Lexical Diversity Metrics

Lexical diversity measures vocabulary richness by quantifying the relationship between unique words (types) and total words (tokens).

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Available Metrics

TTR (Type-Token Ratio)

• Formula: Types / Tokens
• Range: 0 to 1
• Note: Sensitive to text length

CTTR (Corrected TTR)

• Formula: Types / sqrt(2 × Tokens)
• Note: Partially corrects for text length

MSTTR (Mean Segmental TTR)

• Method: Divides text into segments (default 100 words) and averages TTR
• Range: 0 to 1

MATTR (Moving Average TTR)

• Method: Calculates TTR for a moving window and averages
• Range: 0 to 1
• Note: More stable across text lengths

MTLD (Measure of Textual Lexical Diversity)

• Method: Calculates mean length of word strings maintaining TTR above threshold
• Note: Text-length independent

Maas

• Formula: (log(Tokens) - log(Types)) / log(Tokens)²
• Note: Lower values = higher diversity (inverse scale)

Yule's K

• Method: Based on word frequency distribution
• Note: Lower values = higher diversity (inverse scale)

Simpson's D

• Method: Probability two randomly selected words are the same
• Range: 0 to 1
• Note: Lower values = higher diversity (inverse scale)

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Usage Notes

• MTLD and MATTR are more stable across different text lengths
• TTR is sensitive to text length - compare only similar-length texts
• Maas, Yule's K, and Simpson's D use inverse scales (lower = more diverse)

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