o The 1990 Decennial Census of Population and Housing.
o An adjustment for undercoverage in the 1990 census.
o Statistics on births, deaths, immigration, and emigration.
o Statistics on the size of the Armed Forces.
The estimation procedure for the March supplement included a further adjustment so husband and wife of a household received the same weight. The independent population estimates include some, but not all, undocumented immigrants.
ACCURACY OF THE ESTIMATES
Since the CPS estimates come from a sample, they may differ from figures from a complete census using the same questionnaires, instructions, and enumerators. A sample survey estimate has two possible types of error: sampling and nonsampling. The accuracy of an estimate depends on both types of error, but the full extent of the nonsampling error is unknown. Consequently, one should be particularly careful when interpreting results based on a relatively small number of cases or on small differences between estimates. The standard errors for CPS estimates primarily indicate the magnitude of sampling error. They also partially measure the effect of some nonsampling errors in responses and enumeration, but do not measure systematic biases in the data. (Bias is the average overall possible samples of the differences between the sample estimates and the desired value.)
Nonsampling variability. Several sources of nonsampling error include the following:
o Inability to get information about all sample cases.
o Definitional difficulties.
o Differences in interpretation of questions.
o Respondents' inability or unwillingness to provide correct information.
o Respondents' inability to recall information.
o Errors made in data collection, such as recording and coding data.
o Errors made in processing the data.
o Errors made in estimating values for missing data.
o Failure to represent all units with the sample (undercoverage).
CPS undercoverage results from missed housing units and missed persons within sample households. Overall CPS undercoverage is estimated to be about 8 percent. CPS undercoverage varies with age, sex, and race. Generally, undercoverage is larger for males than for females and larger for Blacks and other races combined than for Whites. As described previously, ratio estimation to independent age-sex-race-Hispanic population controls partially corrects for the bias due to undercoverage. However, biases exist in the estimates to the extent that missed persons in missed households or missed persons in interviewed households have different characteristics from those of interviewed persons in the same age-sex-race-origin-state group.
A common measure of survey coverage is the coverage ratio, the estimated population before ratio adjustment divided by the independent population control. Table A shows CPS coverage ratios for age-sex-race groups for March 1995. The CPS coverage ratios can exhibit some variability from month to month. Other Census Bureau household surveys experience similar coverage.
Table A. CPS Coverage Ratios NonBlack Black All Persons Age M F M F M F Total 0-14 0.929 0.964 0.850 0.838 0.916 0.943 0.929 15 0.933 0.895 0.763 0.824 0.905 0.883 0.895 16-19 0.881 0.891 0.711 0.802 0.855 0.877 0.866 20-29 0.847 0.897 0.660 0.811 0.823 0.884 0.854 30-39 0.904 0.931 0.680 0.845 0.877 0.920 0.899 40-49 0.928 0.966 0.816 0.911 0.917 0.959 0.938 50-59 0.953 0.974 0.896 0.927 0.948 0.969 0.959 60-64 0.961 0.941 0.954 0.953 0.960 0.942 0.950 65-69 0.919 0.972 0.982 0.984 0.924 0.973 0.951 70+ 0.993 1.004 0.996 0.979 0.993 1.002 0.998 15+ 0.914 0.945 0.767 0.874 0.898 0.927 0.918 0+ 0.918 0.949 0.793 0.864 0.902 0.931 0.921
These coverage ratios are for March 1995.
For additional information on nonsampling error including the possible impact on CPS data when known, refer to Statistical Policy Working Paper 3, An Error Profile: Employment as Measured by the Current Population Survey, Office of Federal Statistical Policy and Standards, U.S. Department of Commerce, 1978 and Technical Paper 40, The Current Population Survey: Design and Methodology, Bureau of the Census, U.S. Department of Commerce.
Comparability of data. Data obtained from the CPS and other sources are not entirely comparable. This results from differences in interviewer training and experience and in differing survey processes. This is an example of nonsampling variability not reflected in the standard errors. Use caution when comparing results from different sources.
