Stratified sampling - Revision history

2A11:FC84:82E3:B44E:185B:BBAB:CE52:EC53: /* References */

2024-08-23T15:03:05Z

References

← Previous revision		Revision as of 15:03, 23 August 2024
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	<ref name=minimax-sampling>{{cite journal\|last1=Shahrokh Esfahani\|first1=Mohammad\|last2=Dougherty, Edward R.\|title=Effect of separate sampling on classification accuracy\|journal=Bioinformatics\|date=2014\|volume=30\|issue=2\|pages=242–250\|doi=10.1093/bioinformatics/btt662\|pmid=24257187\|author2-link=Edward R. Dougherty\|doi-access=free}}</ref>		<ref name=minimax-sampling>{{cite journal\|last1=Shahrokh Esfahani\|first1=Mohammad\|last2=Dougherty, Edward R.\|title=Effect of separate sampling on classification accuracy\|journal=Bioinformatics\|date=2014\|volume=30\|issue=2\|pages=242–250\|doi=10.1093/bioinformatics/btt662\|pmid=24257187\|author2-link=Edward R. Dougherty\|doi-access=free}}</ref>
	}}		}}
			нжЕя

	==Further reading==		==Further reading==

Zingarese: Reverted edits by 170.246.145.202 (talk): disruptive edits (HG) (3.4.12)

2024-07-17T16:47:48Z

Reverted edits by 170.246.145.202 (talk): disruptive edits (HG) (3.4.12)

← Previous revision		Revision as of 16:47, 17 July 2024
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	== Example==		== Example==
	Assume that we need to estimate the average number of votes for each candidate in an election. Assume that a country has 3 towns: Town A has 1 million factory workers, Town B has 2 million office workers and Town C has 3 million retirees. We can choose to get a random sample of size 60 over the entire population but there is some chance that the resulting random sample is poorly balanced across these towns and hence is biased, causing a significant error in estimation (when the outcome of interest has a different distribution, in terms of the parameter of interest, between the towns). Instead, if we choose to take a random sample of 10, 20 and 30 from Town A, B and C respectively, then we can produce a smaller error in estimation for the same total sample size. This method is generally used when a population is not a homogeneous group.		Assume that we need to estimate the average number of votes for each candidate in an election. Assume that a country has 3 towns: Town A has 1 million factory workers, Town B has 2 million office workers and Town C has 3 million retirees. We can choose to get a random sample of size 60 over the entire population but there is some chance that the resulting random sample is poorly balanced across these towns and hence is biased, causing a significant error in estimation (when the outcome of interest has a different distribution, in terms of the parameter of interest, between the towns). Instead, if we choose to take a random sample of 10, 20 and 30 from Town A, B and C respectively, then we can produce a smaller error in estimation for the same total sample size. This method is generally used when a population is not a homogeneous group.
	йКОЖ

	==Stratified sampling strategies==		==Stratified sampling strategies==

170.246.145.202: /* Example */

2024-07-17T16:47:36Z

Example

← Previous revision		Revision as of 16:47, 17 July 2024
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	== Example==		== Example==
	Assume that we need to estimate the average number of votes for each candidate in an election. Assume that a country has 3 towns: Town A has 1 million factory workers, Town B has 2 million office workers and Town C has 3 million retirees. We can choose to get a random sample of size 60 over the entire population but there is some chance that the resulting random sample is poorly balanced across these towns and hence is biased, causing a significant error in estimation (when the outcome of interest has a different distribution, in terms of the parameter of interest, between the towns). Instead, if we choose to take a random sample of 10, 20 and 30 from Town A, B and C respectively, then we can produce a smaller error in estimation for the same total sample size. This method is generally used when a population is not a homogeneous group.		Assume that we need to estimate the average number of votes for each candidate in an election. Assume that a country has 3 towns: Town A has 1 million factory workers, Town B has 2 million office workers and Town C has 3 million retirees. We can choose to get a random sample of size 60 over the entire population but there is some chance that the resulting random sample is poorly balanced across these towns and hence is biased, causing a significant error in estimation (when the outcome of interest has a different distribution, in terms of the parameter of interest, between the towns). Instead, if we choose to take a random sample of 10, 20 and 30 from Town A, B and C respectively, then we can produce a smaller error in estimation for the same total sample size. This method is generally used when a population is not a homogeneous group.
			йКОЖ

	==Stratified sampling strategies==		==Stratified sampling strategies==

174.111.193.186: Fixing typos and grammar

2024-06-27T22:23:25Z

Fixing typos and grammar

← Previous revision		Revision as of 22:23, 27 June 2024
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	In [[statistical survey]]s, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation ('''stratum''') independently.		In [[statistical survey]]s, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation ('''stratum''') independently.

