Measure and statistical test for cross-correlation between paired neuronal spike trains with small sample size

Recent development of multi-unit recording techniques such as optical recording and multi-electrode arrays makes it possible to record neuronal activities from tens or hundreds of neurons simultaneously. To analyze functional connections between these neurons, cross-correlation analysis has been most commonly applied to the hundreds to thousands of pairs of these neurons. However, conventional cross-correlation data needs statistical tests for significance especially when the sample size of recorded spike trains is small. Here, a multiple hypergeometric model based on a transformation of the cross-correlogram data to a 2 x J table has been suggested. The exact p value for significance can be obtained by the generalized Fisher's method with small sample size and a cross-correlation coefficient for the strength of cross-correlation can be obtained based on the R-square analogue for nominal data. For large sample size, chi 2 test can be applied based on the same transformation. Examples of real spike train data set and simulation show that the methods are applicable to the data of multi-unit activity with only tens of spikes. These methods are especially useful when thousands of cross-correlograms need to be screened quickly and automatically.