 
Summary: A relative position code for saccades in dorsal
premotor cortex
Bijan Pesaran, Matthew J. Nelson and Richard A. Andersen
Supplementary Material
Estimation bias in the statistical test for separability
The idealized neuronal responses in Fig 2 show that separability is associated with a
first singular value whose amplitude is large compared with the second singular value. It
is difficult to establish statistical significance by directly comparing the amplitude of the
first and second singular values as they are ordered amplitudes with the first singular
value being necessarily larger than the second. To avoid this problem, we defined
separability by a significantly (p < 0.05) large first singular value compared to the first
singular value calculated when trial conditions were randomized by permuting the rows
and columns of the response matrix (Randomization test, 10,000 permutations). Unlike
permuting the trial labels and then recalculating the response matrix, permuting the rows
and columns preserves the variability of the response matrix.
To test whether the above procedure for testing for separability is subject to
estimation bias, we simulated the idealized neuronal responses for the six cases
presented in Fig 2 as we varied the amount of data available for estimation. We
generated 3, 5, 10, 100, 1000 or 10000 simulated trials for each configuration by
drawing the number of spikes in each trial from a Poisson distribution with a mean rate
