# The Sample Size Matters: To What Extent the Participant Reduction Affects the Outcomes of a Neuroscientific Research. A Case-Study in Neuromarketing Field

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Sample and Design

#### 2.2. Neurophysiological Data Recording

- Index 3: descriptor of the autonomic response, namely, the emotional index (EI), computed as the combination between the SCL and the HR measures, as described by Vecchiato and colleagues [52].

#### 2.3. Data Analysis and Statistics

- Group-mean values of the index (function of t, i.e., the task duration), for each of the 630 combinations. We so obtained 630 vectors ‘v630’ (thus resulting in a matrix 630 x t);
- Pearson correlation between each ‘v630’ (630 x t) and the vector ‘v’ (1 x t), containing the mean values of the index computed over the entire population (36 subjects);
- Mean Squared Error (MSE) to describe the error committed considering each ‘v630’ rather than ‘v’ along each task (within-task variability):$$MSE=\frac{{{\displaystyle \sum}}_{i=1}^{t}{\left(v{630}_{i}-{v}_{i}\right)}^{2}}{t}$$

- 4.
- The standard deviation of the 630 values assumed by the vectors ‘v630’, for every second of the task itself (between-groups variability):$$STD=\sqrt{\frac{{{\displaystyle \sum}}_{n=1}^{630}{\left(v{630}_{n}-\overline{v630}\right)}^{2}}{630}}$$

^{−5}[53]. The Shapiro Wilk test [54] of normality demonstrated that data (the Rho correlation coefficients, MSE, and STD values) were not Gaussian; hence, the non-parametric Friedman test [55] was performed to assess the difference between groups. Specifically, the subgroups of subjects (32, 28, 24, 20, 16) were considered as within factors for the analysis run over the Rho values resulting from the correlation analysis, the MSE and the STD values. The analysis was performed for each of the three considered indices and each of the four selected spots. Nemenyi post-hoc test [56], specifically conceived for non-parametric repeated measures ANOVA (i.e., the Friedman test), was applied to further analyse the significant effects and interactions.

## 3. Results

#### 3.1. The Effect of the Index

^{−5}). The Friedman test evidenced a significant decreasing effect of the mean rho values depending on the sub-groups, Figure 2a (Friedman chi-squared = 1868, p-value < 2.2 × 10

^{−16}). The post-hoc analysis showed that rho significantly decreased from 32 to 16 subjects, assuming different values for each subgroup (p < 0.05).

^{−16}): it was significantly lower for 32 subjects, increasing with the sample size reduction. The highest error was committed considering 16 subjects instead of 36. All the groups were significantly different as showed by the Nemenyi test.

^{−16}). It was lower for 32 subjects, increasing with the reduction of the sample size. The post-hoc analysis demonstrated that STD was significantly different for each subgroup.

^{−5}). Concerning the subgroups of 24, 20, and 16 subjects, 13 over 630, 92 over 630, and 237 over 630 correlations were respectively not significant. The Friedman analysis on rho, MSE, and STD showed the effect of the groups, with a significant increase of rho (Friedman chi-squared = 1868, p-value < 2.2 × 10

^{−16}), a significant increase of MSE (Friedman chi-squared = 1932.3, p-value < 2.2 × 10

^{−16}), and a significant increase of STD from 32 to 16 subjects (Friedman chi-squared = 124, p-value < 2.2 × 10

^{−16}). The post-hoc Nemenyi test evidenced that all the subgroups assumed different values of rho, MSE, and STD.

^{−5}). The Friedman analysis on rho, MSE, and STD showed the effect of the groups, with a significant increase of rho (Friedman chi-squared = 2235.5, p-value < 2.2 × 10

^{−16}), a significant increase of MSE (Friedman chi-squared = 2232.1, p-value < 2.2 × 10

^{−16}), and a significant increase of STD from 32 to 16 subjects (Friedman chi-squared = 124, p-value < 2.2 × 10

^{−16}). The post-hoc Nemenyi test evidenced that all the subgroups assumed different values of rho, MSE, and STD.

