Figure 4. Population decoding and correlations. A, An example population showing the decoding performance of the population (black) and the best individual unit (gray) plotted against coherence. The two data sets were both fitted with a Weibull curve to determine the threshold, defined as the level of coherence that achieves 82% correct. B, Population thresholds plotted against the threshold of the best unit for all populations. All populations had thresholds lower than the threshold of the best individual unit. C, Another example population, showing the performance of the standard decoding procedure (black), performance when correlations were removed (light gray), and performance when correlations were ignored (dark gray). D, Effects of correlations. The thresholds from the standard decoding procedure are plotted against the thresholds obtained when correlations were removed, showing a statistically significant decrease in the median threshold (p = 0.025, Wilcoxon signed-rank test). Star symbols represent populations in which the difference is statistically significant (p < 0.05; bootstrap). E, Effects of ignoring correlations. The thresholds from the standard decoding procedure are plotted against the thresholds obtained when correlations were ignored, showing a small but statistically significant increase in the median threshold (p = 0.007, Wilcoxon signed-rank test). F, The change in thresholds when correlations were ignored was significantly positively correlated with change in thresholds when correlations were removed (Spearman’s ρ = 0.647, p = 0.005). The change in threshold was calculated as the standard threshold minus the remove or ignore correlations threshold. Therefore, for the x-axis, negative values represent populations which had lower (better performance) thresholds in the standard decoding compared to decoding when correlations where ignored. These were the units that were above the line of unity in E, and were the majority of populations. For the y-axis, positive values indicate populations that had higher thresholds (worse performance) for the standard decoder in comparison to decoding when correlations where removed. These were the units below the line of unit in D and were the majority of the populations.