Sample size matters in calculating Pillai scores.

Area of Science:

• Linguistics
• Sociophonetics
• Quantitative Linguistics

Background:

• Pillai scores are standard for quantifying vowel overlap in sociolinguistics.
• Lack of established thresholds leads to inconsistent interpretations of vowel merger.
• Pillai scores' parametric nature makes them sensitive to sample size variations.

Purpose of the Study:

• To investigate the impact of sample size on Pillai score reliability.
• To determine if unequal group sizes affect Pillai score calculations.
• To establish guidelines for using Pillai scores to identify merged vowels.

Main Methods:

• Utilized generated data from simulated, underlyingly merged vowels.
• Analyzed the relationship between sample size and Pillai score accuracy.
• Assessed the influence of unequal class sizes on Pillai score computation.

Main Results:

• Larger sample sizes yield more reliable Pillai scores for vowel overlap.
• Unequal group sizes do not significantly impact Pillai score calculations.
• Substantial data are required to achieve reliably low Pillai scores for merged vowels.

Conclusions:

• Recommends strategies for enhancing Pillai score reliability in sociolinguistic research.
• Provides a formula to aid researchers in setting appropriate thresholds for merged vowel detection.
• Offers practical guidance and a case study for applying these recommendations.