Survey Information Continued
Since many states allow pickups, small vans, and sport utility vehicles to be registered as either cars or trucks, passenger car files were searched and any such vehicles were included in the sampling frame. Some vehicles, such as "off-highway" trucks used exclusively on private property, do not have to be registered. These vehicles were not included in the sampling frame and had no chance of being selected.
The annual vehicle registration date varies among the states. A few states use the calendar year for registering all vehicles. Most states require owners to register their vehicles on a staggered basis to permit a distribution of the renewal workload throughout all months. Most states also allow preregistration or permit "grace periods" to better distribute the annual registration workload.
Registration practices for commercial vehicles differ greatly among the states. Some states register a tractor-semitrailer combination as a single unit; others register the tractor and the semitrailer separately. For either method of registration, only the power units are included in the registered truck counts.
The sampling frame for the supplementary universe was also stratified by geography and truck characteristics. The truck characteristics were the same ones used to stratify the frame for the initial sample. However, the geographic strata were defined differently. The 50 states and the District of Columbia were partitioned into four mutually exclusive geographic strata. Each "state" was included in one, and only one, geographic stratum. These geographic strata were used instead of those used for the initial sample because of cost and processing constraints. Within each geographic-by-truck stratum, a simple random sample of truck registrations was selected. Thus, an additional 20 geographic-by-truck strata were used to stratify the sampling frame for the supplementary universe, resulting in a total of 275 geographic-by-truck strata from which to select truck registrations for the entire 1997 VIUS sample.
The size of the supplementary sample for the entire United States was approximately 3,000 truck registrations.
Estimation. National estimates of the number of trucks were computed in the following manner. For the initial and supplementary samples, weighted estimates of the number of trucks were computed for each geographic-by-truck stratum. The weight for a given truck was the product of two factors: the reciprocal of the truck's probability of selection and a nonresponse adjustment factor. (See the Reliability of Estimates section for a description of the nonresponse adjustment procedure.) The geographic-by-truck stratum estimates from the initial and supplementary samples were summed to form the national estimates. National estimates of truck miles were computed using the same method. National estimates of average miles per truck were computed by dividing the national estimates of truck miles by the national estimates of the number of trucks.
Sampling error. Because the estimates are based on a sample, the Census Bureau does not expect exact agreement with the results that would be obtained from a complete enumeration of the truck registrations included in the sampling frame. However, because each truck represented on the sampling frame has a known probability of selection into the sample, it is possible to estimate the sampling variability of the survey estimates.
The particular sample used in this survey is one of a large number of samples of the same size that could have been selected using the same design. If all possible samples had been surveyed, under the same conditions, an estimate of an unknown population value could have been obtained from each sample. These samples give rise to a distribution of estimates for the unknown population value. A statistical measure of the variability among these estimates is the standard error, which can be approximated from any one sample. The standard error is defined as the square root of the variance. The coefficient of variation (or relative standard error) of an estimate is the standard error of the estimate divided by the estimate. Note that measures of sampling variability, such as the standard error or coefficient of variation, are estimated from the sample and are also subject to sampling variability. (Technically, we should refer to the estimated standard error or the estimated coefficient of variation of an estimator.) It is important to note that the standard error and coefficient of variation only measure sampling variability. They do not capture any systematic biases in the estimates. Published measures of sampling variability for the 1997 VIUS appear in the U.S. Summary and state PDF files. For the U.S. Summary file, Tables 2b and 3b provide estimated measures of sampling variability for the estimates shown in Tables 2a and 3a. Coefficients of variation are given for the two left-most column estimates in Table 11, and for the column and row total estimates in all other tables except Tables A, 1a, and 1b. For each state file, the measures of sampling variability are shown in Table 2. The procedure for approximating coefficients of variation of other estimates is covered in Appendix A of the U.S. Summary file. All coefficients of variation are expressed as percentages.
The estimate from a particular sample and the approximate standard error associated with the estimate can be used to construct a confidence interval. A confidence interval is a range about a given estimator that has a specified probability of containing its corresponding, unknown population value. If, for each possible sample, an estimate of an unknown population value and its approximate standard error were obtained, then:
For approximately 90 percent of the possible samples, the interval from 1.65 standard errors below to 1.65 standard errors above the estimate would include the unknown population value.
For approximately 95 percent of the possible samples, the interval from two standard errors below to two standard errors above the estimate would include the unknown population value.
Nonsampling error. Nonsampling error encompasses all other factors that contribute to the total error of a sample survey estimate and may also occur in censuses. It is often helpful to think of nonsampling error as arising from deficiencies or mistakes in the survey process. In the 1997 VIUS, nonsampling error can be attributed to many sources: (1) inability to obtain information about all trucks in the sample; (2) response errors; (3) differences in the interpretation of the questions; (4) mistakes in coding or keying the data obtained; and (5) other errors of collection, response, coverage, and processing. Although no direct measurement of the potential biases because of nonsampling error has been obtained, precautionary steps were taken in all phases of the collection, processing, and tabulation of the data in an effort to minimize its influence.
A potential source of bias in the estimates is nonresponse. Nonresponse is defined as the inability to obtain all the intended measurements or responses about all the selected trucks. Two types of nonresponse are often distinguished. Unit nonresponse is used to describe the inability to obtain any of the substantive measurements about a sampled truck. In most cases of unit nonresponse, the questionnaire was never returned to the Census Bureau after several attempts to elicit a response. Approximately 84.5 percent of the questionnaires were returned with substantive data. Item nonresponse occurs either when a question is unanswered or the response to the question fails computer edits. The procedures used to account for unit and item nonresponse are discussed below.
Unit nonresponse is handled in the estimation procedure by reweighting. To apply this method of nonresponse adjustment, we make the assumption that the population of trucks can be divided into a finite number of mutually exclusive adjustment cells so that within each cell, all the population elements possess similar characteristics and share a similar probability of responding, if selected in the sample. The adjustment cells for the 1997 VIUS are identical to the sampling strata. A nonresponse adjustment factor is computed for each adjustment cell and is equal to the ratio of the number of truck registrations selected into the sample to the number of responses received within each adjustment cell. In this sense, reweighting allocates characteristics to the nonrespondents in proportion to the characteristics observed for the respondents within each adjustment cell. The amount of bias introduced by this nonresponse adjustment procedure depends on the extent to which the nonrespondents differ, characteristically, from the respondents in each adjustment cell.
For item nonresponse, a missing value is replaced by a predicted value obtained from an appropriate model for nonresponse. This procedure is called imputation. To impute annual miles and lifetime miles, we divide the sample into a finite number of mutually exclusive cells based on state of registration, truck type, and model year. For each cell, estimates of average annual miles and average lifetime miles are computed based on those trucks in the cell for which annual miles and lifetime miles have been reported. Missing values are then replaced with the appropriate average values. A slightly different imputation procedure is used for length and average weight (empty weight plus cargo weight). For these data items, we replace a missing value with data from a truck with similar characteristics for which length and average weight have been reported.
For all other data items, no imputation is performed. Instead, separate estimates are published in a "Not reported" category. For example, a respondent who did not indicate the major use of his or her truck would be included in the estimate for the "Not reported" category. Users of the estimates should exercise caution when allocating the estimate for the "Not reported" category to the estimates for the reported categories in the proportions observed for the reported categories. This is because the characteristics of the trucks for which we obtained information may differ significantly from those trucks for which we obtained no information.