#### 3.2. The Effect of the Task

^{−5}), while for the subgroups 32 and 28 for Index2 and Index3. The analysis evidenced that reducing the sample size at 24:10 and 49 over 630 correlations were not significant for Index2 and Index3, respectively. For a sample size of 20 subjects, 8, 90, and 138 over 630 correlations were not significant for the three indices, respectively. Moving on, 16 subjects, 49, 215, and 290 over 630 were not significant for the three indices, respectively. Friedman test on rho, MSE, and STD revealed a significant effect of the groups for the three indices, showing rho decreasing (Index1: Friedman chi-squared = 1879.4, p-value < 2.2 × 10

^{−16}; Index2: Friedman chi-squared = 1800.9, p-value < 2.2 × 10

^{−16}; Index3: Friedman chi-squared = 1888.1, p-value < 2.2 × 10

^{−16}), MSE increasing (Index1: Friedman chi-squared = 2124.8, p-value < 2.2 × 10

^{−16}; Index2: Friedman chi-squared = 2151.2, p-value < 2.2 × 10

^{−16}; Index3: Friedman chi-squared = 2182.7, p-value < 2.2 × 10

^{−16}), and STD increasing (Index1: Friedman chi-squared = 124, p-value < 2.2 × 10

^{−16}; Index2: Friedman chi-squared = Friedman chi-squared = 124, p-value < 2.2 × 10

^{−16}; Index3: Friedman chi-squared = 124, p-value < 2.2 × 10

^{−16}). The post-hoc test showed that all the comparisons between groups were significant.

#### 3.3. The Effect of the Time

^{−5}). Concerning Index1, 12, 53, and 136 correlations over 630 were not significant in subgroups 24, 20, and 16, respectively, while for Index3, 2, 63, and 216 correlations were not significant in those subgroups. Considering Index2, the number of not-significant correlations increased from the subgroup of 28 subjects in which 23 correlations were not significant, while 115, 290, and 408 over 630 correlations were not significant for the subgroups of 24, 20, and 16 subjects, respectively. Friedman test on rho values revealed a significant effect of the groups for the three indices, showing a rho decreasing related to the reduction of the sample size (Index1: Friedman chi-squared = 1712.1, p-value < 2.2 × 10

^{−16}; Index2: Friedman chi-squared = 1586.3, p-value < 2.2 × 10

^{−16}; Index3: Friedman chi-squared = 2017.2, p-value < 2.2 × 10

^{−16}). Post-hoc test showed that all the comparisons between groups were significant. The analysis of SPOT4, showed that all the correlations were significant for the subgroups of 32 subjects, for both Index1 and Index3 (p < 8 × 10

^{−5}). Concerning Index1 63, 214, 335 and 464 correlations over 630 were not significant in subgroups 28, 24, 20 and 16 respectively, while for Index3, 19, 122, 296 and 423 correlations were not significant in those subgroups. Considering Index2, the number of not-significant correlations increased, already from the subgroup of 32 subjects in which 7 correlations were not significant, while 82, 203, 342, 450 over 630 correlations were not significant for the subgroups of 28, 24, 20 and 16 subjects, respectively. Friedman test on rho values revealed a significant effect of the groups for the three indices, showing rho decrease related to the reduction of the sample size (Index1: Friedman chi-squared = 1510.9, p-value < 2.2 × 10

^{−16}; Index2: Friedman chi-squared = 1263, p-value < 2.2 × 10

^{−16}; Index3: Friedman chi-squared = 1617.6, p-value < 2.2 × 10

^{−16}). The post-hoc test showed that all the comparisons between groups were significant.

