# 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]

## Notes

1. ^ Auffarth, B., Lopez, M., Cerquides, J. (2010). Comparison of redundancy and relevance measures for feature selection in tissue classification of CT images. Advances in Data Mining. Applications and Theoretical Aspects. p. 248--262. Springer. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.170.1528
2. ^ Pomeroy, S.L. et al. Gene Expression-Based Classification and Outcome Prediction of Central Nervous System Embryonal Tumors. Nature 415, 436–442.