(C1 > R1, C2, C2 - btl_O12),  
    btr_O11 = 0,  
    btr_O21 = R1,  
    btr_O12 = C1,  
    btr_O22 = C2 - R1,  
    upp = btl_O11 / R1,  
    low = btr_O11 / R1,  
    op = O11 / R1,  
    AM = op / upp  
  ) |>  
  dplyr::select(-starts_with("btr_"), -starts_with("btl_"),   
                -upp, -low, -op) |>  
    
  # χ²  
  dplyr::mutate(  
    X2 = (O11 - E11)^2 / E11 + (O12 - E12)^2 / E12 +   
         (O21 - E21)^2 / E21 + (O22 - E22)^2 / E22  
  ) |>  
    
  # Association measures  
  dplyr::mutate(  
    phi = sqrt(X2 / N),  
    MS = min(O11 / C1, O11 / R1),  
    Dice = (2 * O11) / (R1 + C1),  
    LogDice = log((2 * O11) / (R1 + C1)),  
    MI = log2(O11 / E11),  
    t.score = (O11 - E11) / sqrt(O11),  
    z.score = (O11 - E11) / sqrt(E11),  
    PMI = log2((O11 / N) / ((O11 + O12) / N * (O11 + O21) / N)),  
    DeltaP12 = (O11 / (O11 + O12)) - (O21 / (O21 + O22)),  
    DeltaP21 = (O11 / (O11 + O21)) - (O12 / (O12 + O22)),  
    DP = (O11 / R1) - (O21 / R2),  
    LogOddsRatio = log(((O11 + 0.5) * (O22 + 0.5)) /   
                       ((O12 + 0.5) * (O21 + 0.5))),  
    G2 = 2 * (O11 * log(O11 / E11) + O12 * log(O12 / E12) +   
              O21 * log(O21 / E21) + O22 * log(O22 / E22))  
  ) |>  
    
  # Significance  
  dplyr::mutate(  
    Sig_corrected = dplyr::case_when(  
      p / Rws > .05 ~ "n.s.",  
      p / Rws > .01 ~ "p < .05*",  
      p / Rws > .001 ~ "p < .01**",  
      p / Rws <= .001 ~ "p < .001***",  
      TRUE ~ "N.A."  
    ),  
    p = round(p, 5)  
  ) |>  
    
  # Filter  
  dplyr::filter(  
    Sig_corrected != "n.s.",  
    E11 < O11  
  ) |>  
  dplyr::arrange(desc(DeltaP12)) |>  
  dplyr::select(-O12, -O21, -O22, -R1, -R2, -C1, -C2,   
                -E11, -E12, -E21, -E22, -Rws) |>  
  dplyr::ungroup()  

