STATISTICAL SIGNIFICANCE OF DATA
Row and Column Factors
The tables
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 the figure below, an excerpt
from Table HC1-4a of this report. This table shows that 32.6 million
single-family housing units were located in suburban areas.
Multiplying 9.9 (the row factor) by 0.7 (the column factor) yields
an approximate RSE of 6.94 percent.
Table HC1-4a. Housing Unit Characteristics by Type of Housing Unit,
Million U.S. Households, 2001 - PRELIMINARY DATA
______________________________________________________________________________________________________________
| | |
| | Type of Housing Unit |
| |_______________________________________________________|
| | | | |
| | | Multifamily | |
| | |___________________________| |
| | | | | |
Housing Unit | Total |Single-Family| Two to Four | Five or More| Mobile Home |
Characteristics | | | Units | Units | |
|_________|_____________|_____________}_____________|_____________| RSE
| | | | | | Row
RSE Column Factor: | 0.6 | 0.7 | 1.2 | 1.1 | 1.6 |Factors
____________________________________|_________|_____________|_____________|_____________|_____________|_______
|
Total............................... 107.0 73.7 9.5 17.0 6.8 | 6.1
|
Metropolitan Statistical Area |
Urban............................. 85.5 57.2 8.1 16.1 4.1 | 7.0
Central City.................... 40.0 24.6 4.9 9.2 1.4 | 10.2
------------------------------------------------------------------------------------------------------|-------
Suburban........................ 45.5 32.6 3.2 6.9 2.8 | 9.9
------------------------------------------------------------------------------------------------------|-------
Rural............................. 21.5 16.5 1.4 0.9 2.7 | 14.5
______________________________________________________________________________________________________|_______
Source: Energy Information Administration, Office of Energy Markets and End Use, Forms EIA-457 A, B, C of
the 2001 Residential Energy Consumption Survey.
Standard Errors
Since 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 32.6 million
single-family housing units located in the suburbs in 2001, multiply
32.6 million housing units by .0693 (the approximate RSE). The
result, 2.26 million housing units, is the approximate standard
error for the estimate.
Confidence Levels
-
For each of
the estimates given in the tables, 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 that, 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 estimated 32.6
million single-family housing units located in the suburbs in
2001:
-
-
1. Multiply
9.9 (the RSE row factor) by 0.7 (the RSE column factor), which
yields 6.93 percent (the approximate RSE).
-
2. Multiply
.0693 (the approximate RSE) by 32.6 million households (the
estimate), which yields 2.26 million housing units (the
approximate standard error).
-
3. Multiply
2.26 million housing units by 1.96, which yields 4.4 million
housing units (approximate 2 standard errors).
-
4. To
determine the bottom of the range, subtract 4.4 million housing
units from 32.6 million housing units, which yields 28.2 million
housing units.
-
5. To
determine the top of the range, add 4.4 million housing units to
32.6 million housing units, which yields 37.0 million housing
units.
It can then be
said with 95-percent confidence that, in 2001, between 28.2 million
and 37.0 million of the single-family housing units were located in
the suburbs.
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, x1is the first
estimate, and x2is 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, in 2001, 32.6 million single-family housing units were
located in the suburbs, while 24.6 million single-family housing
units were located in the central city, for an estimated difference
of 8.0 million housing units. The standard error for the 32.6
million suburban single-family housing units estimate
(x1) is 2.26, and the standard error for the 24.6 million
central city single-family housing units estimate (x2) is
1.76:
Multiplying 2.86 by 1.96 yields 5.6 million housing units.
Since 5.6 housing units is less than the 8.0 million housing units
difference between the 2001 suburban and central city single-family
housing unit estimates, the difference is statistically significant.
Contact:
- Stephanie.Battles@eia.doe.gov
- Stephanie Battles
- RECS Survey Manager
- Phone: (202) 586-7237
- Fax: (202) 586-0018
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