#### 3.4. Rho-Sample Size Relationship

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Larson, M.J.; Carbine, K.A. Sample size calculations in human electrophysiology (EEG and ERP) studies: A systematic review and recommendations for increased rigor. Int. J. Psychophysiol.
**2017**, 111, 33–41. [Google Scholar] [CrossRef] - Button, K.S.; Ioannidis, J.P.; Mokrysz, C.; Nosek, B.A.; Flint, J.; Robinson, E.S.; Munafò, M.R. Power failure: Why small sample size undermines the reliability of neuroscience. Nat. Rev. Neurosci.
**2013**, 14, 365–376. [Google Scholar] [CrossRef] [PubMed][Green Version] - Eng, J. Sample size estimation: How many individuals should be studied? Radiology
**2003**, 227, 309–313. [Google Scholar] [CrossRef] [PubMed][Green Version] - Sanders, N.; Choo, S.; Nam, C.S. The EEG cookbook: A practical guide to neuroergonomics research. In Cognitive Science and Technology; Springer: Berlin, Germany, 2020; pp. 33–51. [Google Scholar]
- Mao, Z.; Jung, T.P.; Lin, C.T.; Huang, Y. Predicting EEG sample size required for classification calibration. In Proceedings of the Foundations of Augmented Cognition: Neuroergonomics and Operational Neuroscience—AC 2016, Toronto, ON, Canada, 17–22 July 2016; Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer: Cham, Switzerland, 2016; Volume 9743, pp. 57–68. [Google Scholar] [CrossRef]
- Anderson, S.F.; Kelley, K.; Maxwell, S.E. Sample-size planning for more accurate statistical power: A method adjusting sample effect sizes for publication bias and uncertainty. Psychol. Sci.
**2017**, 28, 1547–1562. [Google Scholar] [CrossRef] [PubMed][Green Version] - Sim, J.; Saunders, B.; Waterfield, J.; Kingstone, T. Can sample size in qualitative research be determined a priori? Int. J. Soc. Res. Methodol.
**2018**, 21, 619–634. [Google Scholar] [CrossRef] - Javanmard, A.; Montanari, A. Debiasing the lasso: Optimal sample size for Gaussian designs. Ann. Stat.
**2018**, 46, 2593–2622. [Google Scholar] [CrossRef][Green Version] - Combrisson, E.; Jerbi, K. Exceeding chance level by chance: The caveat of theoretical chance levels in brain signal classification and statistical assessment of decoding accuracy. J. Neurosci. Methods
**2015**, 250, 126–136. [Google Scholar] [CrossRef] - Baker, D.H.; Vilidaite, G.; Lygo, F.A.; Smith, A.K.; Flack, T.R.; Gouws, A.D.; Andrews, T.J. Power contours: Optimising sample size and precision in experimental psychology and human neuroscience. Psychol. Methods
**2021**, 26, 295–314. [Google Scholar] [CrossRef] - Guttmann-Flury, E.; Sheng, X.; Zhang, D.; Zhu, X. A priori sample size determination for the number of subjects in an EEG experiment. In Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS), Berlin, Germany, 23–27 July 2019; pp. 5180–5183. [Google Scholar] [CrossRef]
- Nosek, B.A.; Spies, J.R.; Motyl, M. Scientific Utopia: II. Restructuring incentives and practices to promote truth over publishability. Perspect. Psychol. Sci.
**2012**, 7, 615–631. [Google Scholar] [CrossRef] [PubMed][Green Version] - Arico, P.; Borghini, G.; Di Flumeri, G.; Sciaraffa, N.; Babiloni, F. Passive BCI beyond the lab: Current trends and future directions. Physiol. Meas.
**2018**, 39, 08TR02. [Google Scholar] [CrossRef] - Di Flumeri, G.; Aricò, P.; Borghini, G.; Sciaraffa, N.; Di Florio, A.; Babiloni, F. The dry revolution: Evaluation of three different eeg dry electrode types in terms of signal spectral features, mental states classification and usability. Sensors
**2019**, 19, 1365. [Google Scholar] [CrossRef][Green Version] - Ayaz, H.; Dehais, F. Neuroergonomics: The Brain at Work and in Everyday Life; Elsevier: Amsterdam, The Netherlands, 2018. [Google Scholar]
- Mühl, C.; Jeunet, C.; Lotte, F. EEG-based workload estimation across affective contexts. Front. Neurosci.
**2014**, 8, 114. [Google Scholar] [CrossRef][Green Version] - Berka, C.; Levendowski, D.J.; Lumicao, M.N.; Yau, A.; Davis, G.; Zivkovic, V.T.; Olmstead, R.E.; Tremoulet, P.D.; Craven, P.L. EEG correlates of task engagement and mental workload in vigilance, learning, and memory tasks. Aviat. Space Environ. Med.
**2007**, 78, B231–B244. [Google Scholar] - Di Flumeri, G.; De Crescenzio, F.; Berberian, B.; Ohneiser, O.; Kramer, J.; Aricò, P.; Borghini, G.; Babiloni, F.; Bagassi, S.; Piastra, S. Brain–computer interface-based adaptive automation to prevent out-of-the-loop phenomenon in air traffic controllers dealing with highly automated systems. Front. Hum. Neurosci.
**2019**, 13, 296. [Google Scholar] [CrossRef] [PubMed][Green Version] - Karthaus, M.; Wascher, E.; Getzmann, S. Proactive vs. reactive car driving: EEG evidence for different driving strategies of older drivers. PLoS ONE
**2018**, 13, e0191500. [Google Scholar] [CrossRef][Green Version] - Di Flumeri, G.; Borghini, G.; Aricò, P.; Sciaraffa, N.; Lanzi, P.; Pozzi, S.; Vignali, V.; Lantieri, C.; Bichicchi, A.; Simone, A.; et al. EEG-based mental workload neurometric to evaluate the impact of different traffic and road conditions in real driving settings. Front. Hum. Neurosci.