token	N	O11	p	AM	X2	phi	MS	Dice	LogDice	MI	t.score	z.score	PMI	DeltaP12	DeltaP21	DP	LogOddsRatio	G2	Sig_corrected
natural	142	3	0.01168	1.0000000	10.1229562	0.26699892	0.09090909	0.16666667	-1.791759	2.1053530	1.3295320	2.7579474	2.1053530	0.7841727	0.09090909	0.7841727	3.2241080		p < .001***
selection	142	3	0.01168	1.0000000	10.1229562	0.26699892	0.09090909	0.16666667	-1.791759	2.1053530	1.3295320	2.7579474	2.1053530	0.7841727	0.09090909	0.7841727	3.2241080		p < .001***
by	142	2	0.05274	1.0000000	6.7004329	0.21722373	0.06060606	0.11428571	-2.169054	2.1053530	1.0855583	2.2518546	2.1053530	0.7785714	0.06060606	0.7785714	2.8553749		p < .001***
preservation	142	2	0.05274	1.0000000	6.7004329	0.21722373	0.06060606	0.11428571	-2.169054	2.1053530	1.0855583	2.2518546	2.1053530	0.7785714	0.06060606	0.7785714	2.8553749		p < .001***
acts	142	1	0.23239	1.0000000	3.3264560	0.15305472	0.03030303	0.05882353	-2.833213	2.1053530	0.7676056	1.5923017	2.1053530	0.7730496	0.03030303	0.7730496	2.3132967		p < .01**
been	142	1	0.23239	1.0000000	3.3264560	0.15305472	0.03030303	0.05882353	-2.833213	2.1053530	0.7676056	1.5923017	2.1053530	0.7730496	0.03030303	0.7730496	2.3132967		p < .01**
clearly	142	1	0.23239	1.0000000	3.3264560	0.15305472	0.03030303	0.05882353	-2.833213	2.1053530	0.7676056	1.5923017	2.1053530	0.7730496	0.03030303	0.7730496	2.3132967		p < .01**
conclude	142	1	0.23239	1.0000000	3.3264560	0.15305472	0.03030303	0.05882353	-2.833213	2.1053530	0.7676056	1.5923017	2.1053530	0.7730496	0.03030303	0.7730496	2.3132967		p < .01**
exclusively	142	1	0.23239	1.0000000	3.3264560	0.15305472	0.03030303	0.05882353	-2.833213	2.1053530	0.7676056	1.5923017	2.1053530	0.7730496	0.03030303	0.7730496	2.3132967		p < .01**
favoured	142	1	0.23239	1.0000000	3.3264560	0.15305472	0.03030303	0.05882353	-2.833213	2.1053530	0.7676056	1.5923017	2.1053530	0.7730496	0.03030303	0.7730496	2.3132967		p < .01**
has	142	1	0.23239	1.0000000	3.3264560	0.15305472	0.03030303	0.05882353	-2.833213	2.1053530	0.7676056	1.5923017	2.1053530	0.7730496	0.03030303	0.7730496	2.3132967		p < .01**
main	142	1	0.23239	1.0000000	3.3264560	0.15305472	0.03030303	0.05882353	-2.833213	2.1053530	0.7676056	1.5923017	2.1053530	0.7730496	0.03030303	0.7730496	2.3132967		p < .01**
may	142	1	0.23239	1.0000000	3.3264560	0.15305472	0.03030303	0.05882353	-2.833213	2.1053530	0.7676056	1.5923017	2.1053530	0.7730496	0.03030303	0.7730496	2.3132967		p < .01**
seen	142	1	0.23239	1.0000000	3.3264560	0.15305472	0.03030303	0.05882353	-2.833213	2.1053530	0.7676056	1.5923017	2.1053530	0.7730496	0.03030303	0.7730496	2.3132967		p < .01**
but	142	1	0.41205	0.5000000	0.8143612	0.07572937	0.03030303	0.05714286	-2.862201	1.1053530	0.5352113	0.7850502	1.1053530	0.2714286	0.02112872	0.2714286	1.2055101	0.6865228	p < .01**
is	142	1	0.41205	0.5000000	0.8143612	0.07572937	0.03030303	0.05714286	-2.862201	1.1053530	0.5352113	0.7850502	1.1053530	0.2714286	0.02112872	0.2714286	1.2055101	0.6865228	p < .01**
means	142	1	0.41205	0.5000000	0.8143612	0.07572937	0.03030303	0.05714286	-2.862201	1.1053530	0.5352113	0.7850502	1.1053530	0.2714286	0.02112872	0.2714286	1.2055101	0.6865228	p < .01**
that	142	1	0.41205	0.5000000	0.8143612	0.07572937	0.03030303	0.05714286	-2.862201	1.1053530	0.5352113	0.7850502	1.1053530	0.2714286	0.02112872	0.2714286	1.2055101	0.6865228	p < .01**
we	142	1	0.41205	0.5000000	0.8143612	0.07572937	0.03030303	0.05714286	-2.862201	1.1053530	0.5352113	0.7850502	1.1053530	0.2714286	0.02112872	0.2714286	1.2055101	0.6865228	p < .01**
nature	142	1	0.55064	0.3333333	0.1750446	0.03510995	0.03030303	0.05555556	-2.890372	0.5203905	0.3028169	0.3626659	0.5203905	0.1031175	0.01195441	0.1031175	0.6854251	0.1611769	p < .01**

