A lexical density measure computed by sliding a fixed-size token window across a text, calculating the type–token ratio (unique types divided by tokens) within each window, and reporting the average (or time series) of those local ratios; designed to reduce sensitivity of plain TTR to overall text length and to highlight local variation in lexical diversity.

Principle

Averaging local TTR values across overlapping windows stabilises estimates of lexical diversity by diluting the influence of extreme short- or long-text bias and by sampling different textual positions, so the resulting metric better reflects typical lexical variety at the chosen scale.

Demonstration

Illustrative scenario: Given a 10,000-token novel, a researcher selects a 500-token sliding window with step 100, computes TTR for each window (unique types ÷ 500), then averages those TTRs to obtain MATTR. Recognition: MATTR yields a single value less affected by the novel’s total length and by an unusually lexical or repetitive chapter than a single-document TTR would.

Misapplication

Using MATTR with an inappropriately large window equal to the entire text reduces it to ordinary TTR; using an excessively small window increases variance and can reflect sentence-level idiosyncrasies. Similarly, averaging across heterogeneous genres or unnormalized tokenization without stratification produces misleading comparisons.

Consequence

When properly parameterised, MATTR permits more stable comparisons of lexical diversity across texts of different lengths and internal structure, informing stylistic analysis, readability assessment, and preprocessing decisions for NLP pipelines; however, results depend causally on window size, step, tokenisation, and whether lemmatisation or lowercasing were applied.

Reversal

If texts are extremely short (shorter than the window) or if window size is set to the whole document, MATTR collapses to the ordinary TTR or becomes undefined. For corpora with sharp topical shifts, averaging can mask meaningful local changes in vocabulary that a windowed time series would reveal but a single aggregated average would conceal.

Boundary

Clearly within: a tokenised prose text analysed with a fixed numeric window and consistent tokenisation rules. Boundary case: comparing MATTRs computed with different window sizes or tokenisation strategies — interpretation depends on those choices. Clearly outside: measures of lexical richness computed without sliding windows (e.g., Guiraud’s R) or frequency-spectrum summaries that do not average local TTRs.

Semantic Tension

Window size and step create a trade-off between stability (larger windows, more overlap) and sensitivity to local variation (smaller windows, less overlap); the desire for comparability across texts conflicts with the need to preserve meaningful intra-textual variation.

Synthesis

MATTR is a pragmatic compromise between single-value TTRs (highly length-sensitive) and fully local analyses: it uses controlled, local sampling to produce a more stable indicator of lexical diversity at a chosen observational scale, but its interpretability requires explicit reporting of windowing and tokenisation choices.