**2018**, 12, 509. [Google Scholar] [CrossRef] [PubMed][Green Version] - Islam, M.R.; Barua, S.; Ahmed, M.U.; Begum, S.; Aricò, P.; Borghini, G.; Di Flumeri, G. A novel mutual information based feature set for drivers’ mental workload evaluation using machine learning. Brain Sci.
**2020**, 10, 551. [Google Scholar] [CrossRef] [PubMed] - Liu, X.; Zhang, J.; Yin, J.; Bi, S.; Eisenbach, M.; Wang, Y. Monte Carlo simulation of order-disorder transition in refractory high entropy alloys: A data-driven approach. Comput. Mater. Sci.
**2021**, 187, 110135. [Google Scholar] [CrossRef] - Chavarriaga, R.; Khaliliardali, Z.; Gheorghe, L.; Iturrate, I.; Millán, J.D.R. EEG-based decoding of error-related brain activity in a real-world driving task. J. Neural Eng.
**2015**, 12, 066028. [Google Scholar] [CrossRef][Green Version] - Marucci, M.; Di Flumeri, G.; Borghini, G.; Sciaraffa, N.; Scandola, M.; Pavone, E.F.; Babiloni, F.; Betti, V.; Aricò, P. The impact of multisensory integration and perceptual load in virtual reality settings on performance, workload and presence. Sci. Rep.
**2021**, 11, 4831. [Google Scholar] [CrossRef] - Cherubino, P.; Martinez-Levy, A.C.; Caratu, M.; Cartocci, G.; Di Flumeri, G.; Modica, E.; Rossi, D.; Mancini, M.; Trettel, A. Consumer behaviour through the eyes of neurophysiological measures: State-of-the-art and future trends. Comput. Intell. Neurosci.
**2019**, 2019, 1976847. [Google Scholar] [CrossRef] [PubMed][Green Version] - Morin, C. Neuromarketing: The new science of consumer behavior. Society
**2011**, 48, 131–135. [Google Scholar] [CrossRef][Green Version] - Sciaraffa, N.; Borghini, G.; Di Flumeri, G.; Cincotti, F.; Babiloni, F.; Aricò, P. Joint analysis of eye blinks and brain activity to investigate attentional demand during a visual search task. Brain Sci.
**2021**, 11, 562. [Google Scholar] [CrossRef] - Amores, J.; Richer, R.; Zhao, N.; Maes, P.; Eskofier, B.M. Promoting relaxation using virtual reality, olfactory interfaces and wearable EEG. In Proceedings of the 2018 IEEE 15th International Conference on Wearable and Implantable Body Sensor Networks (BSN 2018), Las Vegas, NV, USA, 4–7 March 2018; Volume 2018, pp. 98–101. [Google Scholar] [CrossRef][Green Version]
- Di Flumeri, G.; Aricò, P.; Borghini, G.; Sciaraffa, N.; Maglione, A.G.; Rossi, D.; Modica, E.; Trettel, A.; Babiloni, F.; Colosimo, A.; et al. EEG-based Approach-Withdrawal index for the pleasantness evaluation during taste experience in realistic settings. In Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS), Jeju, Korea, 11–15 July 2017; pp. 3228–3231. [Google Scholar] [CrossRef]
- Yoto, A.; Moriyama, T.; Yokogoshi, H.; Nakamura, Y.; Katsuno, T.; Nakayama, T. Effect of smelling green tea rich in aroma components on EEG activity and memory task performance. Int. J. Affect. Eng.
**2014**, 13, 227–233. [Google Scholar] [CrossRef][Green Version] - Velavan, T.P.; Meyer, C.G. The COVID-19 epidemic. Trop. Med. Int. Health
**2020**, 25, 278–280. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bazzani, A.; Ravaioli, S.; Trieste, L.; Faraguna, U.; Turchetti, G. Is EEG suitable for marketing research? A systematic review. Front. Neurosci.
**2020**, 14, 594566. [Google Scholar] [CrossRef] [PubMed] - Friston, K. Ten ironic rules for non-statistical reviewers. Neuroimage
**2012**, 61, 1300–1310. [Google Scholar] [CrossRef] [PubMed] - Vecchiato, G.; Toppi, J.; Astolfi, L.; Fallani, F.D.V.; Cincotti, F.; Mattia, D.; Bez, F.; Babiloni, F. Spectral EEG frontal asymmetries correlate with the experienced pleasantness of TV commercial advertisements. Med. Biol. Eng. Comput.
**2011**, 49, 579–583. [Google Scholar] [CrossRef] - Cartocci, G.; Cherubino, P.; Rossi, D.; Modica, E.; Maglione, A.G.; Di Flumeri, G.; Babiloni, F. Gender and age related effects while watching TV advertisements: An EEG study. Comput. Intell. Neurosci.
**2016**, 2016, 3795325. [Google Scholar] [CrossRef][Green Version] - Nielsen. Advertising and Audiences: Making Ad Dollars Make Sense. Available online: https://www.nielsen.com/us/en/insights/article/2014/advertising-and-audiences-making-ad-dollars-make-sense/ (accessed on 27 August 2021).
- Belouchrani, A.; Abed-Meraim, K.; Cardoso, J.F.; Moulines, E. A blind source separation technique using second-order statistics. IEEE Trans. Signal. Process.
**1997**, 45, 434–444. [Google Scholar] [CrossRef][Green Version] - Delorme, A.; Makeig, S. EEGLAB: An open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J. Neurosci. Methods
**2004**, 134, 9–21. [Google Scholar] [CrossRef][Green Version] - EEGLAB Wiki. 6. Reject Artifacts. Available online: https://eeglab.org/tutorials/06_RejectArtifacts/ (accessed on 28 May 2021).
- Doppelmayr, M.; Klimesch, W.; Pachinger, T.; Ripper, B. Individual differences in brain dynamics: Important implications for the calculation of event-related band power. Biol. Cybern.