A number of changes were made in data collection and estimation procedures beginning with the January 1994 CPS. The major change was the use of a new questionnaire. The questionnaire was redesigned to measure the official labor force concepts more precisely, to expand the amount of data available, to implement several definitional changes, and to adapt to a computer-assisted interviewing environment. The March supplemental income questions were also modified for adaptation to computer-assisted interviewing, although there were no changes in definitions and concepts. Due to these and other changes, one should use caution when comparing estimates from data collected in 1994 and later years with estimates from earlier years.
Caution should also be used when comparing data from this microdata file, which reflects 1990 census-based population controls, with microdata files from March 1993 and earlier years, which reflect 1980 census-based population controls. This change in population controls had relatively little impact on summary measures such as means, medians, and percentage distributions. It did have a significant impact on levels. For example, use of 1990 based population controls results in about a 1-percent increase in the civilian noninstitutional population and in the number of families and households. Thus, estimates of levels for data collected in 1994 and later years will differ from those for earlier years by more than what could be attributed to actual changes in the population. These differences could be disproportionately greater for certain subpopulation groups than for the total population.
Since no independent population control totals for persons of Hispanic origin were used before 1985, compare Hispanic estimates over time cautiously.
Data users should be aware of the effect of the redesigned CPS sample phase-in period from April 1994 through June 1995 on the metropolitan/nonmetropolitan estimates. During this phase-in period, CPS data were collected from sample designs based on both the 1980 and 1990 censuses. While most CPS estimates have been unaffected by this mixed sample, metropolitan/nonmetropolitan estimates have been affected. The 1990 sample cases were recoded to reflect the 1980 metropolitan/nonmetropolitan definitions to allow the estimates to be comparable with earlier data. The gross error rate for the conversions of central cities/suburbs is not expected to exceed 5%.
Note when using small estimates. Because of the large standard errors involved, summary measures probably do not reveal useful information when computed on a base smaller than 75,000.
Take care in the interpretation of small differences. Even a small amount of nonsampling error can cause a borderline difference to appear significant or not, thus distorting a seemingly valid hypothesis test.
Sampling variability. Sampling variability is variation that occurred by chance because a sample was surveyed rather than the entire population. Standard errors as calculated below are primarily measures of sampling variability, but they may include some nonsampling error.
Standard errors and their use. A number of approximations are required to derive, at a moderate cost, standard errors applicable to estimates from this data. Instead of providing an individual standard error for each estimate, generalized sets of standard errors are provided for various types of characteristics. Thus, the tables show levels of magnitude of standard errors rather than the precise standard errors.
Table B shows parameters to use for basic CPS monthly labor force estimates. The tables in the attachment show parameters for March supplement data including the Hispanic supplement.
The sample estimate and its standard error enable one to construct a confidence interval. A confidence interval is a range that would include the average result of all possible samples with a known probability. For example, if all possible samples were surveyed under essentially the same general conditions and the same sample design, and if an estimate and its standard error were calculated from each sample, then approximately 90 percent of the intervals from 1.645 standard errors below the estimate to 1.645 standard errors above the estimate would include the average result of all possible samples.
A particular confidence interval may or may not contain the average estimate derived from all possible samples. However, one can say with specified confidence that the interval includes the average estimate calculated from all possible samples.
Standard errors may be used to perform hypothesis testing. This is a procedure for distinguishing between population parameters using sample estimates. The most common type of hypothesis is that the population parameters are different. An example of this would be comparing the percentage of Whites with a college education to the percentage of Blacks with a college education.
Tests may be performed at various levels of significance. A significance level is the probability of concluding that the characteristics are different when, in fact, they are the same. For example, to conclude that two parameters are different at the 0.10 level of significance, the absolute value of the estimated difference between characteristics must be greater than or equal to 1.645 times the standard error of the difference.
