Measuring the coherence of intracranial electroencephalograms

Objective: Previous coherence studies of human intracranial electroencephal ograms (EEGs) can be faulted on two methodological issues: (I) coherence es timates in a majority were formed from a very small number of independent s ample spectra, and (2) the statistical significance of coherence estimates was either not reported or was poorly evaluated. Coherence estimator perfor mance may be poor when a small number of independent sample spectra are emp loyed, and the coupling of poor estimation and statistical testing can resu lt in inaccuracy in the measurement of coherence. The performance character istics of the coherence estimator and statistical testing of coherence esti mates are described in this manuscript. Methods: The bias, variance, probability density functions, and confidence intervals of the estimate of magnitude squared coherence (MSC); and power a nalysis for the test of zero MSC were developed from the exact analytic for m of the probability density function of the estimate of MSC for Gaussian r andom processes. The coherence of a single epoch of background EEG, recorde d from a patient with intractable seizures, was evaluated with different pa rameter values to aid in the exposition of the concepts developed here. Results: The statistical characteristics of WOSA coherence estimates are a function of a single estimator parameter, the number of independent sample spectra employed in the estimation. Bias and variance are high, confidence intervals may be large, and the probability of Type II errors is high if a small number of independent sample spectra are employed. A considerable imp rovement in measurement accuracy is possible with careful selection of esti mator parameter values. Conclusions: Coherence measurement accuracy can be improved over previous a pplications by attention to estimator performance and accurate statistical testing of coherence estimates. (C) 1999 Elsevier Science Ireland Ltd. All rights reserved.