Step 6: Visualize KWIC Collocates

# Compare top collocates by different measures  
p1 <- assoc_tb2 |>  
  top_n(15, DeltaP12) |>  
  mutate(token = reorder(token, DeltaP12)) |>  
  ggplot(aes(x = DeltaP12, y = token)) +  
  geom_col(fill = "steelblue", alpha = 0.8) +  
  theme_bw() +  
  labs(title = "Top 15 by ΔP", x = "ΔP", y = "") +  
  theme(panel.grid.minor = element_blank())  
  
p2 <- assoc_tb2 |>  
  top_n(15, phi) |>  
  mutate(token = reorder(token, phi)) |>  
  ggplot(aes(x = phi, y = token)) +  
  geom_col(fill = "tomato", alpha = 0.8) +  
  theme_bw() +  
  labs(title = "Top 15 by Phi", x = "Phi coefficient", y = "") +  
  theme(panel.grid.minor = element_blank())  
  
cowplot::plot_grid(p1, p2, nrow = 1)  

---

Exercises: Implementation

Q1. What is the key difference between the sentence-based method and the KWIC-based method?

Sentence-based is faster and more accurate
KWIC requires more statistical tests
Sentence-based uses entire sentences as context; KWIC uses fixed word windows (e.g., ±5 words)
They produce identical results but use different functions

---

Q2. Why do we calculate expected frequencies (E₁₁, E₁₂, E₂₁, E₂₂)?

Expected frequencies are required by R for statistical tests
To correct for sampling error in small corpora
To normalize frequencies across corpora of different sizes
To determine what co-occurrence frequencies would be expected if words were randomly distributed (independence baseline)

---

Q3. In the code, we filter E11 < O11. Why?

To keep only word pairs that co-occur MORE than expected (attraction), removing pairs that repel
E11 < O11 is required for calculating ΔP
To ensure all p-values are valid
To remove statistical outliers from the analysis

---

Q4. Why do we apply Bonferroni correction to p-values?

Bonferroni correction is always required in corpus linguistics
To control Type I error (false positives) when testing many word pairs simultaneously
To make the p-values comparable across different association measures
To adjust for non-normal distribution of word frequencies

---

N-grams

N-grams are sequences of n adjacent words. Unlike collocations, n-grams:

• Don’t require statistical significance
  
• Are purely positional (based on word order)
  
• Can include function words and non-meaningful sequences

N-grams are useful for:

• Identifying fixed phrases and idioms
  
• Language modeling (predicting next word)
  
• Extracting multi-word expressions
  
• Stylistic analysis

Extracting N-grams with tidytext

We’ll use tidytext::unnest_tokens() to extract bigrams and trigrams:

# Convert text to data frame  
text_df <- data.frame(text = text, stringsAsFactors = FALSE)  
  
# Extract bigrams (2-grams)  
bigrams <- text_df |>  
  tidytext::unnest_tokens(bigram, text, token = "ngrams", n = 2) |>  
  dplyr::count(bigram, sort = TRUE)  
  
# Extract trigrams (3-grams)  
trigrams <- text_df |>  
  tidytext::unnest_tokens(trigram, text, token = "ngrams", n = 3) |>  
  dplyr::count(trigram, sort = TRUE)  

bigram	n
natural selection	3
individuals of	2
means of	2
of the	2
the individuals	2
the preservation	2
a state	1
accumulation of	1
acts exclusively	1
and accumulation	1
and animals	1
and of	1
animals one	1
any one	1
are beneficial	1

Visualizing N-gram Frequencies

# Combine bigrams and trigrams for comparison  
ngram_comparison <- bind_rows(  
  bigrams |> top_n(15, n) |> mutate(type = "Bigram", gram = bigram),  
  trigrams |> top_n(15, n) |> mutate(type = "Trigram", gram = trigram)  
) |>  
  mutate(gram = tidytext::reorder_within(gram, n, type))  
  
ggplot(ngram_comparison, aes(x = n, y = gram, fill = type)) +  
  geom_col(alpha = 0.8, show.legend = FALSE) +  
  facet_wrap(~ type, scales = "free") +  
  tidytext::scale_y_reordered() +  
  scale_fill_manual(values = c("steelblue", "tomato")) +  
  theme_bw() +  
  labs(title = "Top 15 Bigrams and Trigrams",  
       subtitle = "Darwin's Origin of Species",  
       x = "Frequency", y = "") +  
  theme(panel.grid.minor = element_blank())  

N-grams vs. Collocations

Notice that many high-frequency bigrams (like “of the”, “in the”) are not meaningful collocations — they’re just common grammatical sequences. Collocation analysis filters these out by testing statistical significance.