The Census Bureau uses 90-percent confidence intervals and 0.10 levels of significance to determine statistical validity. Consult standard statistical texts for alternative criteria.
Standard errors of estimated numbers. There are two ways
to compute the approximate standard error,
, of an estimated number. The first uses the formula
where f is a factor from Table III, and s is the standard error of the estimate obtained by interpolation from Table I.A or II.A. The second method uses formula (2), from which the standard errors in Tables I.A and II.A were calculated. This formula will provide more accurate results than formula (1).
Here x is the size of the estimate and a and b are the parameters in Table B or Table IV associated with the particular type of characteristic. When calculating standard errors for numbers from cross-tabulations involving different characteristics, use the factor or set of parameters for the characteristic which will give the largest standard error.
Suppose there were 5,360,000 unemployed females in the civilian labor force. Use the appropriate parameters from Table B and formula (2) to get
Number, x 5,360,000 a parameter -0.000016 b parameter 2,465 standard error 113,000 90% conf. int. 5,174,000 to 5,546,000
The standard error is calculated as
the 90-percent confidence interval is calculated as 5,360,000 ± 1.645 x 113,000.
A conclusion that the average estimate derived from all possible samples lies within a range computed in this way would be correct for roughly 90-percent of all possible samples.
Suppose there are 8,419,000 high school graduates aged 20 to 24 years old. Use the appropriate parameters from Table IV and formula (2) to get
Number, x 8,419,000 a parameter -0.000013 b parameter 2,549 Standard error 143,000 90% conf. int. 8,184,000 to 8,654,000
The standard error is calculated as
The 90-percent confidence interval is calculated as 8,419,000 ± 1.645 x 143,000.
A conclusion that the average estimate derived from all possible samples lies within a range computed in this way would be correct for roughly 90 percent of all possible samples.
Table B. Parameters for Computation of Standard Errors for Labor Force
Characteristics: March 1995
Characteristic a b
Labor Force and Not In Labor
Force Data Other than
Agricultural Employment
and Unemployment
Total 1 -0.000016 2,488
Men 1 -0.000029 2,301
Women -0.000026 2,112
Both sexes, 16 to 19 -0.000150 2,040
years
White 1 -0.000017 2,488
Men -0.000032 2,301
Women -0.000029 2,112
Both sexes, 16 to 19 -0.000178 2,040
years
Black -0.000113 2,613
Men -0.000274 2,458
Women -0.000164 2,182
Both sexes, 16 to 19 -0.001145 2,391
years
Hispanic origin -0.000200 2,946
Not In Labor Force (use only
for Total, Total Men, and +0.000005 691
White)
Agricultural Employment
Total or White +0.000686 2,541
Men +0.000755 2,351
Women or
Both sexes, 16 to 19 -0.000022 2,155
years -0.000122 2,626
Black
Hispanic origin +0.011486 2,189
Total or Women
Men or +0.015153 1,269
Both sexes, 16 to 19
years
Unemployment
Total or White -0.000016 2,465
Black -0.000191 2,622
Hispanic origin -0.000099 2,705
1 For not in labor force characteristics, use the Not In Labor Force parameters.
The alternate calculation of the standard error, using formula (1), with f = 1.00 from Table III and s = 142,000 by interpolation from Table I.A is
Standard errors of estimated percentages. The reliability of an estimated percentage, computed using sample data for both numerator and denominator, depends on the size of the percentage and its base. Estimated percentages are relatively more reliable than the corresponding estimates of the numerators of the percentages, particularly if the percentages are 50 percent or more. When the numerator and denominator of the percentage are in different categories, use the factor or parameter from Tables III and IV indicated by the numerator.
The approximate standard error,
, of an estimated percentage can be obtained by use of the formula
In this formula, f is the appropriate factor from Table III and s is the standard error of the estimate obtained by interpolation from Tables I.B.1 through I.B.9 or II.B.1 through II.B.3.
