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In this study, computer simulation examples consisting of various signals with different complexity were compared. It was found that neither approximate entropy (ApEn) nor sample entropy (SampEn) methods was accurate in measuring signals' complexity when the recommended values (e.g., m = 2 and r = 0.1-0.2 times the standard deviation of the signal) were strictly adhered to. However, when we selected the maximum ApEn value as determined by considering many different r values, we were able to correctly discern a signal's complexity for both synthetic and experimental data. However, this requires that many different choices of r values need to be considered. This is a very cumbersome and time-consuming process. Thus, the primary goal of the present work is to illustrate our recently developed method that can automatically select the appropriate tolerance threshold value r, which corresponds to the maximum ApEn value, without resorting to the calculation of ApEn for each of the threshold values selected in the range of zero and one times the standard deviation.