Testing the Gaussianity of the Human EEG During Anesthesia

R. Bender; B. Schultz; A. Schultz; I. Pichlmayr

doi:10.1055/s-0038-1634859

Methods of Information in Medicine, Table of Contents

Methods Inf Med 1992; 31(01): 56-59
DOI: 10.1055/s-0038-1634859

Original Article

Schattauer GmbH

Testing the Gaussianity of the Human EEG During Anesthesia

R. Bender

¹Department of Anesthesiology, Hannover Medical School, Germany

,

B. Schultz

¹Department of Anesthesiology, Hannover Medical School, Germany

,

A. Schultz

¹Department of Anesthesiology, Hannover Medical School, Germany

,

I. Pichlmayr

¹Department of Anesthesiology, Hannover Medical School, Germany

› Author Affiliations

Abstract

Abstract:

The Gaussian properties of human EEGs, which were measured over various stages of general anesthesia, were tested. The basis of the method was to describe the EEG signals by autoregressive models and to test the normality of the regression residuals with the Shapiro-Wilk statistic. The results show that in general the human EEG during anesthesia can be considered as a realization of a Gaussian stochastic process.

Key-words

EEG - Gaussianity - AR Model - Residuals - Shapiro-Wilk Test

Full Text

References

REFERENCES
1 Saunders MG. Amplitude probability density studies on alpha and alpha-like patterns. Electroenceph Clin Neurophysiol 1963; 15: 761-7.
2 Campbell J, Bower E, Dwyer SJ, Lado GV. On the sufficiency of autocorrelation functions as EEG descriptors. IEEE Trans Biomed Eng 1967; 14: 49-52.
3 Weiss MS. Non-Gaussian properties of the EEG during sleep. Electroenceph Clin Neurophysiol 1973; 34: 200-2.
4 McEwen J, Anderson GB. Modelling the stationarity and Gaussianity of spontaneous electroencephalographic activity. IEEE Trans Biomed Eng 1975; 22: 361-9.
5 Dumermuth G, Gasser T, Lange B. Aspects of EEG analysis in the frequency domain. In: Dolce G, Kiinkel H. eds. CEAN -Computerized EEG Analysis. Stuttgart: Fischer Verlag; 1975: 429-57.
6 Elul R. Gaussian behavior of the electroencephalogram: Changes during performance of mental task. Science 1969; 164: 328-31.
7 Persson J. Comments on estimations and tests of EEG amplitude distributions. Electroenceph Clin Neurophysiol 1974; 37: 309-13.
8 Shapiro SS, Wilk MB. An analysis of variance test for normality (complete samples). Biometrika 1965; 52: 591-611.
9 Box GEP, Jenkins GM. Time Series Analysis. Forecasting and Control. 2nd ed).. San Francisco: Holden-Day; 1976
10 Zetterberg LH. Estimation of parameters for a linear difference equation with applications to EEG analysis. Math Biosciences 1969; 05: 227-75.
11 Gersch W. Spectral analysis of EEGs by autoregressive decomposition of time series. Math Biosciences 1970; 07: 205-22.
12 Sato K. Biomedical basis for data processing. In: Yamaguchi N, Fujisawa K. eds. Recent Advances in EEG and EMG Data Processing. Amsterdam: EIsevier/North-Holland Biomedical Press; 1981: 79-84.
13 Lopes FDa Silva. EEG analysis: Theory and practice. In: Niedermayer E, Lopes Da Silva F. eds. Electroencephalography. Munchen: Urban & Schwarzenberg; 1987: 872-97.
14 Tong H. Non-linear Time Series. Oxford: Claredon Press; 1990
15 Pierce DA. Testing normality in autoregressive models. Biometrika 1985; 72: 293-7.
16 Ljung GM, Box GEP. On a measure of lack of fit in time series models. Biometrika 1978; 65: 297-303.
17 Shapiro SS, Wilk MB, Chen MJ. A comparative study of various tests for normality. J Am Statist Assoc 1968; 63: 1343-72.
18 Kugler J. Elektroenzephalographie in Klinik und Praxis. Stuttgart, New York: Thieme Verlag; 1981
19 Jansen BH, Hasman A, Lenten R, Visser SL. Usefulness of autoregressive models to classify EEG-segments. Biomed Techn 1979; 24: 216-23.
20 SAS. SAS Language Guide, Release 6.03 Edition. Cary. NC: SAS Institute Inc; 1988
21 SAS. SAS Procedures Guide, Release 6.03 Edition. Cary, NC: SAS Institute Inc; 1988
22 SAS. SAS/STAT User’s Guide, Release 6.03 Edition. Cary, NC: SAS Institute Inc; 1988
23 SAS, SAS/GRAPH User’s Guide. Release 6.03 Edition. Cary, NC: SAS Institute Inc; 1988
24 Lomnicki ZA. Tests for departure from normality in the case of a linear stochastic process. Metrika 1961; 04: 37-62.
25 Gasser T. Goodness-of-fit tests for correlated data. Biometrika 1975; 62: 563-70.
26 Mallows CL. Linear processes are nearly Gaussian. J Appl Prob 1967; 04: 313-29.
27 Granger CWJ, Newbold P. Forecasting Economic Time Series. New York: Academic Press; 1977