For n-grams, you might want to filter by:

• Removing stopwords
  
• Setting minimum frequency thresholds
  
• Focusing on content words only
  

---

Quick Reference

Key Functions

Task	Function	Package
Create feature co-occurrence matrix	fcm()	quanteda
Extract KWIC contexts	tokens_select()	quanteda
Extract n-grams	unnest_tokens(token = "ngrams")	tidytext
Calculate association measures	Custom code (see tutorial)	dplyr
Tokenize sentences	tokenize_sentences()	tokenizers

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Choosing an Association Measure

Your Goal	Recommended Measure
General collocation analysis	Gries’ AM or \(\Delta P\)
Directional associations	\(\Delta P\) (asymmetric)
Rare but strong associations	PMI or PPMI
Common fixed phrases	t-score or Dice
Significance testing	G² (with p-value)
Mutual dependence	Minimum Sensitivity (MS)
Effect size	Phi coefficient

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Workflow Checklist

1. Choose context unit: Sentences, paragraphs, fixed windows, documents?
   
2. Tokenize and clean: Lowercase, remove punctuation, handle possessives
   
3. Create co-occurrence matrix: Use fcm() or KWIC extraction
   
4. Calculate contingency table: O11, O12, O21, O22, R1, R2, C1, C2, N
   
5. Calculate expected frequencies: E11, E12, E21, E22
   
6. Compute association measures: Choose 2–3 measures for comparison
   
7. Apply significance testing: Fisher’s exact + Bonferroni correction
   
8. Filter results: Remove non-significant, repulsive, or rare pairs
   
9. Visualize and interpret: Compare rankings across measures
   
10. Report findings: Specify method, measures, thresholds, top collocates

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Common Pitfalls

1. Using χ² without checking expected frequencies → Use G² instead
   
2. Not applying multiple comparison correction → Bonferroni or FDR
   
3. Treating n-grams as collocations → N-grams ≠ statistically tested
   
4. Ignoring asymmetry → Use \(\Delta P\) or Gries’ AM for directional associations
   
5. Not filtering by minimum frequency → Rare words inflate PMI
   
6. Relying on single measure → Compare multiple measures
   
7. Not specifying context window → Always report how co-occurrence was defined
   
8. Forgetting to center/normalize → Different corpora need comparable measures

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Citation & Session Info

Schweinberger, Martin. 2026. Analyzing Collocations and N-grams in R. Brisbane: The University of Queensland. url: https://ladal.edu.au/tutorials/coll/coll.html (Version 2026.02.24).

@manual{schweinberger2026coll,  
  author = {Schweinberger, Martin},  
  title = {Analyzing Collocations and N-grams in R},  
  note = {https://ladal.edu.au/tutorials/coll/coll.html},  
  year = {2026},  
  organization = {The University of Queensland, Australia. School of Languages and Cultures},  
  address = {Brisbane},  
  edition = {2026.02.24}  
}  

sessionInfo()  

R version 4.4.2 (2024-10-31 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows 11 x64 (build 26200)

Matrix products: default


locale:
[1] LC_COLLATE=English_United States.utf8 
[2] LC_CTYPE=English_United States.utf8   
[3] LC_MONETARY=English_United States.utf8
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.utf8    

time zone: Australia/Brisbane
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices datasets  utils     methods   base     

other attached packages:
 [1] tokenizers_0.3.0          cowplot_1.2.0            
 [3] tidytext_0.4.2            lubridate_1.9.4          
 [5] forcats_1.0.0             purrr_1.0.4              
 [7] readr_2.1.5               tidyr_1.3.2              
 [9] tibble_3.2.1              tidyverse_2.0.0          
[11] checkdown_0.0.13          sna_2.8                  
[13] statnet.common_4.11.0     tm_0.7-16                
[15] NLP_0.3-2                 stringr_1.5.1            
[17] dplyr_1.2.0               quanteda.textplots_0.95  
[19] quanteda.textstats_0.97.2 quanteda_4.2.0           
[21] Matrix_1.7-2              network_1.19.0           
[23] igraph_2.1.4              ggdendro_0.2.0           
[25] GGally_2.2.1              flextable_0.9.11         
[27] factoextra_1.0.7          ggplot2_4.0.2            
[29] FactoMineR_2.11          

