Difference between revisions of "Stratified sample"
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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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s0904401.png" /> possess one and only one of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s0904402.png" /> possible marks. Then the original sample can be broken into <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s0904403.png" /> samples of sizes <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s0904404.png" />, respectively <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s0904405.png" />: |
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− | + | <table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s0904406.png" /></td> </tr></table> | |
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− | + | where the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s0904407.png" />-th sample <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s0904408.png" /> contains only those elements of the original sample which have the mark <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s0904409.png" />. As a result of this decomposition, the original sample becomes stratified into <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s09044010.png" /> strata <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s09044011.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s09044012.png" />, where the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s09044013.png" />-th stratum contains information about the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s09044014.png" />-th mark. This notion gives rise, for example, to realizations of the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s09044015.png" />-component of a two-dimensional random variable <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s09044016.png" /> whose second component <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090440/s09044017.png" /> has a discrete distribution. | |
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− | + | ====References==== | |
+ | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> S.S. Wilks, "Mathematical statistics" , Wiley (1962)</TD></TR></table> | ||
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====Comments==== | ====Comments==== | ||
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====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> W.G. Cochran, "Sampling techniques" , Wiley (1977)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> W.G. Cochran, "Sampling techniques" , Wiley (1977)</TD></TR></table> |
Revision as of 14:53, 7 June 2020
A sample which is broken up into several samples of smaller sizes by certain distinguishing marks (characteristics). Let each element of some sample of size possess one and only one of
possible marks. Then the original sample can be broken into
samples of sizes
, respectively
:
![]() |
where the -th sample
contains only those elements of the original sample which have the mark
. As a result of this decomposition, the original sample becomes stratified into
strata
,
, where the
-th stratum contains information about the
-th mark. This notion gives rise, for example, to realizations of the
-component of a two-dimensional random variable
whose second component
has a discrete distribution.
References
[1] | S.S. Wilks, "Mathematical statistics" , Wiley (1962) |
Comments
References
[a1] | W.G. Cochran, "Sampling techniques" , Wiley (1977) |
Stratified sample. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stratified_sample&oldid=48869