	'''Stratification''' is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be ''[[Collectively exhaustive events\|collectively exhaustive]]'' and ''[[Mutual exclusivity\|mutually exclusive]]'': every element in the population must be assigned to one and only one stratum. Then ~~samling~~ is done is each stratum for example by [[simple random sampling]]. The objective is to improve the precision of the sample by reducing [[sampling error]]. It can produce a [[weighted mean]] that has less variability than the [[arithmetic mean]] of a [[simple random sample]] of the population.		'''Stratification''' is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be ''[[Collectively exhaustive events\|collectively exhaustive]]'' and ''[[Mutual exclusivity\|mutually exclusive]]'': every element in the population must be assigned to one and only one stratum. Then sampling is done in each stratum, for example: by [[simple random sampling]]. The objective is to improve the precision of the sample by reducing [[sampling error]]. It can produce a [[weighted mean]] that has less variability than the [[arithmetic mean]] of a [[simple random sample]] of the population.

	In [[computational statistics]], stratified sampling is a method of [[variance reduction]] when [[Monte Carlo method]]s are used to estimate population statistics from a known population.<ref name="varred17">{{cite journal\|last1=Botev\|first1=Z.\|last2=Ridder\|first2=A.\|title=Variance Reduction\|journal= Wiley StatsRef: Statistics Reference Online\|date=2017\|pages=1–6\|doi=10.1002/9781118445112.stat07975\|isbn=9781118445112}}</ref>		In [[computational statistics]], stratified sampling is a method of [[variance reduction]] when [[Monte Carlo method]]s are used to estimate population statistics from a known population.<ref name="varred17">{{cite journal\|last1=Botev\|first1=Z.\|last2=Ridder\|first2=A.\|title=Variance Reduction\|journal= Wiley StatsRef: Statistics Reference Online\|date=2017\|pages=1–6\|doi=10.1002/9781118445112.stat07975\|isbn=9781118445112}}</ref>

ScapeProf: Clarified that the sampling in stratum doesn’t have to be SRS.

2024-06-23T05:35:17Z

Clarified that the sampling in stratum doesn’t have to be SRS.

← Previous revision		Revision as of 05:35, 23 June 2024
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	In [[statistical survey]]s, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation ('''stratum''') independently.		In [[statistical survey]]s, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation ('''stratum''') independently.

	'''Stratification''' is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be ''[[Collectively exhaustive events\|collectively exhaustive]]'' and ''[[Mutual exclusivity\|mutually exclusive]]'': every element in the population must be assigned to one and only one stratum. Then [[simple random sampling]] ~~is applied within each stratum~~. The objective is to improve the precision of the sample by reducing [[sampling error]]. It can produce a [[weighted mean]] that has less variability than the [[arithmetic mean]] of a [[simple random sample]] of the population.		'''Stratification''' is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be ''[[Collectively exhaustive events\|collectively exhaustive]]'' and ''[[Mutual exclusivity\|mutually exclusive]]'': every element in the population must be assigned to one and only one stratum. Then samling is done is each stratum for example by [[simple random sampling]]. The objective is to improve the precision of the sample by reducing [[sampling error]]. It can produce a [[weighted mean]] that has less variability than the [[arithmetic mean]] of a [[simple random sample]] of the population.

	In [[computational statistics]], stratified sampling is a method of [[variance reduction]] when [[Monte Carlo method]]s are used to estimate population statistics from a known population.<ref name="varred17">{{cite journal\|last1=Botev\|first1=Z.\|last2=Ridder\|first2=A.\|title=Variance Reduction\|journal= Wiley StatsRef: Statistics Reference Online\|date=2017\|pages=1–6\|doi=10.1002/9781118445112.stat07975\|isbn=9781118445112}}</ref>		In [[computational statistics]], stratified sampling is a method of [[variance reduction]] when [[Monte Carlo method]]s are used to estimate population statistics from a known population.<ref name="varred17">{{cite journal\|last1=Botev\|first1=Z.\|last2=Ridder\|first2=A.\|title=Variance Reduction\|journal= Wiley StatsRef: Statistics Reference Online\|date=2017\|pages=1–6\|doi=10.1002/9781118445112.stat07975\|isbn=9781118445112}}</ref>

ScapeProf: Removed part where it said issue if you can’t partition sample space. This is always possible; just make the leftovers it’s own strata.

