Due to the discrete nature of experimental trials and the fact that MI results cannot be lower than 0, noise tends to bias MI results upwards (Treves and Panzeri, 1995; Panzeri et al., 2007). To assess the likelihood that a given MI result is not simply the result of noise, we calculated a p value for each MI result by randomizing the joint observations 100 times and recalculating the MI for these null surrogates. The randomization procedure preserved the marginal distributions. The p value was then calculated as the proportion of null surrogates with a MI result greater than or equal to the observed value in the real data. In the case where all null MI values were less than the result from the real data, the p value was set to 0.005 = 0.5 × (1/100) due to the resolution associated with using 100 null surrogates.
