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- 1. Statistics 101: Proportions, ratios, and rates ArchivedStats in brief: 89-20-00062021003Description:
In this video, viewers will learn the differences between three types of measure: proportions, ratios, and rates. In addition, viewers by the end of this video will be able to determine how each measure is calculated and when it is best to use one measure rather than the other.
Release date: 2021-05-03 - Articles and reports: 12-001-X201400111886Description:
Bayes linear estimator for finite population is obtained from a two-stage regression model, specified only by the means and variances of some model parameters associated with each stage of the hierarchy. Many common design-based estimators found in the literature can be obtained as particular cases. A new ratio estimator is also proposed for the practical situation in which auxiliary information is available. The same Bayes linear approach is proposed for obtaining estimation of proportions for multiple categorical data associated with finite population units, which is the main contribution of this work. A numerical example is provided to illustrate it.
Release date: 2014-06-27 - Articles and reports: 12-001-X201100111450Description:
This paper examines the efficiency of the Horvitz-Thompson estimator from a systematic probability proportional to size (PPS) sample drawn from a randomly ordered list. In particular, the efficiency is compared with that of an ordinary ratio estimator. The theoretical results are confirmed empirically with of a simulation study using Dutch data from the Producer Price Index.
Release date: 2011-06-29 - Articles and reports: 12-001-X201100111451Description:
In the calibration method proposed by Deville and Särndal (1992), the calibration equations take only exact estimates of auxiliary variable totals into account. This article examines other parameters besides totals for calibration. Parameters that are considered complex include the ratio, median or variance of auxiliary variables.
Release date: 2011-06-29 - Articles and reports: 12-001-X200900211043Description:
Business surveys often use a one-stage stratified simple random sampling without replacement design with some certainty strata. Although weight adjustment is typically applied for unit nonresponse, the variability due to nonresponse may be omitted in practice when estimating variances. This is problematic especially when there are certainty strata. We derive some variance estimators that are consistent when the number of sampled units in each weighting cell is large, using the jackknife, linearization, and modified jackknife methods. The derived variance estimators are first applied to empirical data from the Annual Capital Expenditures Survey conducted by the U.S. Census Bureau and are then examined in a simulation study.
Release date: 2009-12-23 - Articles and reports: 11-522-X20050019450Description:
Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. Demnati and Rao (2004) proposed a new approach to deriving Taylor linearization variance estimators that leads directly to a unique variance estimator that satisfies the above considerations for general designs.
Release date: 2007-03-02 - Articles and reports: 11-522-X20050019458Description:
The proposed paper presents an alternative methodology that gives the data the possibility of defining homogenous groups determined by a bottom up classification of the values of observed details. The problem is then to assign a non respondent business to one of these groups. Several assignment procedures, based on explanatory variables available in the tax returns, are compared, using gross or distributed data: parametric and non parametric classification analyses, log linear models, etc.
Release date: 2007-03-02 - 8. Cold deck and ratio imputation ArchivedArticles and reports: 12-001-X20000015180Description:
Imputation is a common procedure to compensate for nonresponse in survey problems. Using auxiliary data, imputation may produce estimators that are more efficient than the one constructed by ignoring nonrespondents and re-weighting. We study and compare the mean squared errors of survey estimators based on data imputed using three difference imputation techniques: the commonly used ratio imputation method and two cold deck imputation methods that are frequently adopted in economic area surveys conducted by the U.S. Census Bureau and the U.S. Bureau of Labor Statistics.
Release date: 2000-08-30 - Surveys and statistical programs – Documentation: 11-522-X19990015682Description:
The application of dual system estimation (DSE) to matched Census / Post Enumeration Survey (PES) data in order to measure net undercount is well understood (Hogan, 1993). However, this approach has so far not been used to measure net undercount in the UK. The 2001 PES in the UK will use this methodology. This paper presents the general approach to design and estimation for this PES (the 2001 Census Coverage Survey). The estimation combines DSE with standard ratio and regression estimation. A simulation study using census data from the 1991 Census of England and Wales demonstrates that the ratio model is in general more robust than the regression model.
Release date: 2000-03-02 - Surveys and statistical programs – Documentation: 11-522-X19990015692Description:
Electricity rates that vary by time-of-day have the potential to significantly increase economic efficiency in the energy market. A number of utilities have undertaken economic studies of time-of-use rates schemes for their residential customers. This paper uses meta-analysis to examine the impact of time-of-use rates on electricity demand pooling the results of thirty-eight separate programs. There are four key findings. First, very large peak to off-peak price ratios are needed to significantly affect peak demand. Second, summer peak rates are relatively effective compared to winter peak rates. Third, permanent time-or-use rates are relatively effective compared to experimental ones. Fourth, demand charges rival ordinary time-of-use rates in terms of impact.
Release date: 2000-03-02
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- 1. Statistics 101: Proportions, ratios, and rates ArchivedStats in brief: 89-20-00062021003Description:
In this video, viewers will learn the differences between three types of measure: proportions, ratios, and rates. In addition, viewers by the end of this video will be able to determine how each measure is calculated and when it is best to use one measure rather than the other.