2024-06-22T15:36:10Z

Removed part where it said issue if you can’t partition sample space. This is always possible; just make the leftovers it’s own strata.

← Previous revision		Revision as of 15:36, 22 June 2024
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	==Disadvantages==		==Disadvantages==
	Stratified sampling is not useful when the population cannot be exhaustively partitioned into disjoint subgroups.
	It would be a misapplication of the technique to make subgroups' sample sizes proportional to the amount of data available from the subgroups, rather than scaling sample sizes to subgroup sizes (or to their variances, if known to vary significantly—e.g. using an [[F-test\|F test]]). Data representing each subgroup are taken to be of equal importance if suspected variation among them warrants stratified sampling. If subgroup variances differ significantly and the data needs to be stratified by variance, it is not possible to simultaneously make each subgroup sample size proportional to subgroup size within the total population. For an efficient way to partition sampling resources among groups that vary in their means, variance and costs, see [[Sample size#Stratified sample size\|"optimum allocation"]].		It would be a misapplication of the technique to make subgroups' sample sizes proportional to the amount of data available from the subgroups, rather than scaling sample sizes to subgroup sizes (or to their variances, if known to vary significantly—e.g. using an [[F-test\|F test]]). Data representing each subgroup are taken to be of equal importance if suspected variation among them warrants stratified sampling. If subgroup variances differ significantly and the data needs to be stratified by variance, it is not possible to simultaneously make each subgroup sample size proportional to subgroup size within the total population. For an efficient way to partition sampling resources among groups that vary in their means, variance and costs, see [[Sample size#Stratified sample size\|"optimum allocation"]].
	The problem of stratified sampling in the case of unknown class priors (ratio of subpopulations in the entire population) can have a deleterious effect on the performance of any analysis on the dataset, e.g. classification.<ref name=minimax-sampling/> In that regard, [[minimax\|minimax sampling ratio]] can be used to make the dataset robust with respect to uncertainty in the underlying data generating process.<ref name=minimax-sampling/>		The problem of stratified sampling in the case of unknown class priors (ratio of subpopulations in the entire population) can have a deleterious effect on the performance of any analysis on the dataset, e.g. classification.<ref name=minimax-sampling/> In that regard, [[minimax\|minimax sampling ratio]] can be used to make the dataset robust with respect to uncertainty in the underlying data generating process.<ref name=minimax-sampling/>

24.5.126.110 at 03:36, 26 April 2024

2024-04-26T03:36:07Z

← Previous revision		Revision as of 03:36, 26 April 2024
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	In [[statistical survey]]s, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation ('''stratum''') independently.		In [[statistical survey]]s, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation ('''stratum''') independently.

	'''Stratification''' is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be ''[[Collectively exhaustive events\|collectively exhaustive]]'' and ''[[Mutual exclusivity\|mutually exclusive]]'': every element in the population must ~~not~~ be assigned to one and only one stratum. Then [[simple random sampling]] is applied within each stratum. The objective is to improve the precision of the sample by reducing [[sampling error]]. It can produce a [[weighted mean]] that has less variability than the [[arithmetic mean]] of a [[simple random sample]] of the population.		'''Stratification''' is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be ''[[Collectively exhaustive events\|collectively exhaustive]]'' and ''[[Mutual exclusivity\|mutually exclusive]]'': every element in the population must be assigned to one and only one stratum. Then [[simple random sampling]] is applied within each stratum. The objective is to improve the precision of the sample by reducing [[sampling error]]. It can produce a [[weighted mean]] that has less variability than the [[arithmetic mean]] of a [[simple random sample]] of the population.

