Date Approved


Graduate Degree Type


Degree Name

Engineering (M.S.E.)

Degree Program

School of Engineering

First Advisor

Samhita Rhodes

Second Advisor

Gordon Alderink

Third Advisor

Nicholas Baine

Academic Year



Approximate entropy (ApEn) and sample entropy (SampEn) are statistical methods designed to quantify the regularity or predictability of a time series. Although ApEn has been a prominent choice for use, it is currently unclear as to which method and parameter selection combination is optimal for its application in biomechanics. The goal of this thesis was to examine the difference between ApEn and SampEn related to center of pressure (COP) data during standing balance tasks, while also refining tolerance r, to determine entropy optimization. Six participants completed five 30-second, feet together and tandem standing, trials under eyes-open and eyes-closed conditions. Ground reaction force platform data (1200 Hz) was collected and downsampled to provide a 60 Hz COP time series. ApEn and SampEn were calculated using a constant pattern length, i.e., m = 2, and multiple values of r (tolerance). Four separate one-way analysis of variance analyses (ANOVA) were conducted for ApEn and SampEn in the anterior posterior (AP) and medial lateral (ML) directions. Dunnett's intervals were applied to the one-way ANOVA analyses to determine which conditions differed significantly. ApEn and SampEn provided comparable results in the predictability of patterns for different stability conditions, with increasing instability being associated with greater unpredictability. The selection of r had a relatively consistent effect on mean ApEn and SampEn values across r = 0.15 – 0.25*SD, where both entropy methods tended to decrease as r increased. Mean SampEn values were generally lower than ApEn values. The results suggest that both ApEn and SampEn indices were equally effective in quantifying the level of center of pressure signal regularity during quiet tandem standing postural balance tests.