Here is the imaginary component of the cross-spectrum in the jth trial. Sample size is a concern when using WPLI and hence we used WPLI-debiased, which estimates the squared WPLI. WPLI-debiased has negligible sample size bias for data sets of small sample size61. To test for the difference in WPLI-debiased coherence across experimental conditions, we first averaged the WPLI-debiased theta-band coherence across the appropriate time window for each channel pair (for example, 400–1,100 ms following the target stimulus as the delay related WPLI-debiased theta coherence and 700 ms prior to fixation point onset as the baseline WPLI-debiased coherence in the memory-guided saccade task). Then, we performed a t-test to investigate whether there is a statistically significant difference across experimental conditions. We performed the comparison of WPLI-debiased coherence between correct and error trials with the adjusted number of correct trials relative to errors and the results showed significant effects as we have reported in this manuscript. We also used a permutation test to further validate the results obtained by the t-tests. In this test, we pooled the data from two conditions
