# Signal-to-noise statistic

From HandWiki

In mathematics the **signal-to-noise statistic** distance between two vectors *a* and *b* with mean values [math]\displaystyle{ \mu _a }[/math] and [math]\displaystyle{ \mu _b }[/math] and standard deviation [math]\displaystyle{ \sigma _a }[/math] and [math]\displaystyle{ \sigma _b }[/math] respectively is:

- [math]\displaystyle{ D_{sn} = {(\mu _a - \mu _b) \over (\sigma _a + \sigma _b)} }[/math]

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)

## Notes

- ↑ 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.
- ↑ Golub, T.R. et al. (1999) Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring. Science 286, 531-537,
- ↑ Slonim D.K. et al. (2000) Class Prediction and Discovery Using Gene Expression Data. Procs. of the Fourth Annual International Conference on Computational Molecular Biology Tokyo, Japan April 8 - 11, p263-272
- ↑ Pomeroy, S.L. et al. (2002) Gene Expression-Based Classification and Outcome Prediction of Central Nervous System Embryonal Tumors. Nature 415, 436–442.

Original source: https://en.wikipedia.org/wiki/Signal-to-noise statistic.
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