	In [[computational statistics]], stratified sampling is a method of [[variance reduction]] when [[Monte Carlo method]]s are used to estimate population statistics from a known population.<ref name="varred17">{{cite journal\|last1=Botev\|first1=Z.\|last2=Ridder\|first2=A.\|title=Variance Reduction\|journal= Wiley StatsRef: Statistics Reference Online\|date=2017\|pages=1–6\|doi=10.1002/9781118445112.stat07975\|isbn=9781118445112}}</ref>		In [[computational statistics]], stratified sampling is a method of [[variance reduction]] when [[Monte Carlo method]]s are used to estimate population statistics from a known population.<ref name="varred17">{{cite journal\|last1=Botev\|first1=Z.\|last2=Ridder\|first2=A.\|title=Variance Reduction\|journal= Wiley StatsRef: Statistics Reference Online\|date=2017\|pages=1–6\|doi=10.1002/9781118445112.stat07975\|isbn=9781118445112}}</ref>

24.5.126.110 at 03:32, 26 April 2024

2024-04-26T03:32:34Z

← Previous revision		Revision as of 03:32, 26 April 2024
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	In [[statistical survey]]s, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation ('''stratum''') independently.		In [[statistical survey]]s, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation ('''stratum''') independently.

	'''Stratification''' is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be ''[[Collectively exhaustive events\|collectively exhaustive]]'' and ''[[Mutual exclusivity\|mutually exclusive]]'': every element in the population must be assigned to one and only one stratum. Then [[simple random sampling]] is applied within each stratum. The objective is to improve the precision of the sample by reducing [[sampling error]]. It can produce a [[weighted mean]] that has less variability than the [[arithmetic mean]] of a [[simple random sample]] of the population.		'''Stratification''' is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be ''[[Collectively exhaustive events\|collectively exhaustive]]'' and ''[[Mutual exclusivity\|mutually exclusive]]'': every element in the population must not be assigned to one and only one stratum. Then [[simple random sampling]] is applied within each stratum. The objective is to improve the precision of the sample by reducing [[sampling error]]. It can produce a [[weighted mean]] that has less variability than the [[arithmetic mean]] of a [[simple random sample]] of the population.

	In [[computational statistics]], stratified sampling is a method of [[variance reduction]] when [[Monte Carlo method]]s are used to estimate population statistics from a known population.<ref name="varred17">{{cite journal\|last1=Botev\|first1=Z.\|last2=Ridder\|first2=A.\|title=Variance Reduction\|journal= Wiley StatsRef: Statistics Reference Online\|date=2017\|pages=1–6\|doi=10.1002/9781118445112.stat07975\|isbn=9781118445112}}</ref>		In [[computational statistics]], stratified sampling is a method of [[variance reduction]] when [[Monte Carlo method]]s are used to estimate population statistics from a known population.<ref name="varred17">{{cite journal\|last1=Botev\|first1=Z.\|last2=Ridder\|first2=A.\|title=Variance Reduction\|journal= Wiley StatsRef: Statistics Reference Online\|date=2017\|pages=1–6\|doi=10.1002/9781118445112.stat07975\|isbn=9781118445112}}</ref>

2601:447:C601:3690:2944:33F8:3778:AC58 at 01:41, 21 November 2023

2023-11-21T01:41:02Z

← Previous revision		Revision as of 01:41, 21 November 2023
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	==Stratified sampling strategies==		==Stratified sampling strategies==
	#''Proportionate allocation'' uses a [[sampling fraction]] in each of the strata that are proportional to that of the total population. For instance, if the population consists of ''n'' total individuals, ''m'' of which are male and ''f'' female (and where ''m'' + ''f'' = ''n''), then the relative size of the two samples (''x''<sub>1</sub> = ''m''/''n'' males, ''x''<sub>2</sub> = ''f''/''n'' females) should reflect this proportion.		#''Proportionate allocation'' uses a [[sampling fraction]] in each of the strata that are proportional to that of the total population. For instance, if the population consists of ''n'' total individuals, ''m'' of which are male and ''f'' female (and where ''m'' + ''f'' = ''n''), then the relative size of the two samples (''x''<sub>1</sub> = ''m''/''n'' males, ''x''<sub>2</sub> = ''f''/''n'' females) should reflect this proportion.
	#''Optimum allocation'' (or ''disproportionate allocation'') - The sampling fraction of each stratum is proportionate to both the proportion (as above) and the [[standard deviation]] of the distribution of the variable. Larger samples are taken in the strata with the greatest variability to generate the least possible overall sampling variance.		#''Optimum allocation'' (or ''disproportionate allocation'') – The sampling fraction of each stratum is proportionate to both the proportion (as above) and the [[standard deviation]] of the distribution of the variable. Larger samples are taken in the strata with the greatest variability to generate the least possible overall sampling variance.