**1998**, 79, 49–57. [Google Scholar] [CrossRef] - Klimesch, W. EEG alpha and theta oscillations reflect cognitive and memory performance: A review and analysis. Brain Res. Rev.
**1999**, 29, 169–195. [Google Scholar] [CrossRef] - Skrandies, W. Global field power and topographic similarity. Brain Topogr.
**1990**, 3, 137–141. [Google Scholar] [CrossRef] [PubMed] - Society for Psychophysiological Research Ad Hoc Committee on Electrodermal Measures; Boucsein, W.; Fowles, D.C.; Grimnes, S.; Ben-Shakhar, G.; Roth, W.T.; Dawson, M.E.; Filion, D.L. Publication recommendations for electrodermal measurements. Psychophysiology
**2012**, 49, 1017–1034. [Google Scholar] [CrossRef] - Pan, J.; Tompkins, W.J. A real-time QRS detection algorithm. IEEE Trans. Biomed. Eng.
**1985**, BME-32, 230–236. [Google Scholar] [CrossRef] [PubMed] - Benedek, M.; Kaernbach, C. A continuous measure of phasic electrodermal activity. J. Neurosci. Methods
**2010**, 190, 80–91. [Google Scholar] [CrossRef] [PubMed][Green Version] - Klimesch, W. Alpha-band oscillations, attention, and controlled access to stored information. Trends Cogn. Sci.
**2012**, 16, 606–617. [Google Scholar] [CrossRef][Green Version] - Magosso, E.; De Crescenzio, F.; Ricci, G.; Piastra, S.; Ursino, M. EEG alpha power is modulated by attentional changes during cognitive tasks and virtual reality immersion. Comput. Intell. Neurosci.
**2019**, 2019, 7051079. [Google Scholar] [CrossRef] [PubMed][Green Version] - Briesemeister, B.B.; Tamm, S.; Heine, A.; Jacobs, A.M. Approach the good, withdraw from the bad—A review on frontal alpha asymmetry measures in applied psychological research. Psychology
**2013**, 4, 261–267. [Google Scholar] [CrossRef][Green Version] - Modica, E.; Cartocci, G.; Rossi, D.; Martinez Levy, A.C.; Cherubino, P.; Maglione, A.G.; Di Flumeri, G.; Mancini, M.; Montanari, M.; Perrotta, D.; et al. Neurophysiological responses to different product experiences. Comput. Intell. Neurosci.
**2018**, 2018, 9616301. [Google Scholar] [CrossRef] - Cartocci, G.; Modica, E.; Rossi, D.; Inguscio, B.; Arico, P.; Martinez Levy, A.C.; Mancini, M.; Cherubino, P.; Babiloni, F. Antismoking campaigns’ perception and gender differences: A comparison among EEG indices. Comput. Intell. Neurosci.
**2019**, 2019, 7348795. [Google Scholar] [CrossRef][Green Version] - Davidson, R.J.; Ekman, P.; Saron, C.D.; Senulis, J.A.; Friesen, W.V. Approach-withdrawal and cerebral asymmetry: Emotional expression and brain physiology I. J. Pers. Soc. Psychol.
**1990**, 58, 330–341. [Google Scholar] [CrossRef] - Vecchiato, G.; Maglione, A.G.; Cherubino, P.; Wasikowska, B.; Wawrzyniak, A.; Latuszynska, A.; Latuszynska, M.; Nermend, K.; Graziani, I.; Leucci, M.R.; et al. Neurophysiological tools to investigate consumer’s gender differences during the observation of TV commercials. Comput. Math. Methods Med.
**2014**, 2014, 912981. [Google Scholar] [CrossRef] - Bonferroni, C.E. Teoria Statistica delle Classi e Calcolo delle Probabilità—Google Libri. Available online: https://books.google.it/books/about/Teoria_statistica_delle_classi_e_calcolo.html?id=3CY-HQAACAAJ&redir_esc=y (accessed on 24 August 2021).
- Shapiro, S.S.; Wilk, M. An analysis of variance test for normality (complete samples). Biometrika
**1965**, 52, 591–611. [Google Scholar] [CrossRef] - Friedman, M. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Am. Stat. Assoc.
**1937**, 32, 675. [Google Scholar] [CrossRef] - Nemenyi, P.B. Distribution-Free Multiple Comparisons; ProQuest: Ann Arbor, MI, USA, 1963. [Google Scholar]
- Xu, J.; Zhong, B. Review on portable EEG technology in educational research. Comput. Hum. Behav.
**2018**, 81, 340–349. [Google Scholar] [CrossRef] - Cohen, J. Statistical Power Analysis for the Behavioral Sciences; Routledge: New York, NY, USA, 1988. [Google Scholar]
- Mukaka, M.M. Statistics corner: A guide to appropriate use of correlation coefficient in medical research. Malawi Med. J.
**2012**, 24, 69–71. Available online: www.mmj.medcol.mw (accessed on 1 July 2021). [PubMed] - Vabalas, A.; Gowen, E.; Poliakoff, E.; Casson, A.J. Machine learning algorithm validation with a limited sample size. PLoS ONE
**2019**, 14, e0224365. [Google Scholar] [CrossRef] - Khodayari-Rostamabad, A.; Reilly, J.P.; Hasey, G.M.; de Bruin, H.; MacCrimmon, D.J. A machine learning approach using EEG data to predict response to SSRI treatment for major depressive disorder. Clin. Neurophysiol.
**2013**, 124, 1975–1985. [Google Scholar] [CrossRef] - Zander, T.O.; Andreessen, L.M.; Berg, A.; Bleuel, M.; Pawlitzki, J.; Zawallich, L.; Krol, L.R.; Gramann, K. Evaluation of a dry EEG system for application of passive brain-computer interfaces in autonomous driving. Front. Hum. Neurosci.
**2017**, 11, 78. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kar, S.; Bhagat, M.; Routray, A. EEG signal analysis for the assessment and quantification of driver’s fatigue. Transp. Res. Part F Traffic Psychol. Behav.
**2010**, 13, 297–306. [Google Scholar] [CrossRef] - Noshadi, S.; Abootalebi, V.; Sadeghi, M.T.; Shahvazian, M.S. Selection of an efficient feature space for EEG-based mental task discrimination. Biocybern. Biomed. Eng.
**2014**, 34, 159–168. [Google Scholar] [CrossRef] - Frederick, J.A. Psychophysics of EEG alpha state discrimination. Conscious. Cogn.
**2012**, 21, 1345–1354. [Google Scholar] [CrossRef] [PubMed][Green Version] - Dietrich, A.; Kanso, R. A review of EEG, ERP, and neuroimaging studies of creativity and insight. Psychol. Bull.
**2010**, 136, 822–848. [Google Scholar] [CrossRef]

