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Estimates and sampling errors for Establishment Surveys International Workshop on Industrial Statistics Beijing, China, 8-10 July 2013

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Weighting procedures Important to calculate appropriate weights based on probabilities of selection Important to calculate appropriate weights based on probabilities of selection Maintain information on geographic, stratification and identification codes of all sample establishments with corresponding probabilities of selection Maintain information on geographic, stratification and identification codes of all sample establishments with corresponding probabilities of selection This spreadsheet or database with the sample establishments can be used for calculating the weights This spreadsheet or database with the sample establishments can be used for calculating the weights

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Calculation of weights – list frame Probability of selection for sample establishments in stratum h (ISIC group, employment size) in list frame Probability of selection for sample establishments in stratum h (ISIC group, employment size) in list frame Weight for sample establishments in stratum h Weight for sample establishments in stratum h

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Calculation of weights – area frame Overall probability includes components from each sampling stage Overall probability includes components from each sampling stage Weight Weight

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Adjusting weights for nonresponse Unit nonresponse Unit nonresponse Important to determine reason for non-interview Important to determine reason for non-interview Sample establishment no longer exists (death)Sample establishment no longer exists (death) Respondent not availableRespondent not available RefusalRefusal Weight adjustment should be done within each ISIC group and size stratum Weight adjustment should be done within each ISIC group and size stratum

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Types of estimates in Establishment Surveys Weighted totals Weighted totals Weighted total revenue, number of employees, etc.Weighted total revenue, number of employees, etc. W hi = weight of i-th establishment in stratum h Y hi = value of variable Y for i-th establishment in stratum h Y hi = value of variable Y for i-th establishment in stratum h

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Adjusting weights (continued) Very large establishments that do not respond may require special adjustment procedures Very large establishments that do not respond may require special adjustment procedures Special follow-up to complete responseSpecial follow-up to complete response Imputation based on historical dataImputation based on historical data Adjustment procedure may vary by size of establishment Adjustment procedure may vary by size of establishment

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Non-interview adjustment factor Calculating weight adjustment factor Calculating weight adjustment factor W’ h =adjusted weight for the establishments in stratum h W’ h =adjusted weight for the establishments in stratum h n h ’ =number of valid sample establishments selected in stratum h (excluding those which no longer exist) n h ’ =number of valid sample establishments selected in stratum h (excluding those which no longer exist) n h ” =number of establishments with completed interviews in stratum h (including replacements) n h ” =number of establishments with completed interviews in stratum h (including replacements)

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Types of estimates (continued) Means and proportions Means and proportions Expressed as ratio of two totalsExpressed as ratio of two totals Variables X and Y can be continuous values or binomial (0,1) variables

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Ratio estimates of totals Ratio estimation useful for estimating totals, using auxiliary information from frame or administrative sources and growth rate from survey data Ratio estimation useful for estimating totals, using auxiliary information from frame or administrative sources and growth rate from survey data Numerator and denominator of ratio should be highly correlatedNumerator and denominator of ratio should be highly correlated

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Ratio estimates of totals (continued) Improves accuracy of results when reliable information for denominator variable is available for entire frame Improves accuracy of results when reliable information for denominator variable is available for entire frame Example 1: estimating total value of production from annual survey when census data are available from previous year Example 1: estimating total value of production from annual survey when census data are available from previous year Example 2: estimating total rice production when total area of cultivated rice land is available, together with post- harvest data on rice production by hectare from a sample survey Example 2: estimating total rice production when total area of cultivated rice land is available, together with post- harvest data on rice production by hectare from a sample survey

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Indexes Index of Industrial Production Index of Industrial Production Y = output I p = price index I q = volume index t = current period t-1 = previous period

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Types of error in estimates from sample surveys Sampling error of an estimate – variability in value of estimate based on a sample of the population Sampling error of an estimate – variability in value of estimate based on a sample of the population Measured by the standard error, or square root of the varianceMeasured by the standard error, or square root of the variance Nonsampling error – all other types of error Nonsampling error – all other types of error Examples: response error, other measurement errors, nonresponse, coding, data entry and processing errorsExamples: response error, other measurement errors, nonresponse, coding, data entry and processing errors Can result in biasCan result in bias

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Total error Measured by the mean square error (MSE) Measured by the mean square error (MSE) MSE measures accuracy of survey estimate MSE measures accuracy of survey estimate MSE = Variance + Bias 2 MSE = Variance + Bias 2 Variance is measure of precision Variance is measure of precision

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Accuracy of survey estimates Accuracy depends on both sampling and nonsampling error Accuracy depends on both sampling and nonsampling error Publication of results from Economic Surveys should include annex with table of sampling errors and confidence intervals for most important estimates Publication of results from Economic Surveys should include annex with table of sampling errors and confidence intervals for most important estimates Calculation of variances should reflect any stratification and clustering in the sample design Calculation of variances should reflect any stratification and clustering in the sample design

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Software for tabulating sampling errors from complex samples SPSS – Complex Samples module SPSS – Complex Samples module Stata Stata Ultimate cluster or Taylor series variance estimator Ultimate cluster or Taylor series variance estimator Variance formula takes into account the stratification and clustering in the sample design Variance formula takes into account the stratification and clustering in the sample design See formulas See formulas

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Preparing data files for calculation of standard errors Data file should include sample design information Data file should include sample design information Stratum code Stratum code PSU code (for example, PSU identification) PSU code (for example, PSU identification) Weight Weight Sampling fraction for stratum Sampling fraction for stratum

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Preparing data files (continued) Certainty establishments included in data file for calculation of variances Certainty establishments included in data file for calculation of variances Sampling rate = 1Sampling rate = 1 Variance component from certainty stratum is 0Variance component from certainty stratum is 0 Results in lower coefficients of variationResults in lower coefficients of variation

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