	A real-world example of using stratified sampling would be for a political [[Statistical survey\|survey]]. If the respondents needed to reflect the diversity of the population, the researcher would specifically seek to include participants of various minority groups such as race or religion, based on their proportionality to the total population as mentioned above. A stratified survey could thus claim to be more representative of the population than a survey of [[simple random sampling]] or [[systematic sampling]]. Both mean and variance can be corrected for disproportionate sampling costs using [[Sample_size_determination#Stratified_sample_size\|stratified sample sizes]].		A real-world example of using stratified sampling would be for a political [[Statistical survey\|survey]]. If the respondents needed to reflect the diversity of the population, the researcher would specifically seek to include participants of various minority groups such as race or religion, based on their proportionality to the total population as mentioned above. A stratified survey could thus claim to be more representative of the population than a survey of [[simple random sampling]] or [[systematic sampling]]. Both mean and variance can be corrected for disproportionate sampling costs using [[Sample_size_determination#Stratified_sample_size\|stratified sample sizes]].
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	# If measurements within strata have a lower standard deviation (as compared to the overall standard deviation in the population), stratification gives a smaller error in estimation.		# If measurements within strata have a lower standard deviation (as compared to the overall standard deviation in the population), stratification gives a smaller error in estimation.
	# For many applications, measurements become more manageable and/or cheaper when the population is grouped into strata.		# For many applications, measurements become more manageable and/or cheaper when the population is grouped into strata.
	# When it is desirable to have estimates of the population [[Statistical parameter\|parameters]] for groups within the population - stratified sampling verifies we have enough samples from the strata of interest.		# When it is desirable to have estimates of the population [[Statistical parameter\|parameters]] for groups within the population – stratified sampling verifies we have enough samples from the strata of interest.
	If the population density varies greatly within a region, stratified sampling will ensure that estimates can be made with equal accuracy in different parts of the region, and that comparisons of sub-regions can be made with equal [[statistical power]]. For example, in [[Ontario]] a survey taken throughout the province might use a larger sampling fraction in the less populated north, since the disparity in population between north and south is so great that a sampling fraction based on the provincial sample as a whole might result in the collection of only a handful of data from the north.		If the population density varies greatly within a region, stratified sampling will ensure that estimates can be made with equal accuracy in different parts of the region, and that comparisons of sub-regions can be made with equal [[statistical power]]. For example, in [[Ontario]] a survey taken throughout the province might use a larger sampling fraction in the less populated north, since the disparity in population between north and south is so great that a sampling fraction based on the provincial sample as a whole might result in the collection of only a handful of data from the north.

2603:6081:2100:29F:4401:C71A:ADAA:619A: /* Stratified sampling strategies */

2023-08-26T20:02:29Z

Stratified sampling strategies

← Previous revision		Revision as of 20:02, 26 August 2023
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	#''Optimum allocation'' (or ''disproportionate allocation'') - The sampling fraction of each stratum is proportionate to both the proportion (as above) and the [[standard deviation]] of the distribution of the variable. Larger samples are taken in the strata with the greatest variability to generate the least possible overall sampling variance.		#''Optimum allocation'' (or ''disproportionate allocation'') - The sampling fraction of each stratum is proportionate to both the proportion (as above) and the [[standard deviation]] of the distribution of the variable. Larger samples are taken in the strata with the greatest variability to generate the least possible overall sampling variance.

	A real-world example of using stratified sampling would be for a political [[Statistical survey\|survey]]. If the respondents needed to reflect the diversity of the population, the researcher would specifically seek to include participants of various minority groups such as race or religion, based on their proportionality to the total population as mentioned above. A stratified survey could thus claim to be more representative of the population than a survey of [[simple random sampling]] or [[systematic sampling]].		A real-world example of using stratified sampling would be for a political [[Statistical survey\|survey]]. If the respondents needed to reflect the diversity of the population, the researcher would specifically seek to include participants of various minority groups such as race or religion, based on their proportionality to the total population as mentioned above. A stratified survey could thus claim to be more representative of the population than a survey of [[simple random sampling]] or [[systematic sampling]]. Both mean and variance can be corrected for disproportionate sampling costs using [[Sample_size_determination#Stratified_sample_size\|stratified sample sizes]].

	==Advantages==		==Advantages==