Appendix C

Quality of the Data
Appendix C

Quality of the Data

Introduction

This appendix discusses several issues relating to the quality of the Residential Transportation Energy Consumption

Survey (RTECS) data and to the interpretation of conclusions based on these data. The first section discusses undercoverage of the vehicle stock in the residential sector. The second section discusses the effects of using July 1991

as a time reference for the survey. The remainder of this appendix discusses the treatment of sampling and

nonsampling errors in the RTECS, the quality of specific data items such as the Vehicle Identification Number (VIN)

and fuel prices, and poststratification procedures used in the 1991 RTECS.

The quality of the data collection and the processing of the data affects the accuracy of estimates based on survey

data. All the statistics published in this report such as total vehicle miles traveled (VMT) are estimates of population

values. These estimates are based on observations from a randomly chosen subset of the entire population of

occupied housing units. Consequently, the estimates always differ from the true population values. Because the

RTECS is a sample survey, data from the 1991 RTECS are subject to various sources of nonsampling and sampling

error.

Nonsampling error is a measure of variability due to the conduct of the survey. These errors can include:

population undercoverage during sampling; questionnaire wording and format; response bias and variance; interviewer

error; coding and/or keypunching error; and nonresponse bias. Nonsampling errors are treated in several sections

of this appendix. The main section pertains to the imputation procedures used for item nonresponses, and the special

treatment given to the fuel efficiency, reported in miles per gallon (MPG), of pre-1975 vehicles.

Sampling error is a measure of the variability in the data because a sample of households was surveyed rather than

the entire population. The different samples that could be selected would each produce different values for the

survey statistics. Because the survey used probability sampling techniques, it is possible to estimate the size of the

sampling error for any statistic. These estimates can be used as a guide in making inferences from the sample

estimates to the total population. The final section on sampling error pertains to estimating the magnitude of the

error and the presentation of sampling errors as row and column factors in the detailed tables of this report.

Noncovered Residential Vehicles

The RTECS is a subsample of the Residential Energy Consumption Survey (RECS). Therefore, any type of

household not covered in the RECS would affect the type of household vehicles not covered in the RTECS. The

following types of individuals or families were not covered by RECS and, hence, the vehicles corresponding to these

households were not covered by RTECS.

Families or individuals living in group quarters such as college dormitories, military barracks, or large

boarding houses (10 or more unrelated adults).

Families or individuals living in recreation vehicles or other vehicles.

Energy Information Administration/Household Vehicles Energy Consumption 1991 145
Families or individuals with no fixed address.

The effect of these omissions is an underestimation of the total number of vehicles in the residential sector and an

underestimation in the number of miles driven, gallons consumed, and dollars spent.

July 1991 as a Reference for Number of Households

The design of RTECS calls for households to be followed for the 1991 calendar year. Consequently, households

formed during 1991 are represented in the sample by households that existed at the time the 1990 RECS was fielded.

Hence, RTECS may have an over-representation of established households at the expense of newly formed households.

The decision to follow households for the entire year and not add a sample of households formed during 1991 means

that as the survey progressed through 1991, the estimate of the number of vehicles accumulated a negative bias. This

happens for several reasons.

When established households separate, only part of the household is followed by RTECS. If the part of

the household that is not followed takes a vehicle with them, that vehicle is counted as a disposed vehicle.

Any vehicle acquired by a household member that leaves the household is not included in the RTECS.

The number of households for the 1991 RTECS is set equal to the Current Population Survey (CPS)

estimate of the number of households as of July 1991. (See the section below on poststratification.)

RTECS does not provide for an increasing number of households from January to December. The

household number for July is the number used for the entire year. This has the effect of overestimating the

number of households and vehicles for January 1991 and underestimating the number for December 1991.

Nonsampling Error

Nonsampling errors are due to the conduct of the survey, and include both random errors and systematic errors or

biases. The magnitudes of nonsampling biases cannot be estimated from the sample data. Thus, avoidance of

systematic biases is a primary objective of all stages of survey design. (See Appendix A, "How the Survey was

Conducted," for a discussion of procedures implemented to minimize all types of nonsampling errors.) Subsequent

to conducting a survey, problems of unit nonresponse and item nonresponse need to be addressed. The treatment

in the RTECS of these types of errors are discussed in separate sections below.

Unit Nonresponse

Unit nonresponse is the type of nonresponse that occurs when no data are available for an entire sampled household.

Most unit nonresponse cases are caused by the respondent being unavailable or the respondent’s refusal to cooperate.

