Difference between revisions of "Stratified sample"
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| + | $#C+1 = 17 : ~/encyclopedia/old_files/data/S090/S.0900440 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 $ 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) $: | ||
| + | |||
| + | $$ | ||
| + | |||
| + | where the $ i $- | ||
| + | th sample $ X _ {i1} \dots X _ {in _ {i} } $ | ||
| + | contains only those elements of the original sample which have the mark $ i $. | ||
| + | As a result of this decomposition, the original sample becomes stratified into $ k $ | ||
| + | strata $ X _ {i1} \dots X _ {in _ {i} } $, | ||
| + | $ i = 1 \dots k $, | ||
| + | where the $ i $- | ||
| + | th stratum contains information about the $ i $- | ||
| + | th mark. This notion gives rise, for example, to realizations of the $ X $- | ||
| + | component of a two-dimensional random variable $ ( X, Y) $ | ||
| + | whose second component $ Y $ | ||
| + | has a discrete distribution. | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> S.S. Wilks, "Mathematical statistics" , Wiley (1962)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> S.S. Wilks, "Mathematical statistics" , Wiley (1962)</TD></TR></table> | ||
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====Comments==== | ====Comments==== | ||
| − | |||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> W.G. Cochran, "Sampling techniques" , Wiley (1977)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> W.G. Cochran, "Sampling techniques" , Wiley (1977)</TD></TR></table> | ||
Revision as of 08:23, 6 June 2020
A sample which is broken up into several samples of smaller sizes by certain distinguishing marks (characteristics). Let each element of some sample of size $ N \geq 2 $
possess one and only one of $ k \geq 2 $
possible marks. Then the original sample can be broken into $ k $
samples of sizes $ n _ {1} \dots n _ {k} $,
respectively $ ( n _ {1} + \dots + n _ {k} = N) $:
$$
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
| [1] | S.S. Wilks, "Mathematical statistics" , Wiley (1962) |
Comments
References
| [a1] | W.G. Cochran, "Sampling techniques" , Wiley (1977) |
How to Cite This Entry:
Stratified sample. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stratified_sample&oldid=48869
Stratified sample. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stratified_sample&oldid=48869
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article