Signal-to-noise statistic

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

${\displaystyle D_{sn}={(\mu _{a}-\mu _{b}) \over (\sigma _{a}+\sigma _{b})}}$

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][3][4]

See also

• Distance
• Uniform norm
• Manhattan distance
• Signal-to-noise ratio
• Signal to noise ratio (imaging)