Alternatively, formula (4) will provide more accurate results:
Here x is the total number of persons, families, households, or unrelated individuals in the base of the percentage, p is the percentage (0 <= p <= 100), and b is the parameter in Table IV associated with the characteristic in the numerator of the percentage.
Suppose that of the 8,419,000 high school graduates aged 20 to 24, 12 percent were Black. Use the appropriate parameter from Table IV and formula (4) to get
Percentage, p 12.0 Base, x 8,419,000 b parameter 3,454 Standard error 0.7 90% conf. int. 11.0 to 13.0
The standard error is calculated as
The 90-percent confidence interval for the percentage of high school graduates aged 20 to 24 who were Black is calculated as 12.0 ± 1.645 x 0.7.
The alternate calculation of the standard error, using formula (3), with f = 1.16 from Table III and s = 0.6 by interpolation from Table I.B.I is
Standard error of a difference. The standard error of the difference between two sample estimates is approximately equal to
where
and
are the standard errors of the estimates, x and y. The estimates
can be numbers, percentages, ratios, etc. This will represent
the actual standard error quite accurately for the difference
between estimates of the same characteristic in two different
areas, or for the difference between separate and uncorrelated
characteristics in the same area. However, if there is a high
positive (negative) correlation between the two characteristics,
the formula will overestimate (underestimate) the true standard
error.
Suppose 8,419,000 persons 25 to 29 years old and 8,228,000 persons 20 to 24 years old had completed four years of high school and no more. Use the appropriate parameters from Table IV and formulas (4) and (5) to get
x y difference
Estimate 8,419,000 8,228,000 191,000
a parameter -0.000013 -0.000013 -
b parameter 2,549 2,549 -
Standard error 143,000 142,000 202,000
90% conf. int. 8,184,000 7,994,000 -141,000
to 8,654,000 to 8,462,000 to 523,000
The standard error of the difference is calculated as
The 90-percent confidence interval around the difference is calculated as 191,000 ± 1.645 x 202,000. Since this interval contains zero, we cannot conclude, at the 10-percent significance level, that the number of persons who completed four years of high school and no more is different for 20 to 24 year olds and 25 to 29 year olds.
Suppose that of 6,285,000 employed males between 20-24 years of age, 1,516,000 or 24.1 percent were part-time workers, and of the 5,824,000 employed females between 20-24 years of age, 2,169,000 or 37.2 percent were part-time workers. Use the appropriate parameters from Table B and formulas (4) and (5) to get
x y difference Percentage 24.1 37.2 13.1 Number, x 6,285,000 5,824,000 - b parameter 2,301 2,112 - Standard error 0.8 0.9 1.2 90% conf. int. 22.8 to 25.4 35.7 to 38.7 11.1 to 15.1
The standard error of the difference is calculated as
The 90-percent confidence interval around the difference is calculated as 13.1 ± 1.645 x 1.2. Since this interval does not include zero, we can conclude with 90 percent confidence that the percentage of part-time female workers between 20-24 years of age is greater than the percentage of part-time male workers between 20-24 years of age.
Standard error of a mean for grouped data . The formula used to estimate the standard error of a mean for grouped data is
In this formula, y is the size of the base of the distribution and b is a parameter from Table IV. The variance, S² , is given by the following formula:
where
,
the mean of the distribution, is estimated by
c is the number of groups; i indicates a specific group, thus taking on values 1 through c.
is the
estimated proportion of households, families or persons whose
values, for the characteristic (x-values) being considered, fall
in group i.
is (Z i-1
+ Z i)/2 where Z i-1 and Z i are the lower and upper interval
boundaries, respectively, for group i.
is assumed to be the most representative value for the characteristic
for households, families, and unrelated individuals or persons
in group i. Group c is open-ended, i.e., no upper interval boundary
exists. For this group the approximate average value is
Standard error of a ratio. Certain estimates may be calculated as the ratio of two numbers. The standard error of a ratio, x/y, may be computed using
The standard error of the numerator,
, and that of the denominator,
, may be calculated using formulas described earlier. In formula
(10), r represents the correlation between the numerator and the
denominator of the estimate.