**Figure 1.**The graph represents the trend of ‘v’, the mean value of Index1 computed over the entire population (36 subjects) during SPOT1 (ALL). The dashed lines show the trend of the maximum and minimum values (Max, Min) of the index among the ‘v630’ for each second, in each subgroup of subjects (32, 28, 24, 20, 16).

**Figure 2.**The box plots represent the effect of the subgroup of subjects on (

**a**) Rho values, (

**b**) MSE values, and (

**c**) STD values, computed for Index 1, during the SPOT 1.

**Figure 3.**Graphical representation of the trend of rho correlation coefficient at reducing the sample size (subgroups) with respect to the ‘full population index’ (36 participants). Tasks (

**a**) and (

**b**) were 30 s long, Task (

**c**) 20 s, and Task (

**d**) 15 s long.

**Table 1.**Number of significant correlations (#s.c.) and eventual decreasing as percentage of the total number of combinations (630), median ± std of rho, MSE, and STD for the three indices (I1, I2, I3) and the five subgroups of subjects (32, 28, 24, 20, 16) during SPOT1.

SPOT1(30 s) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

#s.c. (p < 8 × 10^{−5}) | Rho | MSE | STD | |||||||||

I1 | I2 | I3 | I1 | I2 | I3 | I1 | I2 | I3 | I1 | I2 | I3 | |

32 | 630 * | 630 * | 630 * | 0.96 ± 0.02 | 0.94 ± 0.02 | 0.97 ± 0.01 | 0.012 ± 0.01 | 0.014 ± 0.01 | 0.001 ± 0.0005 | 0.12 ± 0.02 | 0.13 ± 0.01 | 0.03 ± 0.003 |

28 | 630 * | 630 * | 630 * | 0.91 ± 0.04 | 0.89 ± 0.05 | 0.94 ± 0.02 | 0.029 ± 0.02 | 0.032 ± 0.02 | 0.002 ± 0.001 | 0,18 ± 0.03 | 0,19 ± 0.02 | 0.05 ± 0.004 |