Release date: 2021-05-03 - Articles and reports: 12-001-X201400111886Description:
Bayes linear estimator for finite population is obtained from a two-stage regression model, specified only by the means and variances of some model parameters associated with each stage of the hierarchy. Many common design-based estimators found in the literature can be obtained as particular cases. A new ratio estimator is also proposed for the practical situation in which auxiliary information is available. The same Bayes linear approach is proposed for obtaining estimation of proportions for multiple categorical data associated with finite population units, which is the main contribution of this work. A numerical example is provided to illustrate it.
Release date: 2014-06-27 - Articles and reports: 12-001-X201100111450Description:
This paper examines the efficiency of the Horvitz-Thompson estimator from a systematic probability proportional to size (PPS) sample drawn from a randomly ordered list. In particular, the efficiency is compared with that of an ordinary ratio estimator. The theoretical results are confirmed empirically with of a simulation study using Dutch data from the Producer Price Index.
Release date: 2011-06-29 - Articles and reports: 12-001-X201100111451Description:
In the calibration method proposed by Deville and Särndal (1992), the calibration equations take only exact estimates of auxiliary variable totals into account. This article examines other parameters besides totals for calibration. Parameters that are considered complex include the ratio, median or variance of auxiliary variables.
Release date: 2011-06-29 - Articles and reports: 12-001-X200900211043Description:
Business surveys often use a one-stage stratified simple random sampling without replacement design with some certainty strata. Although weight adjustment is typically applied for unit nonresponse, the variability due to nonresponse may be omitted in practice when estimating variances. This is problematic especially when there are certainty strata. We derive some variance estimators that are consistent when the number of sampled units in each weighting cell is large, using the jackknife, linearization, and modified jackknife methods. The derived variance estimators are first applied to empirical data from the Annual Capital Expenditures Survey conducted by the U.S. Census Bureau and are then examined in a simulation study.
Release date: 2009-12-23 - Articles and reports: 11-522-X20050019450Description:
Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. Demnati and Rao (2004) proposed a new approach to deriving Taylor linearization variance estimators that leads directly to a unique variance estimator that satisfies the above considerations for general designs.
Release date: 2007-03-02 - Articles and reports: 11-522-X20050019458Description:
The proposed paper presents an alternative methodology that gives the data the possibility of defining homogenous groups determined by a bottom up classification of the values of observed details. The problem is then to assign a non respondent business to one of these groups. Several assignment procedures, based on explanatory variables available in the tax returns, are compared, using gross or distributed data: parametric and non parametric classification analyses, log linear models, etc.
Release date: 2007-03-02 - 8. Cold deck and ratio imputation ArchivedArticles and reports: 12-001-X20000015180Description:
Imputation is a common procedure to compensate for nonresponse in survey problems. Using auxiliary data, imputation may produce estimators that are more efficient than the one constructed by ignoring nonrespondents and re-weighting. We study and compare the mean squared errors of survey estimators based on data imputed using three difference imputation techniques: the commonly used ratio imputation method and two cold deck imputation methods that are frequently adopted in economic area surveys conducted by the U.S. Census Bureau and the U.S. Bureau of Labor Statistics.
Release date: 2000-08-30 - Articles and reports: 12-001-X19960022985Description:
Telephone surveys in the U.S. are subject to coverage bias because about 6 percent of all households do not have a telephone at any particular point in time. The bias resulting from this undercoverage can be important since those who do not have a telephone are generally poorer and have other characteristics that differ from the telephone population. Poststratification and the other usual methods of adjustment often do not fully compensate for this bias. This research examines a procedure for adjusting the survey estimates based on the observation that some households have a telephone for only part of the year, often due to economic circumstances. By collecting data on interruptions in telephone service in the past year, statistical adjustments of the estimates can be made which may reduce the bias in the estimates but which at the same time increase variances because of greater variability in weights. This paper considers a method of adjustment using data collected from a national telephone survey. Estimates of the reductions in bias and the effect on the mean square error of the estimates are computed for a variety of statistics. The results show that when the estimates from the survey are highly related to economic conditions the telephone interruption adjustment procedure can improve the mean square error of the estimates.
Release date: 1997-01-30
Reference (2)
Reference (2) ((2 results))
- Surveys and statistical programs – Documentation: 11-522-X19990015682Description:
The application of dual system estimation (DSE) to matched Census / Post Enumeration Survey (PES) data in order to measure net undercount is well understood (Hogan, 1993). However, this approach has so far not been used to measure net undercount in the UK. The 2001 PES in the UK will use this methodology. This paper presents the general approach to design and estimation for this PES (the 2001 Census Coverage Survey). The estimation combines DSE with standard ratio and regression estimation. A simulation study using census data from the 1991 Census of England and Wales demonstrates that the ratio model is in general more robust than the regression model.
Release date: 2000-03-02 - Surveys and statistical programs – Documentation: 11-522-X19990015692Description:
Electricity rates that vary by time-of-day have the potential to significantly increase economic efficiency in the energy market. A number of utilities have undertaken economic studies of time-of-use rates schemes for their residential customers. This paper uses meta-analysis to examine the impact of time-of-use rates on electricity demand pooling the results of thirty-eight separate programs. There are four key findings. First, very large peak to off-peak price ratios are needed to significantly affect peak demand. Second, summer peak rates are relatively effective compared to winter peak rates. Third, permanent time-or-use rates are relatively effective compared to experimental ones. Fourth, demand charges rival ordinary time-of-use rates in terms of impact.
Release date: 2000-03-02
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