## 1 Introduction
PS excels over coherence analysis in terms of being able to account for nonlinearity [16]. Moreover, a study has shown that differences have been found in terms of the synchronization between within-band connections and between-band connections (e.g., within the delta band; between the delta and theta bands) [17]. This study in particular also discovered that AD patients showed much a lower strength of synchronization for between-frequency band analysis when compared to HC. PS has several indices of measurement, with the **phase-lag index (PLI)** and **phase-locking value (PLV)** being the most-used measures [18]. The PLI takes a time-series of phase differences and computes the asymmetry corresponding to the distribution of these phase differences [19]. In a recent PS study using the PLI as the index of choice, results showed that in AD patients, the lower alpha band presented a decrease in functional connectivity situated in the posterior region [20]. On the other hand, PLV looks at the consistency in phase difference. The PLV value ranges from zero, indicating random phase differences, to one, indicating a fixed phase difference [21]. For example, a study performing cross-frequency coupling (CFC), using PLV on AD patients, reached the conclusion that oscillations in the alpha band, and more specifically around the dominant peak, are phase-locked with the gamma band power [22]. Results were observable in the posterior region of the brain, suggesting that AD elicits a region-specific change in functional connectivity. It is noteworthy that functional connectivity entails its own drawbacks too. In a comprehensive review of different methods for functional connectivity analysis and their caveats, [PERSON] and [PERSON] indicated that many of the connectivity measures are prone to volume conduction and hence can yield false positive results [16]. This is particularly the case for methods using unipolar derivations with a common reference. However, as it will be further explained in this paper, this study employed bipolar EEG montages, thus greatly diminishing the issue. The same review study [16] highlighted another disadvantage of functional connectivity, namely the signal-to-noise ratio (SNR) problem; an excessive amount of noise in the signal of interest during the EEG signal retrieval may cause false connectivity results. In sum, the current state-of-the-art calls for a comparison between computational methods that are used for diagnosis of Alzheimer's disease. The reviewed literature focusing on spectral analysis and functional connectivity demonstrates a scarcity of studies employing both methods in diagnosis of AD. It should be mentioned that although spectral analysis and functional connectivity analysis have different applications from a physiological perspective, applying both methods on a single dataset can be useful in determining the more accurate method in the diagnosis of AD based on brain activity. This is the gap that this study aimed to address. So far, several studies have reported the outcomes of either of the two methods [23; 24]. However, conducting a connectivity analysis and comparing it with a spectral analysis using the same dataset presents two advantages; (1) it shows which method can yield the most accurate and complete information in AD diagnosis [3], and (2) it can identify the affected ROIs instead of solely looking at whether the patient suffers from AD, which is believed to help predicting AD in its early stages of development [12]. The proposed study serves as a comparison between two methods in qEEG, namely the spectral and functional connectivity analyses. Having highlighted the advantages of PS over other connectivity measures, this study aimed to investigate the performance of PS in differentiating AD patients from HCs as compared to conventional FFT. This is done with the goal of identifying the most efficient method in implementation of machine-assisted diagnosis tools in the future clinical assessment of AD.