24 | 628 (−0.3%) | 617 (−2.1%) | 630 * | 0.87 ± 0.06 | 0.84 ± 0.07 | 0.90 ± 0.03 | 0,05 ± 0.03 | 0,053 ± 0.03 | 0,004 ± 0.002 | 0.23 ± 0.04 | 0.23 ± 0.03 | 0.07 ± 0.007 |

20 | 597 (−5.2%) | 538 (−14.6%) | 630 * | 0.81 ± 0,08 | 0.76 ± 0.10 | 0.86 ± 0.04 | 0,079 ± 0.06 | 0,089 ± 0.05 | 0,007 ± 0.003 | 0.30 ± 0.05 | 0.31 ± 0.04 | 0.09 ± 0.007 |

16 | 479 (−23.9%) | 393 (−37.6%) | 618 (−1.9%) | 0.74 ± 0.12 | 0.69 ± 0.12 | 0.79 ± 0.06 | 0.128 ± 0.08 | 0.136 ± 0.08 | 0.011 ± 0.005 | 0.37 ± 0.06 | 0.38 ± 0.04 | 0.11 ± 0.01 |

**Table 2.**Number of significant correlations (#s.c.) and eventual decreasing as percentage of the total number of combinations (630), median ± std of rho, MSE, and STD for the three indices (I1, I2, I3) and the five subgroups of subjects (32, 28, 24, 20, 16) during SPOT2.

SPOT2 (30 s) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

#s.c. (p < 8 × 10^{−5}) | Rho | MSE | STD | |||||||||

I1 | I2 | I3 | I1 | I2 | I3 | I1 | I2 | I3 | I1 | I2 | I3 | |

32 | 630 * | 630 * | 630 * | 0.98 ± 0.007 | 0.95 ± 0.02 | 0.94 ± 0.02 | 0.02 ± 0.01 | 0.02 ± 0.01 | 0.001 ± 0.00 | 0.14 ± 0.02 | 0.13 ± 0.02 | 0.03 ± 0.004 |

28 | 630 * | 630 * | 630 * | 0.96 ± 0.01 | 0.9 ± 0.04 | 0.88 ± 0.04 | 0.04 ± 0.01 | 0.04 ± 0.02 | 0.002 ± 0.00 | 0.21 ± 0.02 | 0.19 ± 0.03 | 0.05 ± 0.006 |

24 | 630 * | 620 (−1.6%) | 598 (−5.1%) | 0.94 ± 0.03 | 0.84 ± 0.07 | 0.81 ± 0.07 | 0.07 ± 0.03 | 0.07 ± 0.03 | 0.004 ± 0.001 | 0.27 ± 0.04 | 0.26 ± 0.05 | 0.07 ± 0.008 |

20 | 622 (−1.2%) | 540 (−14.3%) | 492 (−21.9%) | 0.91 ± 0.06 | 0.78 ± 0.10 | 0.74 ± 0.11 | 0.12 ± 0.05 | 0.11 ± 0.05 | 0.007 ± 0.003 | 0.34 ± 0.04 | 0.32 ± 0.06 | 0.08 ± 0.01 |

16 | 581 (−7.8%) | 415 (−34.1%) | 340 (−46%) | 0.86 ± 0.08 | 0.70 ± 0.13 | 0.67 ± 0.14 | 0.18 ± 0.07 | 0.17 ± 0.07 | 0.01 ± 0.004 | 0.42 ± 0.06 | 0.40 ± 0.07 | 0.1 ± 0.02 |

**Table 3.**Number of significant correlations (#s.c.) and eventual decrease as percentage of the total number of combinations (630), median ± std of rho values for the three indices (I1, I2, I3), and the five subgroups of subjects (32, 28, 24, 20, 16) during SPOT3 and SPOT4.

SPOT3 (20 s) | SPOT4 (15 s) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

#s.c. (p < 8 × 10^{−5}) | Rho | #s.c. (p < 8 × 10^{−5}) | Rho | |||||||||

I1 | I2 | I3 | I1 | I2 | I3 | I1 | I2 | I3 | I1 | I2 | I3 | |

32 | 630 * | 630 * | 630 * | 0.98 ± 0.01 | 0.95 ± 0.03 | 0.98 ± 0.01 | 630 * | 623 (−1.1%) | 630 * | 0.96 ± 0.026 | 0.96 ± 0.04 | 0.97 ± 0.01 |

28 | 630 * | 607 (−3.6%) | 630 * | 0.95 ± 0.03 | 0.88 ± 0.06 | 0.95 ± 0.02 | 567 (−10%) | 548 (−13%) | 611 (−3%) | 0.92 ± 0.04 | 0.93 ± 0.05 | 0.94 ± 0.02 |