For one type of ratio, the denominator is a count of families or households and the numerator is a count of persons in those families or households with a certain characteristic. If there is at least one person with the characteristic in every family or household, use 0.7 as an estimate of r. An example of this type is the mean number of children per family with children.
For all other types of ratios, r is assumed to be zero. If r is actually positive (negative), then this procedure will provide an overestimate (underestimate) of the standard error of the ratio. Examples of this type are the mean number of children per family and the poverty rate.
NOTE: For estimates expressed as the ratio of x per 100 y or x per 1,000 y, multiply formula (10) by 100 or 1,000, respectively, to obtain the standard error.
Suppose there are 641,000 male movers from abroad and 501,000 female movers from abroad. The ratio of male movers, x, to female movers, y, is 1.28. The standard error of this ratio is calculated as follows:
x y ratio
Estimate 641,000 501,000 1.28
a parameter -0.000035 -0.000035 -
b parameter 2,626 2,626 -
Standard error 41,000 36,000 0.12
90% conf. int. 573,600 441,800 1.08 to 1.48
to 708,400 to 560,200
Using formula (10) with r = 0, the estimate of the standard error is
Standard error of a median. The sampling variability of an estimated median depends on the form of the distribution and the size of the base. One can approximate the reliability of an estimated median by determining a confidence interval about it. (See the section on sampling variability for a general discussion of confidence intervals.)
Estimate the 68-percent confidence limits of a median based on sample data using the following procedure.
1. Determine, using formula (4), the standard error of the estimate of 50 percent from the distribution.
2. Add to and subtract from 50 percent the standard error determined in step 1.
3. Using the distribution of the characteristic, determine upper and lower limits of the 68-percent confidence interval by calculating values corresponding to the two points established in step 2.
Use the following formula to calculate the upper and lower limits.
where
= estimated
upper and lower bounds for the confidence interval (0 <= p
<= 1). For purposes of calculating the confidence interval,
p takes on the values determined in step 2. Note that
estimates
the median when p = 0.50.
N = for distribution of numbers: the total number of units (persons, households, etc.) for the characteristic in the distribution.
= for distribution of percentages: the value 1.0.
p = the values obtained in step 2.
= the
lower and upper bounds, respectively, of the interval containing
.
= for
distribution of numbers: the estimated number of units (persons,
households, etc.) with values of the characteristic greater than
or equal to A1 and A2, respectively.
= for distribution of percentages: the estimated percentage of units (persons, households, etc.) having values of the characteristic greater than or equal to A1 and A2, respectively.
4. Divide the difference between the two points determined in step 3 by two to obtain the standard error of the median.
A report by the Bureau of the Census shows the following distribution and median income for families in 1989.
Total families 66,090
Under $5,000 .................................................. 2,398
$5,000 to $9,999 ............................................... 4,141
$10,000 to $14,999 ............................................ 5,354
$15,000 to $19,999 ............................................ 5,565
$20,000 to $24,999 ............................................ 5,461
$25,000 to $29,999 ............................................ 5,576
$30,000 to $34,999 ............................................ 5,294
$35,000 to $39,999 ............................................ 4,959
$40,000 to $44,999 ............................................ 4,464
$45,000 to $49,999 ............................................ 3,689
$50,000 to $54,999 ............................................ 3,545
$55,000 to $59,999 ............................................ 2,595
$60,000 to $64,999 ............................................ 2,278
$65,000 to $69,999 ............................................ 1,839
$70,000 to $74,999 ............................................ 1,463
$75,000 to $79,999 ............................................ 1,251
$80,000 to $84,999 ............................................ 1,036
$85,000 to $89,999 ............................................ 774
$ 90,000 to $94,999 ............................................ 695
$95,000 to $99,999 ............................................ 518
$100,000 and over. ............................................ 3,197
Median income.................................................. $34,213
1. Using formula (4) with b = 2,058, the standard error of 50 percent on a base of 66,090,000 is about 0.3 percent.
2. To obtain a 68-percent confidence interval on an estimated median, add to and subtract from 50 percent the standard error found in step 1. This yields percent limits of 49.7 and 50.3.