Unit nonresponse for the 1991 RTECS must be addressed in the context of the unit nonresponse for the 1990 RECS,

since the 1991 RTECS sample was drawn from households that responded to the 1990 RECS. Thus, in all cases,

at least the RECS data were available for every RTECS household, therefore, no RTECS household was a total

146 Energy Information Administration/Household Vehicles Energy Consumption 1991
nonrespondent. Generally, weight adjustment was the method used to reduce unit nonresponse bias in the RECS

statistics and that adjustment carried over automatically to the RTECS subsample. (See Housing Characteristics

1990 (published May 1992), DOE/EIA-0314(90) Appendix A, for a discussion of unit nonresponse adjustment.)

Imputation Procedures for Item Nonresponse

Item nonresponse occurs when the respondents do not know the answer or refuse to answer a question, or when an

interviewer does not ask a question or does not record an answer. To facilitate "full-sample" data analyses,

imputations were made to provide the most probable responses when responses were missing. The following

imputation techniques were used: hot-decking, predictive mean matching, and regression.

Hot-Deck Procedure

The most commonly used technique of imputation for the RTECS was the hot-deck procedure. In hot-decking, when

a certain response is missing for a given household or vehicle, another household or vehicle called a donor is

randomly chosen to furnish its reported value for that missing item. The value is then assigned to the nonrespondent

household or vehicle. To serve as a potential donor, a household or vehicle had to be similar to the nonrespondent

in characteristics correlated with the missing item.

The RTECS items that were imputed using the hot-deck procedure were pre-1975 vehicle characteristics and fuel

grade. Household demographic items such as family income and ethnic background were hot-decked as part of the

RECS. (See Housing Characteristics 1990 (published May 1992), DOE/EIA-0314(90), Appendix C, for a discussion

of imputation of household characteristics.)

Predictive Mean Matching

Predictive mean matching was used for imputing changes in vehicle stock to households when those households were

not followed for the complete duration of the RTECS. Changes to the vehicle stock were defined as acquisitions,

dispositions, or a combination of both. In an ideal RTECS, a beginning vehicle stock inventory reported in the 1990

RECS interview would be followed throughout the 1991 RTECS calendar year and, at the time of each RTECS

contact, changes in vehicle stock would be reported. However, because in some cases it was impossible to follow

a household for the entire RTECS year due to attrition, it was unknown if, for these households, vehicle stock

changes were made.

In the 1991 RTECS, 795 households (26 percent) were not followed for the entire RTECS calendar year. This figure

represents the percentage of households that had imputations with respect to change in their vehicle stock. Within

these households, 149 vehicles (2.4 percent) of the 6,084 total RTECS sample vehicles were imputed as acquisitions

and 164 (2.7 percent) of the total sample vehicles were imputed as disposed vehicles.

To impute vehicle stock changes in the 1991 RTECS, logistic regression equations were used to compute a predicted

probability (or propensity) of a household making a change in the vehicle stock during the RTECS data year. These

propensities were computed for all households in the data set including households lost through attrition. For each

household that was not followed during the year, a donor household was found by selecting the respondent household

with a propensity closest in value to the "lost" household. This procedure of matching a donor and recipient using

a prediction model is called "predictive mean matching." Once a donor household was found, it provided all vehicle

Energy Information Administration/Household Vehicles Energy Consumption 1991 147
stock changes, if any, to the "lost" household.13 The independent variables were the following four household attributes: (1) age of head of household; (2) number of drivers in the household; (3) total number of vehicles; and

(4) vintage of household’s newest vehicle.

Backward elimination was used to fit the final models. The binary response variable took a value of 1 if the

respondent changed vehicle stock, and 0 if otherwise. The equations were independently fitted and employed within

categories defined by (1) time of last contact which could be the RECS interview, the RTECS Beginning-of-Year

(B-O-Y) interview, or the RTECS Mid-Year (M-Y) interview, and (2) the number of vehicles in the household at

the time of last contact (expressed as two categories: one vehicle, and more than one vehicle). Use of these

categories excluded the possibility, for example, of a recipient household (one that was not tracked) with one vehicle

being matched to a donor household that had disposed of two of its three vehicles. To achieve additional

consistency, the matching procedure was carried out within geographic cells defined by the nine Census divisions

and Metropolitan Statistical Area (MSA) versus non-MSA.

13R. Little, "Missing-Data Adjustments in Large Surveys," Journal of Business and Economic Statistics, pp. 287-301.

