kb/data/en.wikipedia.org/wiki/Sexual_dimorphism_measures-2.md

title	chunk	source	category	tags	date_saved	instance
Sexual dimorphism measures	3/3	https://en.wikipedia.org/wiki/Sexual_dimorphism_measures	reference	science, encyclopedia	2026-05-05T03:55:39.844988+00:00	kb-cron

    R
  

{\displaystyle R}

being the real line. The smaller the overlapping area the greater the gap between the two functions

      π
      
        1
      
    
    
      f
      
        1
      
    
  

{\displaystyle \pi _{1}f_{1}}

and

      π
      
        2
      
    
    
      f
      
        2
      
    
  

{\displaystyle \pi _{2}f_{2}}

, in which case the sexual dimorphism is greater. Obviously, this index is a function of the five parameters that characterize a mixture of two normal components

    (
    
      μ
      
        i
      
    
    ,
    
      σ
      
        i
      
      
        2
      
    
    ,
    
      π
      
        1
      
    
    ,
    i
    =
    1
    ,
    2
    )
  

{\displaystyle (\mu _{i},\sigma _{i}^{2},\pi _{1},i=1,2)}

. Its range is in the interval

    (
    0
    ,
    0.5
    ]
  

{\displaystyle (0,0.5]}

, and the interested reader can see, in the work of the authors who proposed the index, the way in which an interval estimate is constructed.

=== Measures based on non-parametric methods === Marini et al. (1999) have suggested the Kolmogorov-Smirnov distance as a measure of sexual dimorphism. The authors use the following form of the statistic,

      max
      
        x
      
    
    ⁡
    
      |
    
    
      F
      
        1
      
    
    (
    x
    )
    −
    
      F
      
        2
      
    
    (
    x
    )
    
      |
    
    ,
  

{\displaystyle \operatorname {max} _{x}|F_{1}(x)-F_{2}(x)|,}

with

      F
      
        i
      
    
    ,
    i
    =
    1
    ,
    2
  

{\displaystyle F_{i},i=1,2}

being sample cumulative distributions corresponding to two independent random samples. Such a distance has the advantage of being applicable whatever the form of the random variable distributions concerned, yet they should be continuous. The use of this distance assumes that two populations are involved. Further, the Kolmogorov-Smirnov distance is a sample function whose aim is to test that the two samples under analysis have been selected from a single distribution. If one accepts the null hypothesis, then there is not sexual dimorphism; otherwise, there is.

== See also == Bateman's principle Digit ratio Gender differences Sexual dimorphism

== References ==