Permutation entropy (PE) is increasingly studied as an EEG biomarker for Alzheimers disease and related dementias. However, PE requires specifying two free parameters (embedding order and delay) whose interaction with sampling rate determines the timescale being measured. No study in the PE-dementia literature has tested whether results are robust across parameterizations. Here we demonstrate they are not. On 1,177 clinical EEGs from the CAUEEG dataset (457 Normal, 414 MCI, 306 Dementia), we computed PE on alpha-band (8-12 Hz) signals using four parameterizations spanning different timescales and state-space sizes, on eyes-closed segments with artifact exclusion and per-segment entropy computation to avoid boundary artifacts. The results diverged dramatically: effect sizes for dementia vs. normal ranged from d = -0.700 (decreased PE, p < 0.0001) to d = +0.709 (increased PE, p < 0.0001) depending solely on parameter choice, with two parameterizations yielding complete nulls (d {approx} 0). The commonly used sub-cycle parameterization (order = 3, delay = 1) produced a large effect by measuring local waveform curvature rather than ordinal pattern complexity. With theoretically appropriate alpha-timescale parameters (order = 5, delay = 5; 100 ms embedding window spanning one full alpha cycle), PE was a complete null (d = -0.025, p = 0.73). To contextualize these findings against conventional spectral analysis, we computed the relative alpha/theta power ratio as a spectral baseline (d = -0.727, AUC = 0.739). We show that PEs null at proper parameters reflects a structural limitation: PEs rank-order design discards all distance information between values, rendering it blind to the regularity structure that distinguishes healthy alpha oscillations from the fragmented activity in dementia. By contrast, alpha-band sample entropy (SE), whose Chebyshev distance metric preserves absolute differences between time points, showed the strongest entropy effect (d = 0.519, age-corrected d = 0.373, AUC = 0.720) and was essentially independent of spectral power (r = -0.043). Combining SE with the spectral power ratio in a bivariate model yielded AUC = 0.786 for dementia detection, demonstrating that these orthogonal features are complementary. The alpha/theta Lempel-Ziv Complexity ratio (d = 0.471, age-corrected d = 0.364) shared 52% of its variance with the power ratio, indicating it largely indexes spectral content. We additionally report a pre-specified validation of the LZC ratio from a discovery dataset (N = 88). These findings indicate that PE results are not comparable across studies unless parameters and sampling rates match exactly, that PE is structurally unsuited to detecting the regularity disruption characteristic of oscillatory pathology, and that distance-based entropy measures like SE deserve priority over ordinal measures in EEG biomarker research for dementia.
