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Vibratory function of the vocal folds is largely determined by the rheological properties or viscoelastic shear properties of the vocal fold lamina propria. To date, investigation of the sample size estimation and statistical experimental design for vocal fold rheological studies is nonexistent. The current work provides the closed-form sample size formulas for two major study designs (i.e. paired and two-group designs) in vocal fold research. Our results demonstrated that the paired design could greatly increase the statistical power compared to the two-group design. By comparing the variance of estimated treatment effect, this study also confirms that ignoring within-subject and within-vocal fold correlations during rheological data analysis will likely increase type I errors. Finally, viscoelastic shear properties of intact and scarred rabbit vocal fold lamina propria were measured and used to illustrate theoretical findings in a realistic scenario and project sample size requirement for future studies.