148 Energy Information Administration/Household Vehicles Energy Consumption 1991
If a recipient household was imputed to have acquired a vehicle, certain attributes for that vehicle were "borrowed"

from the donor household. These attributes were date of acquisition, date of disposal, vehicle type, vehicle make,

model and year, number of cylinders, type of transmission, type of fuel and MPG.

In addition to imputing vehicle acquisitions, some recipient households were imputed to have disposed of some of

their vehicle stock. This occurred when a recipient household was matched to a donor that had disposed of some

of its vehicle stock. The recipient household was imputed to have disposed of the same number of vehicles that the

donor household had disposed of. The vehicles imputed as disposed of by the recipient household were chosen so

that they occupied the same rank in terms of model year, as the vehicles disposed of by the donor household (for

example, the oldest vehicle, or the next oldest).

The predictive mean matching procedure was validated by simulating the imputation task. Of the 2,366 1985 RTECS

donor households, 600 households were randomly selected to act as recipient households. Since the actions of these

600 pseudo-recipient households were known, a direct comparison was made between the known action and the

predicted action.

Overall, the prediction accuracy at the national level was 92.3 percent. That is, the distribution of the observed stock

changes among the 600 recipient households differed from the distribution of the predicted vehicle stock changes

by 46 households. At the regional level, the prediction accuracy was 78.4 percent in the Northeast Census Region,

84.4 percent in the Midwest Census Region, 71.5 percent in the South Census Region and 79.0 percent in the West

Census Region.

Predictive mean matching could not be used for households with zero vehicles in stock. There was an insufficient

number of households with zero vehicles to achieve significant estimates of parameters for the logistic regression

models. For households without vehicles, that were lost from the survey through attrition, a hot-deck procedure was

employed for imputing changes to the vehicle stock.

Regression Procedures

Multiple regressions were used to impute for annual VMT for vehicles imputed as acquired, since two odometer

readings were not available in these cases. Simple linear and multiple regressions were also used to impute annual

mileage for other vehicles when two odometer readings were not obtained. (See Appendix B, "Estimation Methodologies," for details on the imputation of VMT).

Imputation of Vehicle Characteristics for 1975 and Later

Vehicle characteristics that were missing for vehicle model years 1975 and later were imputed using either the VIN

or the Environmental Protection Agency (EPA) certification files (CERT files) containing laboratory test results of

MPG. When the vehicle characteristic was missing from the questionnaire, but the VIN was available, the characteristics from the VIN were used. Additionally, when there was a discrepancy between the VIN and the RTECS

respondent’s answer, the VIN generally overrode the response provided by the respondent. If both the VIN and

questionnaire responses were missing, the vehicle characteristics were imputed from the CERT files. An individual

record from the CERT files was chosen as a donor for a recipient sample vehicle by first narrowing the choice by

using the known vehicle characteristics of the recipient vehicle, and then second, selecting a single CERT record

according to probabilities proportional to vehicle sales. The type of fuel (gasoline or diesel) used in the vehicle was

also imputed using the EPA CERT files (See Appendix B, "Estimation Methodologies," for more details on the use

of EPA CERT files in the 1991 RTECS.)

Energy Information Administration/Household Vehicles Energy Consumption 1991 149
150 Energy Information Administration/Household Vehicles Energy Consumption 1991
Imputation of Vehicle Characteristics and MPG for Pre-1975 Vehicle Model Years

For all RTECS sample vehicles, the questionnaires and VIN’s jointly provided the following vehicle characteristics:

make, model, model year, number of cylinders, engine displacement (liters or cubic inches), transmission type

(automatic or manual), and fuel system type (carbureted, gasoline fuel injected, or diesel). Many of these

characteristics were used to assign EPA test MPG to the sample vehicles. EPA records, in the form of CERT files,

were used to provide these MPG, as well as to provide any vehicle characteristics that were not obtained from the

questionnaire or VIN (See Appendix B, "Estimation Methodologies," for more details.)

The EPA CERT files, however, have only been available since 1975. The 1991 RTECS file contained 556 pre-1975

vehicles (9 percent), and for these vehicles, missing characteristics were imputed by a hot-deck procedure using 1991

respondents as donor vehicles. Each donor and recipient vehicle was paired on as many of the following

characteristics as possible: make, model, model year, transmission type, number of cylinders, and engine

displacement.

