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A [[Sample|sample]] which is broken up into several samples of smaller sizes by certain distinguishing marks (characteristics). Let each element of some sample of size  $  N \geq  2 $
possess one and only one of  $  k \geq  2 $
possible marks. Then the original sample can be broken into  $  k $
samples of sizes  $  n _ {1} \dots n _ {k} $, 
respectively  $  ( n _ {1} + \dots + n _ {k} = N) $:

$$ 

\begin{array}{c}
X _ {11} \dots X _ {1n _ {1}  } ,  \\
X _ {21} \dots X _ {2n _ {2}  } ,  \\
{} \dots \dots \dots  \\
X _ {k1} \dots X _ {kn _ {k}  } ,  \\
\end{array}

$$

where the  $  i $-
th sample  $  X _ {i1} \dots X _ {in _ {i}  } $
contains only those elements of the original sample which have the mark  $  i $. 
As a result of this decomposition, the original sample becomes stratified into  $  k $
strata  $  X _ {i1} \dots X _ {in _ {i}  } $, 
$  i = 1 \dots k $, 
where the  $  i $-
th stratum contains information about the  $  i $-
th mark. This notion gives rise, for example, to realizations of the  $  X $-
component of a two-dimensional random variable  $  ( X, Y) $
whose second component  $  Y $
has a discrete distribution.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  S.S. Wilks,   "Mathematical statistics" , Wiley  (1962)</TD></TR></table>

====Comments====

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  W.G. Cochran,   "Sampling techniques" , Wiley  (1977)</TD></TR></table>