Estimating Water Use in the United States A New Paradigm for the National Water-Use Information Program (2002) / Chapter Skim
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5. Stratified Random Sampling to Estimate Water Use
5. Stratified Random Sampling to Estimate Water Use
Pages 86-99
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From page 86... ...
Statistics derived from the survey results for sampled users would be used to estimate total water use for all users. Compared to the census approach, random sampling reduces the effort involved in collecting water use data, while allowing quantification of the introduced sampling error.
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From page 87... ...
The stratified random sampling approach allows explicit estimation of the error due to sampling. Additional error may result from measurement inaccuracies, deliberate misrepresentation of water use, and the failure to identify or appropriately categorize all users.
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From page 88... ...
developed the result in Equation 5.2 by minimizing variance on the estimate of the mean. The result is identical if calculations are made to minimize variance on a total like total water use.
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From page 89... ...
For all practical purposes, the 1997 data can be taken to represent the entire population of individual withdrawal points in Arkansas, providing us with accurate knowledge of population variances needed to develop a sampling plan. In usual practice, the population standard deviations Oh would be unknown and would be estimated with sample standard deviations or historical population standard deviations.
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From page 90... ...
. If optimal stratified sampling is employed, using the use categories in Table 5.1 as the strata, the total number of samples n needed to estimate water use with the same standard error is determined as follows: L VT + ~ Nh~h = h=1 (1,268,868.8 MG)
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From page 91... ...
Adding an additional requirement that each category have a minimum of two samples results in the corrected values for nh in Table 5.2. TABLE 5.2 Number of Required Samples, by Category, to Achieve Approximately 10% Standard Error in the Water Use Estimate Number of Samples Required, nh Number of Standard Category of Use Withdrawal Points Calculated Corrected Final Error (%)
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From page 92... ...
is obtained. Thus, to achieve 10 percent standard error, the stratified random sampling approach requires 471 samples, less than 1.1 percent of the population.
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From page 93... ...
needed to achieve the target standard error as a function of top stratum size for Arkansas' groundwater and surface water irrigation withdrawals. Note the minimum total sample size required for the groundwater subcategory is less than that for surface water subcategory, even though there are over seven times as many groundwater withdrawal points.
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From page 94... ...
Using the substratum boundary, the minimum total sample size is 110; the single largest withdrawal points should be measured, and a random sample of 109 points (approximately 0.3 percent) should be selected from the remaining 36,052 groundwater withdrawal points.
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From page 95... ...
Using Equation 5.1, it is possible to estimate error variance and standard error for water use estimated from any stratified sampling plan. Water use estimates developed from nonoptimal sampling plans will be expected to have larger standard errors than estimates developed from optimal sampling plans with the same number of total samples.
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From page 96... ...
The statistical data collected during the first complete stratified sampling effort would be used to design an improved sampling plan for future use. A second possibility for developing a sampling plan in the absence of prior statistics is to use category variances available from state programs with substantive data collection efforts in the optimal sampling plan Equations 5.2 and 5.3 with the target state's category numbers.
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From page 97... ...
Can incomplete samples of this kind be used in a stratified random sampling framework to arrive at reasonable estimates of the total water use and its standard error?
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From page 98... ...
However, for groundwater irrigation withdrawals, where the relative variability of withdrawals is much lower than for surface water, the hybrid approach offers no advantage over random sampling. Further guidance is needed to help USGS districts select appropriate statistical sampling techniques for water use estimation in individual states.
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From page 99... ...
However, as a result of diminishing returns (each additional sample progressively provides less information as the sample size increases) , stratified random sampling has the potential for greatly reducing the data collection workload with small, acceptable increases in uncertainty.
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