The MPG for pre-1975 vehicles were imputed using a cold-deck procedure. The donor vehicles were respondents

from the 1985 RTECS. Fuel purchase diaries were used in the 1985 RTECS; therefore, no shortfall adjustments were

needed for the MPG. Cold-decking was performed within categories defined by make, model, model year,

transmission type, and number of cylinders, with collapsing of categories performed where necessary. For example,

MPG could be selected from donor vehicles of a certain size class in either the Pontiacs or the Chevrolets, if they

shared similar model years, transmission type, and the General Motors 350 cubic inch V-8 engine. However, it

appeared that a greater share of the variability in the 1985 RTECS MPG was due to individual driving habits,

automotive maintenance and diary keeping, rather than to vehicle characteristics.

Quality of Specific Data Items

Vehicle Identification Number

The VIN is a unique combination of numbers and letters that when decoded provide the characteristics of a particular

vehicle. Since 1954, the VIN has been used by American automobile manufacturers. Beginning with the 1981

model year, a standard 17-character VIN was assigned to all vehicles sold in the United States. VIN’s were obtained

for most of the vehicles in the 1991 RTECS. The vehicle characteristics from decoded VIN’s were employed in the

1991 RTECS to enhance the accuracy of reported vehicle characteristics. These characteristics were used in

determining vehicle fuel efficiency based on the EPA certification files of test laboratory MPG estimates (See

Appendix A, "How the Survey Was Conducted," for a discussion of the VIN.)

There were three occasions where attempts were made to obtain the VIN’s: the RECS interview, the Beginning-ofYear (B-O-Y) interview, and the End-of-Year (E-O-Y) interview.

A computer software program, VINDICATOR, from the Highway Loss Data Institute, was used to decode the

VIN’s. For VIN’s that could not be decoded immediately using this program, a computer routine was developed

to correct for common errors in the transcription of VIN’s. The vehicle characteristics produced for these "fixed"

VIN’s were then carefully compared to respondent information. Approximately 200 VIN’s were salvaged using this

routine.

Overall, the collection of the VIN was a highly successful endeavor that yielded quality data. VIN’s were obtained

Energy Information Administration/Household Vehicles Energy Consumption 1991 151
for 4,617 (76 percent) of the 6,084 total sample vehicles. Of the 4,617 obtained VIN’s, 3,842 ( 83 percent) were

considered "good" VIN’s. In summary, "good" VIN’s were obtained for 3,842 (63 percent) of the 6,084 sampled

vehicles. (A good VIN was one that did not require correcting for common transcription error before it could be

decoded.)

Vehicle Fuel Price and Expenditures

Vehicle Fuel Price: In the 1991 and 1988 RTECS, compared to previous RTECS, the fuel price data were not

collected via fuel purchase diaries. Instead, fuel prices were determined from Bureau of Labor Statistics (BLS) Retail

Pump Average Gasoline Prices and the Lundberg Survey, Inc., prices. (See Appendix B, "Estimation Methodologies"

for a discussion of the sources of vehicle fuel prices and the assignment of specific prices to the RTECS data.)

To validate the 1988 and 1991 RTECS price methodology prior to the 1988 and 1991 RTECS, the 1985 RTECS

gasoline prices were recalculated and analyzed using the new 1991 methodology (BLS price data). Results of this

analysis suggest that if the 1985 BLS price data had been used in 1985 instead of fuel purchase diary data, the

average vehicle fuel price reported for the 1985 RTECS would have increased by approximately 2 cents per gallon.

For this analysis, only the prices for unleaded regular gasoline, unleaded premium gasoline, and leaded regular

gasoline were recalculated. The prices for leaded premium, diesel, and other fuels were left equal to the prices used

in the 1985 RTECS.

The BLS prices that were used for recalculating the 1985 RTECS prices were monthly 1985 regional retail gasoline

prices for leaded regular, unleaded regular, and unleaded premium. The prices were averaged across months for each

of the above fuel types within each of the four Census regions. One of these average prices was assigned to each

of the RTECS vehicles depending on Census region and on vehicle fuel type used.

Table C1 presents the BLS prices (monthly prices were for 1985) with the corresponding average prices from the

1985 RTECS. Overall, the BLS prices compared well with the corresponding average regional fuel prices from

RTECS. The largest difference corresponded to unleaded premium gasoline.

While there was general consistency between the BLS prices and the 1985 RTECS prices, the differences that did

exist may have stemmed from the differences in the two survey populations and survey collection procedures.

