Signal-to-noise statistic

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> the signal-to-noise statistic <a href="/facts/Distance/hbXlaEFk">distance</a> between two <a href="/facts/Vector_(geometric)/bCLrdksy">vectors</a> a and b with <a href="/facts/Arithmetic_Mean/L3Pv333o">mean</a> values 
 
 
 
 
 μ
 
 a
 
 
 
 
 {\displaystyle \mu _{a}}
 
 and 
 
 
 
 
 μ
 
 b
 
 
 
 
 {\displaystyle \mu _{b}}
 
 and <a href="/facts/Standard_deviation/qSug9BRl">standard deviation</a> 
 
 
 
 
 σ
 
 a
 
 
 
 
 {\displaystyle \sigma _{a}}
 
 and 
 
 
 
 
 σ
 
 b
 
 
 
 
 {\displaystyle \sigma _{b}}
 
 respectively is:

D
          
            s
            n
          
        
        =
        
          
            
              (
              
                μ
                
                  a
                
              
              −
              
                μ
                
                  b
                
              
              )
            
            
              (
              
                σ
                
                  a
                
              
              +
              
                σ
                
                  b
                
              
              )
            
          
        
      
    
    {\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. 
This distance is frequently used to identify vectors that have significant difference. One usage is in <a href="/facts/Bioinformatics/D5x2L8ee">bioinformatics</a> to locate <a href="/facts/Genes/e1swwPY6">genes</a> that are differential <a href="/facts/Gene_expression/alCPohLR">expressed</a> on <a href="/facts/Microarray/LvJeNodc">microarray</a> experiments.

Signal-to-noise statistic open-in-new

Signal-to-noise statistic