Analysis of MT pattern and component data

We computed the partial correlation for the pattern and component predictions using the method developed by Movshon et al. (1985). For each cell, we used the response latency (determined using the method described above) to determine the window over which we calculated these correlations. That is, if a cell's latency was determined to be 50 ms, we calculated the correlations based on tuning curves made from responses 50 ms to 370 ms (the response latency plus the stimulus duration) after the transitions in our dynamic MT stimulus. The partial correlations for the pattern and component predictions are of the form:

$$R_p = \frac{(r_p - r_c~r_{pc})}{\sqrt{(1 - r_c^2) (1 - r_{pc}^2)}}$$

and

$$R_c = \frac{(r_c - r_p~r_{pc})}{\sqrt{(1 - r_p^2) (1 - r_{pc}^2)}},$$

where $r_c$ is the correlation of the data with the component prediction, $r_p$ is the correlation of the data with the pattern prediction, and $r_{pc}$ is the correlation of the two predictions.

Because the sampling distribution of Pearson's $r$ is not normal, we used the Fisher z-transformation for its variance-stabilizing effect. We took each value of $R_p$ or $R_c$ and converted it to a z-score using the following equation (shown for $R_p$):

$$Z_p = \frac{0.5 ^. ln \left(\frac{(1 + R_p)}{(1 - R_p)} \right)} {\sqrt{\frac{1}{df}}},$$

where df is the degrees of freedom, equal to the number of values in the tuning curve minus three (there were twelve directions in our tuning curves). The numerator of the equation is the Fisher z-transformation. Each value of $Z_c$ or $Z_p$ can then be tested for significance. We used a criterion of 1.28, equivalent to p$=$0.90, for this purpose. In order to be judged as a PDS cell, the value of $Z_p$ must exceed the value of $Z_c$ (or zero, if $Z_c$ is negative) by this amount. Similarly, $Z_c$ must exceed $Z_p$ by that same amount (1.28) for a cell to be judged as CDS. If a cell meets neither of these conditions, it remains unclassified.