The BLS population (approximately 85 percent of the total U.S. population) consisted of the U.S. urban,

noninstitutional population excluding households living on military bases. The RTECS population represented both urban and rural areas and included military bases.

BLS prices were based on prices gathered from service stations and sales volume. The 1985 RTECS prices

were produced from fuel quantities and expenditures for individual vehicle refuelings.

The BLS sample was a rotating sample of service stations. Every year approximately one-fifth of the

service stations in the sample were replaced with service stations that consumers reported using in that

year’s "Point of Purchase Survey" conducted by the BLS. Thus, the BLS prices included service stations

where consumers currently purchased fuel as well as stations where they had previously purchased fuel.

The RTECS prices were based entirely on the service stations where consumers were currently purchasing

their vehicle fuel.

152 Energy Information Administration/Household Vehicles Energy Consumption 1991
Table C1. Average Bureau of Labor Statistics Gasoline Prices and 1985 Residential Transportation

Energy Consumption Survey Prices by Census Region and Fuel Type

Census Region

and Fuel Type

Average Price

(dollars per gallon)

1985 RTECS 1985 BLSa

Total U.S.

Total .......................

Unleaded Regular .............

Unleaded Premium ............

Leaded Regular ..............

Leaded Premium ..............

Diesel ......................

Other ......................

$1.1805

1.1848

1.2945

1.1080

1.3087

1.1845

1.1702

$1.1969

1.2001

1.3396

1.1128 b

b

b

Northeast

Total .......................

Unleaded Regular .............

Unleaded Premium ............

Leaded Regular ..............

Leaded Premium ..............

Diesel ......................

Other ......................

1.2033

1.1931

1.3151

1.1358

1.3220

1.2123

1.2209

1.2082

1.2000

1.3327

1.1243 b

b

b

Midwest

Total .......................

Unleaded Regular .............

Unleaded Premium ............

Leaded Regular ..............

Leaded Premium ..............

Diesel ......................

Other ......................

1.1831

1.1916

1.2838

1.1244

1.2495

1.1862

1.1965

1.2098

1.2185

1.3572

1.1333 b

b

b

South

Total .......................

Unleaded Regular .............

Unleaded Premium ............

Leaded Regular ..............

Leaded Premium ..............

Diesel ......................

Other ......................

1.1620

1.1615

1.2795

1.0806

1.2333

1.1706

1.1112

1.1847

1.1805

1.3302

1.0927 b

b

b

West

Total .......................

Unleaded Regular .............

Unleaded Premium ............

Leaded Regular ..............

Leaded Premium ..............

Diesel ......................

Other ......................

1.1909

1.2075

1.3300

1.1170

1.3985

1.1885

1.2040

1.1938

1.2091

1.3562

1.1153 b

b

b

a

BLS average prices in this table were derived by assigning BLS prices to the 1985 RTECS sample vehicles, then producing

national averages using the 1985 RTECS sample weights. b

Prices for these fuels were not collected by BLS; therefore, the 1985 RTECS prices were used.

Energy Information Administration/Household Vehicles Energy Consumption 1991 153
Vehicle Fuel Expenditures: Vehicle fuel expenditures were calculated by multiplying the price paid for fuel by

the quantity of fuel used. Expenditures per household were the sum of the expenditures for each vehicle in the

household. To assess the effect of the 1988 RTECS price methodology on vehicle fuel expenditures, the 1985

household vehicle fuel expenditures were recalculated using the 1985 BLS price data. Table C2 compares average

expenditures by fuel type and Census region using both sources of price data.

The use of BLS prices for the 1985 RTECS would have increased the per household expenditures for vehicle fuel

from $1,274 per year to $1,292 per year. The changes in expenditures reflect differences in the average price of

gasoline between the new 1988 methodology and the 1985 RTECS methodology since the average consumption used

to calculate the expenditures comes from the RTECS data under the new and original methodologies. The estimated

total 1985 U.S. expenditures for vehicle fuel increased from 99.1 billion dollars to 100.4 billion dollars when the

1988 methodology was applied to the 1985 RTECS data.

The 1988 RTECS price methodology seemed to have little effect on the standard errors of expenditure statistics.

When the 1985 RTECS prices were recalculated using 1985 BLS price data, the standard errors of the expenditures

were close to the standard errors reported using the 1985 RTECS fuel purchase diary data. While the standard errors

of the fuel prices were reduced, in some cases by 50 percent, the variability in fuel prices was very small relative

to the variability in gallons of fuel consumed. Therefore, the standard errors of the vehicle fuel expenditures were

largely controlled by the variability in gallons of fuel consumed.