loaded via a namespace (and not attached):
 [1] sandwich_3.1-1          rlang_1.1.7             magrittr_2.0.3         
 [4] multcomp_1.4-28         compiler_4.4.2          systemfonts_1.3.1      
 [7] vctrs_0.7.1             pkgconfig_2.0.3         fastmap_1.2.0          
[10] labeling_0.4.3          rmarkdown_2.30          tzdb_0.4.0             
[13] markdown_2.0            ragg_1.3.3              xfun_0.56              
[16] litedown_0.9            jsonlite_1.9.0          flashClust_1.01-2      
[19] SnowballC_0.7.1         uuid_1.2-1              parallel_4.4.2         
[22] stopwords_2.3           cluster_2.1.6           R6_2.6.1               
[25] stringi_1.8.4           RColorBrewer_1.1-3      estimability_1.5.1     
[28] nsyllable_1.0.1         Rcpp_1.1.1              knitr_1.51             
[31] zoo_1.8-13              timechange_0.3.0        splines_4.4.2          
[34] tidyselect_1.2.1        rstudioapi_0.17.1       yaml_2.3.10            
[37] codetools_0.2-20        lattice_0.22-6          plyr_1.8.9             
[40] withr_3.0.2             S7_0.2.1                askpass_1.2.1          
[43] coda_0.19-4.1           evaluate_1.0.3          survival_3.7-0         
[46] ggstats_0.10.0          zip_2.3.2               xml2_1.3.6             
[49] pillar_1.10.1           janeaustenr_1.0.0       renv_1.1.7             
[52] DT_0.33                 generics_0.1.3          hms_1.1.3              
[55] commonmark_2.0.0        scales_1.4.0            xtable_1.8-4           
[58] leaps_3.2               glue_1.8.0              slam_0.1-55            
[61] gdtools_0.5.0           emmeans_1.10.7          scatterplot3d_0.3-44   
[64] tools_4.4.2             data.table_1.17.0       mvtnorm_1.3-3          
[67] fastmatch_1.1-6         grid_4.4.2              patchwork_1.3.0        
[70] cli_3.6.4               textshaping_1.0.0       officer_0.7.3          
[73] fontBitstreamVera_0.1.1 gtable_0.3.6            digest_0.6.39          
[76] fontquiver_0.2.1        ggrepel_0.9.6           TH.data_1.1-3          
[79] htmlwidgets_1.6.4       farver_2.1.2            htmltools_0.5.9        
[82] lifecycle_1.0.5         multcompView_0.1-10     fontLiberation_0.1.0   
[85] openssl_2.3.2           MASS_7.3-61            

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References

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AI Transparency Statement

This tutorial was developed with the assistance of Claude (claude.ai), a large language model created by Anthropic. Claude was used to help draft the tutorial text, structure the instructional content, generate the R code examples, and write the checkdown quiz questions and feedback strings. All content was reviewed, edited, and approved by the author (Martin Schweinberger), who takes full responsibility for the accuracy and pedagogical appropriateness of the material. The use of AI assistance is disclosed here in the interest of transparency and in accordance with emerging best practices for AI-assisted academic content creation.

References

Ellis, Nick C. 2007. “Language Acquisition as Rational Contingency Learning.” Applied Linguistics 27 (1): 1–24. https://doi.org/https://doi.org/10.1093/applin/ami038.

Gries, Stefan Th. 2013. “50-Something Years of Work on Collocations: What Is or Should Be Next.” International Journal of Corpus Linguistics 18 (1): 137–66.

———. 2022. “What Do (Some of) Our Association Measures Measure (Most)? Association?” Journal of Second Language Studies 5 (1): 1–33. https://doi.org/https://doi.org/10.1075/jsls.21028.gri.

Gries, Stefan Th. 2013. Statistics for Linguistics with R: A Practical Introduction. 2nd ed. Berlin: De Gruyter Mouton.

McEnery, Tony, Richard Xiao, and Yukio Tono. 2006. Corpus-Based Language Studies. London: Routledge London.

Pedersen, Ted. 1998. “Dependent Bigram Identification.” AAAI/IAAI 1197: 1197–null.