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Ann Biomed Eng. 2013 Feb;41(2):349-65. doi: 10.1007/s10439-012-0668-3. Epub 2012 Oct 12.

The appropriate use of approximate entropy and sample entropy with short data sets.

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Nebraska Biomechanics Core Facility, Department of Health, Physical Education, and Recreation, University of Nebraska at Omaha, 6001 Dodge Street, Omaha, NE 68182, USA.


Approximate entropy (ApEn) and sample entropy (SampEn) are mathematical algorithms created to measure the repeatability or predictability within a time series. Both algorithms are extremely sensitive to their input parameters: m (length of the data segment being compared), r (similarity criterion), and N (length of data). There is no established consensus on parameter selection in short data sets, especially for biological data. Therefore, the purpose of this research was to examine the robustness of these two entropy algorithms by exploring the effect of changing parameter values on short data sets. Data with known theoretical entropy qualities as well as experimental data from both healthy young and older adults was utilized. Our results demonstrate that both ApEn and SampEn are extremely sensitive to parameter choices, especially for very short data sets, N ≤ 200. We suggest using N larger than 200, an m of 2 and examine several r values before selecting your parameters. Extreme caution should be used when choosing parameters for experimental studies with both algorithms. Based on our current findings, it appears that SampEn is more reliable for short data sets. SampEn was less sensitive to changes in data length and demonstrated fewer problems with relative consistency.

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