Gasohol

In the 1991 RTECS, a little over 1.6 million households reported that they purchased gasohol. In the 1988 RTECS,

there was no category for "gasohol" in the detailed tables showing "Type of Fuel Purchased" but there is reason to

believe that a small portion of the 81.1 billion gallons of gasoline was gasohol since an estimated 8,138 gallons of

gasohol was sold in 1988. This estimate was derived from Federal Highway Administration Statistics (Department

of Transportation, Washington, D.C., Monthly Gasohol Reported by States--1988, Table MF-33GLA). Only a few

1988 RTECS households reported purchasing gasohol. Gasohol, a mixture of 10 percent ethanol and 90 percent

gasoline, is not sold under the name "gasohol". It is sold as "ethanol blends." Given the disparity between the few

households reporting purchasing gasohol and the amount of gasohol sold, it does seem likely that some households

that reported purchasing gasoline actually bought "gasohol" or "ethanol blends," resulting in an underestimation of

the amount of gasohol consumed in 1988. Whether the use of "ethanol blend" in the questionnaire in place of

"gasohol" would have increased reports of the alcohol fuel is speculative.

Sampling Error

The random differences between the survey estimates and the true population value that occur because of the

particular sample that was selected are known as sampling errors. The average sampling error, averaged over all

possible samples, should be zero. Although the sampling error is nonzero and unknown for the particular sample

chosen, the sample design permits sampling errors to be estimated. The typical magnitude of the sampling error is

measured by the "standard error" of the estimate. Standard errors in this report are given as percents of their

estimated values, that is, as relative standard errors (RSE). The RSE is also known as the coefficient of variation.

154 Energy Information Administration/Household Vehicles Energy Consumption 1991
Table C2. Average Bureau of Labor Statistics Vehicle Fuel Expenditures and 1985 Residential

Transportation Energy Consumption Survey Vehicle Fuel Expenditures by Census

Region and Fuel Type

Census Region

and Fuel Type

Average Expenditures

1985 RTECS 1985 BLSa

Total U.S.

Total .......................

Unleaded Regular .............

Unleaded Premium ............

Leaded Regular ..............

Leaded Premium ..............

Diesel ......................

Other ......................

$1,274

686

213

341

10

22

2

$1,292

695

220

342

b

b

b

Northeast

Total .......................

Unleaded Regular .............

Unleaded Premium ............

Leaded Regular ..............

Leaded Premium ..............

Diesel ......................

Other ......................

1,169

694

225

232

6

12

1

1,174

698

228

229

b

b

b

Midwest

Total .......................

Unleaded Regular .............

Unleaded Premium ............

Leaded Regular ..............

Leaded Premium ..............

Diesel ......................

Other ......................

1,266

724

164

352

5

17

3

1,294

741

174

355

b

b

b

South

Total .......................

Unleaded Regular .............

Unleaded Premium ............

Leaded Regular ..............

Leaded Premium ..............

Diesel ......................

Other ......................

1,321

659

281

348

10

21

2

1,347

670

292

352

b

b

b

West

Total .......................

Unleaded Regular .............

Unleaded Premium ............

Leaded Regular ..............

Leaded Premium ..............

Diesel ......................

Other ......................

1,304

678

147

418

21

39

2

1,307

679

149

417

b

b

b

a

BLS average expenditures in this table were derived by assigning BLS prices by fuel type and region to the 1985 RTECS

sample vehicles, then producing expenditure averages by using the 1985 RTECS quantities of vehicle fuel consumed. b

Prices for these fuels were not collected by BLS; therefore, the 1985 RTECS prices were used in the computations.

Energy Information Administration/Household Vehicles Energy Consumption 1991 155
For a given survey statistic, Y, the relative standard error, RSE(Y) is given by:

(1)

The standard error of Y is SY. Therefore:

(2)

The following sections provide a discussion of the procedure used to estimate sampling variances as well as an

explanation and example of the procedures used to calculate approximate RSE’s for each statistic shown in Tables

6 through 23 in the "Detailed Tables" section of this publication.