3. The lower and upper limits for the interval in which the median falls are $30,000 and $35,000, respectively.
Then, by addition, the estimated numbers of families with an income greater than or equal to $30,000 and $35,000 are 37,597,000 and 32,303,000, respectively.
Using formula (11), the upper limit for the confidence interval of the median is found to be about
Similarly, the lower limit is found to be about
Thus, a 68-percent confidence interval for the median income for families is from $34,100 to $34,500.
4. The standard error of the median is, therefore,
Accuracy of state estimates. The redesign of the CPS following the 1980 census provided an opportunity to increase efficiency and accuracy of state data. All strata are now defined within state boundaries. The sample is allocated among the states to produce state and national estimates with the required accuracy while keeping total sample size to a minimum. Improved accuracy of state data has been achieved with about the same sample size as in the 1970 design.
Since the CPS is designed to produce both state and national estimates, the proportion of the total population sampled and the sampling rates differ among the states. In general, the smaller the population of the state the larger the sampling proportion. For example, in Vermont approximately 1 in every 300 households was sampled each month. In New York the sample was about 1 in every 1,600 households. Nevertheless, the size of the sample in New York is four times larger than in Vermont because New York has a larger population.
Computation of standard errors for state estimates . Standard errors for a state may be obtained by adjusting generalized standard errors given in the tables or by adjusting the a and b parameters and using the standard error equations described earlier.
Multiply the standard errors in Tables I.A, I.B.1 through I.B.9, II.A, and II.B.1 through II.B.3 by f for that state in Table V.
Multiply the a and b parameters in Table IV by f² from Table V to obtain state parameters.
Suppose there were 11,200,000 persons 25 years old and over living in New York, 2,542,000 (22.7 percent) of whom had completed college. Interpolation in Table I.B.1 shows the standard error on 22.7 percent to be approximately 1.0. Table V shows the factor for New York to be 0.89. Thus, the standard error on the estimate of the percentage of persons 25 and older in New York state who had completed college is approximately 0.89 = 0.89 x 1.0.
To obtain state parameters for educational attainment in New York, multiply the parameters in Table IV by f² in Table V for the state of interest. For educational attainment for total or white in New York this gives a = -.000013 x 0.80 = -0.000010 and b = 2,549 x 0.80 = 2,039.
Computation of a factor for groups of states. The factor adjusting standard errors for a group of states may be obtained by computing a weighted sum of the squared factors for the individual states in the group and taking the square root of the result. Depending on the combination of states, the resulting figure can be an overestimate.
The squared factor for a group of n states is given by
where
in the state population and
is obtained from Table V. The 1995 population from the CPS for
each state is also given in Table V.
Suppose a factor for the state group Illinois-Wisconsin-Michigan was required. The appropriate squared factor would be
Multiply the a and b parameters by f², 0.91, to obtain parameters for the state group; multiply standard errors by f, 0.95, for standard errors for this state group.
Computation of standard errors for data for combined years
. Sometimes estimates for multiple years are combined to improve
precision. For example, suppose
is a mean derived from n consecutive years' data, i.e.,
where
the
are
the estimates for the individual years.
Use the formulas described previously to estimate the standard
error,
,of each year's estimate. Then the standard error of
is
where
The correlation between consecutive years, r, is 0.35 for non-Hispanic households and 0.55 for Hispanic households. Correlation between nonconsecutive years is zero. The correlations were derived for income estimates but they can be used for other types of estimates where the year-to-year correlation between identical households is high.
Suppose a mean for three consecutive years for some characteristic is 1,000,000 and the standard errors for the individual years are 67,000, 73,000, and 65,000.