24 | 618 (−1.9%) | 515 (−18.2%) | 628 (−0.3%) | 0.92 ± 0.05 | 0.83 ± 0.08 | 0.92 ± 0.04 | 416 (−33.9%) | 427 (−32.2%) | 508 (−19.3%) | 0.87 ± 0.09 | 0.87 ± 0.13 | 0.89 ± 0.04 |

20 | 577 (−8.4%) | 340 (−46%) | 567 (−10%) | 0.88 ± 0.07 | 0.76 ± 0.13 | 0.87 ± 0.06 | 295 (−53.2%) | 288 (−54.3%) | 334 (−46.9%) | 0.80 ± 0.12 | 0.81 ± 0.19 | 0.84 ± 0.06 |

16 | 494 (−21.6%) | 222 (−64.7%) | 414 (−34.3%) | 0.83 ± 0.10 | 0.70 ± 0.16 | 0.81 ± 0.07 | 166 (−73.7%) | 180 (−71.4%) | 207 (−67.1%) | 0.74 ± 0.17 | 0.77 ± 0.24 | 0.78 ± 0.08 |

**Table 4.**Number of significant correlations (#s.c.) and eventual decreasing as percentage of the total number of combinations (630) for the three indices (INDEX1, INDEX2, INDEX3) and the five subgroups of subjects (32, 28, 24, 20, 16) during SPOT1 (30 s), SPOT2 (30 s), SPOT3 (20 s), and SPOT4 (15 s).

INDEX1 | INDEX2 | INDEX3 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

#s.c. (p < 8 × 10^{−5}) | #s.c. (p < 8 × 10^{−5}) | #s.c. (p < 8 × 10^{−5}) | ||||||||||

30 s | 30 s | 20 s | 15 s | 30 s | 30 s | 20 s | 15 s | 30 s | 30 s | 20 s | 15 s | |

32 | 630 * | 630 * | 630 * | 630 * | 630 * | 630 * | 630 * | 623 (−1.1%) | 630 * | 630 * | 630 * | 630 * |

28 | 630 * | 630 * | 630 * | 567 (−10%) | 630 * | 630 * | 607 (−3,6%) | 548 (−13%) | 630 * | 630 * | 630 * | 611 (−3%) |

24 | 628 (−0.3%) | 630 * | 618 (−1.9%) | 416 (−33.9%) | 617 (−2.1%) | 620 (−1.6%) | 515 (−18.2%) | 427 (−32.2%) | 630 * | 598 (−5.1%) | 628 (−0.3%) | 508 (−19.3%) |

20 | 597 (−5.2%) | 622 (−1.2%) | 577 (−8.4%) | 295 (−53.2%) | 538 (−14.6%) | 540 (−14.3%) | 340 (−46%) | 288 (−54.3%) | 630 * | 492 (−21.9%) | 567 (−10%) | 334 (−46.9%) |

16 | 479 (−23.9%) | 581 (−7.8%) | 494 (−21.6%) | 166 (−73.7%) | 393 (−37.6%) | 415 (−34.1%) | 222 (−64.7%) | 180 (−71.4%) | 618 (−1.9%) | 340 (−46%) | 414 (−34.3%) | 207 (−67.1%) |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vozzi, A.; Ronca, V.; Aricò, P.; Borghini, G.; Sciaraffa, N.; Cherubino, P.; Trettel, A.; Babiloni, F.; Di Flumeri, G.
The Sample Size Matters: To What Extent the Participant Reduction Affects the Outcomes of a Neuroscientific Research. A Case-Study in Neuromarketing Field. *Sensors* **2021**, *21*, 6088.
https://doi.org/10.3390/s21186088

**AMA Style**

Vozzi A, Ronca V, Aricò P, Borghini G, Sciaraffa N, Cherubino P, Trettel A, Babiloni F, Di Flumeri G.
The Sample Size Matters: To What Extent the Participant Reduction Affects the Outcomes of a Neuroscientific Research. A Case-Study in Neuromarketing Field. *Sensors*. 2021; 21(18):6088.
https://doi.org/10.3390/s21186088

**Chicago/Turabian Style**

Vozzi, Alessia, Vincenzo Ronca, Pietro Aricò, Gianluca Borghini, Nicolina Sciaraffa, Patrizia Cherubino, Arianna Trettel, Fabio Babiloni, and Gianluca Di Flumeri.
2021. "The Sample Size Matters: To What Extent the Participant Reduction Affects the Outcomes of a Neuroscientific Research. A Case-Study in Neuromarketing Field" *Sensors* 21, no. 18: 6088.
https://doi.org/10.3390/s21186088