Balanced Half-Sample Replication

For some surveys, a convenient algebraic formula for computing variances can be obtained. However, the RECS

(of which the RTECS is a subsample) used a multistage area sample design of such complexity that it is virtually

impossible to construct an exact algebraic expression for estimating variances (See Housing Characteristics 1990

(published May 1992), DOE/EIA-0314(90) Appendix A). Instead, the method used to estimate sampling variances

for this survey was balanced half-sample replication. This numerical method involves pairing primary sampling units

(PSU) in the strata so that differences between the members of each pair can be used to build an estimate of

sampling variance. The strata were collapsed to 85 new strata to achieve this pairing of PSU’s. Of these 85 strata,

44 each contained two nonself-representing PSU’s belonging to the same Census division, with one PSU constituting

each member of a pair. Of the remaining 41 strata, 32 were each composed of one self-representing PSU; that is,

they consisted of large metropolitan areas that came into the sample with certainty. In each of the latter strata, all

of the PSU’s were treated as a composite PSU, while the segments within the composite PSU were segregated into

two groups representing the two members of a pair. There was no between-PSU component of variance for selfrepresenting PSU’s. The nine remaining strata contained nonself-representing PSU’s that were treated as if they were

self-representing PSU’s. These nine strata were in separate Census divisions, and were not collapsed to form pairs

of nonself-representing PSU’s due to a desire to restrict pairing to within the nine Census divisions, and also due

to the desire to treat Alaska and Hawaii as two separate and unique strata.

Balanced half-sample replication involved repeatedly drawing pair members from the 85 strata. Each replication is

called a "half-sample" because only one member of the pair within each of the 85 strata was selected. The

poststratification procedure described in Appendix A, "How the Survey Was Conducted," was performed independently for each half-sample, so that the resulting variance estimates would reflect the benefits of poststratification.

The sample units drawn into each half-sample and adjusted by poststratification can produce unbiased survey

statistics based on roughly one-half of the data. Using different combinations of members from the 85 pairs, it is

possible to produce a total of 285 = 3.9 X 1025 unique half-samples.

Although desirable for good variance estimation, a large number of half-samples would be computationally infeasible.

However, the method of balanced half-sample replication allows a small number of half-samples (approximately

equal to the number of strata) to produce estimates of variance that are identical to estimates based on all possible

unique half-samples for linear survey statistics. The use of ratio adjustments such as poststratification means that

even a statistic giving the number of households in a category is not a linear statistic. For nonlinear survey statistics,

156 Energy Information Administration/Household Vehicles Energy Consumption 1991
the variance estimate computed using the method of balanced half-samples is approximately equal to the variance

estimate computed using all possible half-samples. With this balancing method each half-sample is constructed by

using an orthogonal matrix to control the selection of pair members from strata. For the RTECS, 128 balanced

half-samples were used in variance estimation.

Energy Information Administration/Household Vehicles Energy Consumption 1991 157
The variances are estimated from the 128 half-sample-based statistics in the following way. Let Y’ be a survey

estimate of characteristic Y for a certain category of housing units (for example, total consumption of vehicle fuel

in the West Census Region). Then, the estimated variance of Y’ is given by:

where Yi’ is the ith half-sample estimate of Y. The standard error of Y’ is given by:

(3)

Row and Column Factors

(4)

RSE’s were calculated for all statistics in this publication, although they cannot be presented due to space limitations.

However, the RSE’s are presented in a generalized form. The method of presenting generalized RSE’s of statistics

uses sets of row and column factors inserted in the top row and right-most column of figures in each table. This

method of presentation allows the readers to calculate an approximate RSE for each statistic. To estimate the RSE

of a statistic in the ith row and jth column of a particular table, the approximation RSEAi,j for the original RSEi,j is

given by:

Where: Ri is the RSE row factor given at the right-most margin of row i in the tables, and Cj is the RSE column

(5)

factor given at the top of column j.

The following example illustrates this procedure:

Referencing the second row of the table (Figure C1) labeled "Northeast," and the third column labeled "Vehicle Miles

Traveled (billion)," yields an estimate of 295 billion miles driven. The RSE row factor is R2 = 4.4, and the RSE

column factor is C3 = 1.1. The approximate RSE for the estimate is, therefore,

The standard error derived from row and column factors can be used to construct confidence intervals as in Figure

(6)

C1, and to perform hypothesis tests by standard statistical methods. However, because the generalized variance

procedure gives only approximate RSE’s, such confidence intervals and statistical tests must also be regarded as only

approximate.

158 Energy Information Administration/Household Vehicles Energy Consumption 1991
For the example above, the RSE determined directly by the half-sample method is actually 5.20 percent, not 4.84

percent.

