# Signal-to-noise statistic

In mathematics the signal-to-noise statistic distance between two vectors a and b with mean values $\mu _a$ and $\mu _b$ and standard deviation $\sigma _a$ and $\sigma _b$ respectively is:

$D_{sn} = {(\mu _a - \mu _b) \over (\sigma _a + \sigma _b)}$

In the case of Gaussian-distributed data and unbiased class distributions, this statistic can be related to classification accuracy given an ideal linear discrimination, and a decision boundary can be derived.[1]

This distance is frequently used to identify vectors that have significant difference. One usage is in bioinformatics to locate genes that are differential expressed on microarray experiments.[2]