Using formula (14), the standard error for the three years combined data is
Therefore, the standard error of the mean, using formula (13), is
STANDARD ERRORS, PARAMETERS AND FACTORS
I. Standard Errors for Persons
A. Estimated Numbers
Use the following table for the listed characteristics by Total or White, Black and other races and Hispanic Origin:
Table I.A. Standard Errors of Estimated Numbers of Persons for Selected Characteristics
· Educational Attainment
· Employment
· Persons by Family Income
· Income
· Marital Status, Household, and Family Characteristics
· Mobility Characteristics (Movers)
Educational Attainment, Labor Force, Marital Status,
Household, Family, and Income
U.S., County, State, Region, or MSA
· Poverty
· Unemployment
B. Estimated Percentages
Use the following tables for standard errors of estimated percentages for characteristics of persons:
Table I.B.1. Educational Attainment: Total or White
Table I.B.2. Employment: All
Table I.B.3. Persons Tabulated by Family Income: Total or White
Table I.B.4. Income: Total or White
Table I.B.5. Marital Status, Household and Family Characteristics: Total or White
Table I.B.6. Mobility: Characteristics (Movers), Educational Attainment, Labor Force, Marital Status, Household, Family, and Income
Table I.B.7. Mobility: U.S., County, State, Regional, or MSA: All
Table I.B.8. Poverty: All
Table I.B.9. Unemployment: Total or White
II. Standard Errors for Families, Households, or Unrelated Individuals
A. Estimated Numbers
Use the following table for the listed characteristics by Total or White, Black and other races and Hispanic Origin:
Table II.A. Standard Errors of Estimated Numbers of Families, Households, or Unrelated Individuals for Selected Characteristics
· Income
· Marital Status, Household, and Family Characteristics
· Poverty
B. Estimated Percentages
Use the following tables for standard errors of estimated percentages for characteristics of families, households, or unrelated individuals:
Table II.B.1 Income: Total or White
Table II.B.2. Marital Status, Household and Family Characteristics and Educational Attainment: Total or White
Table II.B.3. Poverty: All
III. Factors and Parameters
A. Table III. Factors to be Applied to Tables I.B.1 through I.B.9 and Tables II.B.1 through II.B.3.
B. Table IV. a and b Parameters for Standard Error Estimates for Persons and Families
C. Table V. Factors for State Standard Errors and Parameters and Populations
Table I.A. Standard Errors of Estimated Numbers of Persons for Selected Characteristics: March 1995 Size of Estimate(in thousands) Characteristic 25 50 100 250 500 1000 2500 5000 10000 15000 25000 50000 100000 150000 Educational Attainment Total or White 8 11 16 25 36 50 79 111 156 188 236 308 353 300 Black & Other 9 13 19 29 41 57 88 116 140 136 - - - - Hispanic 9 13 19 29 41 57 86 112 125 96 - - - - Persons by Family Income Total or White 11 15 21 34 48 67 106 149 207 250 313 408 462 374 Black & Other 11 16 23 36 50 70 107 141 167 154 - - - - Hispanic Origin 11 16 23 36 50 70 105 135 146 96 - - - - Income Total or White 8 11 15 24 34 48 75 105 147 178 223 293 342 305 Black & Other 8 11 16 25 36 50 76 101 122 117 - - - - Hispanic Origin 8 11 16 25 36 50 75 97 109 84 - - - - Marital Status, Household and Family Total or White 11 16 22 35 49 69 109 153 214 259 325 425 492 427 Black & Other 13 19 26 41 58 81 124 165 199 192 - - - - Hispanic Origin 13 19 26 41 58 81 122 159 177 137 - - - - Mobility Characteristics (Movers) Educational Attainment, Labor Force, Marital Status, Household, family, and Income Total or White 8 12 16 26 36 51 81 114 160 194 245 328 407 416 Black & Other 8 12 16 26 36 51 78 106 135 145 120 - - - Hispanic Origin 8 12 16 26 36 51 78 104 129 132 62 - - - US,County,St, Region or MSA Total or White 13 19 27 42 60 85 134 188 263 319 403 539 664 671 Black & Other 13 19 27 42 60 84 129 174 223 240 200 - - - Hispanic Origin 13 19 27 42 59 83 128 171 212 216 100 - - - Poverty Total or White 15 22 31 49 69 98 154 216 301 364 457 599 690 596 Black & Other 15 22 31 49 68 96 146 194 234 226 - - - - Hispanic Origin 15 22 31 49 68 95 144 186 208 161 - - - -
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. When the characteristic of interest is total state population, the standard error is 0.0.