Energy Information Administration/Household Vehicles Energy Consumption 1991 159
Figure C1. Use of RSE Row and Column Factors

160 Energy Information Administration/Household Vehicles Energy Consumption 1991
Total Vehicle Miles Traveled in the Northeast Census Region = 295 billion miles

R (Northeast Census Region) = 4.4

C (Vehicle Miles Traveled) = 1.1

Approximate RSE

(Total Vehicle Miles Traveled in the Northeast Census Region) = (4.4) X (1.1)

= 4.84 percent

Approximate Standard Error

(Total Vehicle Miles Traveled in the Northeast Census Region) = (4.4) X (1.1) X 295/100

= 14.29 billion miles

Approximate 2 Standard Errors

(95 percent confidence interval) = (1.96) X (14.29)

= 28.01 billion miles

Therefore, with approximately 95 percent confidence, the total vehicle miles traveled in the Northeast

Census Region in 1991 was between 267 billion and 323 billion miles (295 ± 28)

Source: Energy Information Administration, Office of Energy Markets and End Use, the 1991 Residential Transportation Energy

Consumption Survey.

Derivation of Row and Column Factors

The row and column factors are determined from a two-factor analysis of the table of RSE’s on the basis of the twoway model,

Where:

(7)

(log RSE) = the mean of log RSEi,j over all rows i and columns j,

(log RSE)i. = the mean over all columns j for a particular row i, and

(log RSE).j = the mean over all rows i for a particular column j.

The row and column RSE factors are than computed as:

The RSE row factor, Ri, is the geometric mean of the RSE’s in row i. The RSE column factor, Cj, is an adjustment

Energy Information Administration/Household Vehicles Energy Consumption 1991 161
factor with geo- (8)

(9)

metric mean

equal to 1.0.14

Statistics in the

tables in the

"Detailed Tables" section are suppressed by the footnote symbol "Q" if (1) the RSE exceeds 50 percent, or (2) for

tables showing household counts, fewer than 10 sample households were used to compute the statistics, or (3) for

tables showing vehicle counts, fewer than 18 sample vehicles were used to compute the statistics. The estimation

procedure used to obtain the row and column factors does not use RSE’s for statistics that were suppressed by the

footnote "Q" or for statistics with RSE’s that are less than 1.0 percent. In addition, if the statistic for a cell is not

listed for any other reason, the RSE for that cell is not used in the procedure. This convention is used because the

product of the row and column factors frequently is an inaccurate estimate for these RSE’s.

Using these cells in the calculation of the row and column factors may result in factors that give inaccurate RSE

estimates for other cells actually presented in the table.

Whenever a household count is a poststratification control total, its RSE estimate is zero. An example is the cell

in the first row and first column of Table 25. This cell contains an estimate of the national total of households as

of July 1991 (that is, households with and without vehicles). Because the RSE is zero, this cell was not used in the

computation of row and column factors. Zero RSE’s are never used in row and column calculations, because their

inclusion would make the row and column factors inappropriately low for the bulk of the statistics in the tables.

Therefore, RSE’s calculated from row and column factors for the total household count in Table 25 or for any other

poststratification control total, will be inappropriately overestimated.

Determination of the Standard Error of the Difference Between Two Statistics

The procedure used to compute the standard error of the difference between two statistics follows:

This procedure assumes the two statistics are not correlated. The following example illustrates this procedure.

(10)

Households with children drove an average of 22,800 miles per household in 1991. Households without children

drove an average of 16,500 miles, for a difference of 6,300 miles. The RSE’s for households with and without

children are 2.9 and 2.3, respectively. The corresponding standard errors are 661 miles and 380 miles, respectively.

Therefore, the standard error for the difference is:

If 1.96 times the standard error is greater than the difference between the statistics, the difference is not statistically

(11)

significant at the .05 level of significance (the level used to test significance of inferences in this report). In this

example, 1.96 times the standard error equals 1,494 miles, while the difference is 6,300 miles. Therefore, the con14For detailed discussions of the accuracy of the RSE approximation, the procedure for estimating confidence intervals, and the statistical tests

of hypotheses, see Nonresidential Buildings Energy Consumption Survey: Commercial Buildings, Consumption and Expenditures, 1983,

DOE/EIA-0318(83) (Washington, DC, October 1986).

162 Energy Information Administration/Household Vehicles Energy Consumption 1991
clusion is that, in 1991, there was a significant difference in average mileage driven per household, between

households with and without children.

Energy Information Administration/Household Vehicles Energy Consumption 1991 163