These detailed tables are of three types. The tables
displaying the number of households by hours of lighting use and
household characteristics (Tables 4.1 through 4.8) were compiled
from data collected on the RECS Household Questionnaire. The data
in Tables 4.9 through 4.17 are based on information collected
from the RECS Household Questionnaire and estimates derived from
models developed with the Lighting Supplement data. Tables 4.18
through 4.23 contain data collected directly from the Lighting
Supplement. Figure 4.1 provides a summary of the three types of
detailed tables.
| Figure 4.1 Summary of Detailed Tables | ||||
Estimates | ||||
| 4.1- 4.8 | 1993 RECS Household Survey | Weighted Survey Data | 7,111 | Presented in row and column factors |
| 4.9-4.17 | 1993 RECS Household Survey and Lighting Supplement Questionnaire | Regression Estimates | 7,111 | Standard errors of data presented in row and column factors.
Regression model errors not included. |
| 4.18-4.23 | 1993 RECS Lighting Supplement Questionnaire | Unweighted Survey Data | 474 | No estimates of standard errors. |
The sample selected for the RECS Household Questionnaire
was designed to provide population estimates by applying weights
to the household data. In contrast, the Lighting Supplement sample
was designed only to collect data upon which to base a model of
lighting consumption, not to provide population estimates. Consequently,
Tables 4.18 through 4.23 do not contain estimates of standard
errors. Tables 4.1 through 4.17 contain relative standard errors
(RSE's) in terms of row and column factors.
Statistical Significance of Data
Row and Column Factors
Tables 4.1 through 4.17 provide row factors in the far-right column and column factors on the top line of each table. These factors are to be used to determine the Relative Standard Error (RSE) for each estimate, which, in turn, can be used to determine the standard error and the confidence level of the estimate and to determine whether the difference between any two figures is statistically significant. However, since the RSE's are only approximate, standard errors, confidence intervals, and statistical tests must also be regarded as only approximate.
To calculate the RSE for a specific estimate, multiply
the row factor by the column factor, as illustrated in Figure
4.2, an excerpt from Table 4.3 of this report. This table shows
that there are 14.9 million households in the United States that
have three to five rooms and have two lights on one to four hours
a day. Multiplying the row factor (6.3) by the column factor (0.7)
yields a relative standard error of 4.41 percent.
Figure 4.2. Use of RSE Row and Column Factors
| Table 4.3. Light Usage by Total Number of Rooms, Million U.S. Households, 1993 | ||||||
(Excluding Bathrooms) | Row Factors | |||||
| Total | 3.6 | |||||
| Indoor Electric Lights
Total Number of Lights on 1 to 4 Hours | ||||||
| None | 11.8 | |||||
| 1 | 6.8 | |||||
| 2 | 6.3 | |||||
| 3 | 7.8 | |||||
| 4 | 10.9 | |||||
| 5 or More | 10.1 | |||||
| Source: Energy Information Administration, Office of Energy Markets and End Use, 1993 Residential Energy Consumption Survey. | ||||||
Standard Errors
Because the estimates presented in the following
tables are based on a sample of residential housing units, they
are subject to sampling error, or standard error. To determine
the standard error for an estimate in these tables, multiply the
approximate RSE by the estimate. For example, to determine the
standard error of the estimate of the number of households with
three to five rooms that have two lights on one to four hours
per day, multiply .0441 by 14.9 million. The result, .66 million
households, is the approximate standard error for the estimate.
Confidence Levels
For each of the estimates given in Tables 4.1 through 4.17, a 95-percent confidence range can be determined with the estimate at the mid-point. To calculate the 95-percent confidence range for a given figure:
1. Multiply the RSE row factor by the RSE column factor to determine the approximate RSE.
2. Multiply the approximate RSE (divided by 100) by the estimate given in the table to determine the approximate standard error.
3. Multiply the result by 1.96 to determine approximate 2 standard errors.
4. Subtract the result of Step 3 from the given estimate to determine the bottom of the range.
5. Add the result of Step 3 to the given estimate to determine the top of the range.
The result of these steps will yield a range with the property whereby, in repeated surveys, the estimate would fall in the range constructed in this way 95 percent of the time.
For example, to determine the confidence range for the estimate highlighted in Figure 4.2:
1. Multiply 6.3 (the RSE row factor) by 0.7 (the RSE column factor), which yields 4.41 percent (the approximate RSE).
2. Multiply .0441 (the approximate RSE) by 14.9 million households (the estimate), which yields 0.657 million households (the approximate standard error).
3. Multiply 0.657 million households by 1.96, which yields 1.29 million households (approximate 2 standard errors).
4. To determine the bottom of the range, subtract 1.29 million households from 14.9 million, which yields 13.61 million households.
5. To determine the top of the range, add 1.29 million households to 14.9 million, which yields 16.19 million households.
It can then be said with 95-percent confidence that,
in 1993, the number of households with three to five rooms, that
used two lights for one to four hours each day falls between 13.61
and 16.19 million households.
Statistical Significance Between Two Statistics
The difference between any two estimates given in the detailed tables may or may not be statistically significant. Statistical significance for the difference between two independent variables is computed as:
where S is the standard error, x1 is the
first estimate, and x2 is the second estimate. The
result of this computation is to be multiplied by 1.96, and if
this result is less than the difference between the two estimates,
the difference is statistically significant.
For example, from Figure 4.2, you can see that
13.1 million households have three to five rooms and use one light
one to four hours per day. The number of households with six to
eight rooms that use one light one to four hours per day is 7.2
million. The difference between the two estimates is 5.9 million
households. The standard error for the 13.1 million households
(x1) is 0.62 million. The standard error for the 7.2 million (x2)
households is 0.34 million:
Multiplying 0.707 by 1.96 yields 1.39 million households.
Since 1.39 million households is less than the 5.9 million difference
between the two estimates, the difference is statistically significant.
Tables
4.1 Light Usage by Heated Floorspace Category, Millions U.S. Households, 1993
4.2 Light Usage by Heated Floorspace Category, Percent of U.S. Households, 1993
4.3 Light Usage by Total Number of Rooms, Million U. S. Households, 1993
4.4 Light Usage by Total Number of Rooms, Percent of U.S. Households, 1993
4.5 Light Usage by Family Income Category, Million U.S. Households, 1993
4.6 Light Usage by Family Income Category, Percent of U.S. Households, 1993
4.7 Light Usage by Household Size, Million U.S. Households, 1993
4.8 Light Usage by Household Size, Percent of U.S. Households, 1993
4.10 Mean Annual Electricity Consumption for Lighting, by Family Income by Number of Rooms, 1993
4.13 Mean Annual Electricity Expenditures for Lighting, by Family Income by Number of Rooms, 1993
4.18 Number of Lights by Room by Hours Used, 1993
4.19 Number of Lights by Type of Bulb by Hours Used, 1993
4.20 Number of Lights by Bulb Type by Room, 1993
4.21 Number of Households by Daily Kilowatthours by Number of Rooms
4.22 Number of Households by Daily Kilowatthours by Number of Household Members
4.23 Number of Households by Daily Kilowatthours by Family Income