- Not applicable.
Table I.B.1 Standard Errors of Estimated Percentages for Persons
Educational Attainment: March 1995
Total or White
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 3.2 4.5 7.0 9.6 13.8 16.0
50 2.2 3.2 4.9 6.8 9.8 11.3
100 1.6 2.2 3.5 4.8 6.9 8.0
250 1.0 1.4 2.2 3.0 4.4 5.0
500 0.7 1.0 1.6 2.1 3.1 3.6
1,000 0.5 0.7 1.1 1.5 2.2 2.5
2,500 0.3 0.4 0.7 1.0 1.4 1.6
5,000 0.2 0.3 0.5 0.7 1.0 1.1
10,000 0.16 0.2 0.3 0.5 0.7 0.8
25,000 0.10 0.14 0.2 0.3 0.4 0.5
50,000 0.07 0.10 0.16 0.2 0.3 0.4
100,000 0.05 0.07 0.11 0.2 0.2 0.3
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table I.B.2 Standard Errors of Estimated Percentages for Persons Employment:
March 1995
Total or White
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 3.1 4.4 6.9 9.5 13.7 15.8
50 2.2 3.1 4.9 6.7 9.7 11.2
100 1.6 2.2 3.4 4.7 6.8 7.9
250 1.0 1.4 2.2 3.0 4.3 5.0
500 0.7 1.0 1.5 2.1 3.1 3.5
1,000 0.5 0.7 1.1 1.5 2.2 2.5
2,500 0.3 0.4 0.7 0.9 1.4 1.6
5,000 0.2 0.3 0.5 0.7 1.0 1.1
10,000 0.16 0.2 0.3 0.5 0.7 0.8
25,000 0.10 0.14 0.2 0.3 0.4 0.5
50,000 0.07 0.10 0.15 0.2 0.3 0.4
100,000 0.05 0.07 0.11 0.1 0.2 0.2
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table I.B.3 Standard Errors of Estimated Percentages for Persons
Tabulated by Family Income: March 1995
Total or White
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 4.2 6.0 9.3 12.8 18.4 21.3
50 3.0 4.2 6.6 9.0 13.0 15.1
100 2.1 3.0 4.6 6.4 9.2 10.6
250 1.3 1.9 2.9 4.0 5.8 6.7
500 0.9 1.3 2.1 2.9 4.1 4.8
1,000 0.7 0.9 1.5 2.0 2.9 3.4
2,500 0.4 0.6 0.9 1.3 1.8 2.1
5,000 0.3 0.4 0.7 0.9 1.3 1.5
10,000 0.2 0.3 0.5 0.6 0.9 1.1
25,000 0.13 0.19 0.3 0.4 0.6 0.7
50,000 0.09 0.13 0.2 0.3 0.4 0.5
100,000 0.07 0.09 0.15 0.2 0.3 0.3
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table I.B.4 Standard Errors of Estimated Percentages for Persons
Income: March 1995
Total or White
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 3.0 4.2 6.6 9.0 13.0 15.1
50 2.1 3.0 4.6 6.4 9.2 10.7
100 1.5 2.1 3.3 4.5 6.5 7.5
250 0.9 1.3 2.1 2.9 4.1 4.8
500 0.7 0.9 1.5 2.0 2.9 3.4
1,000 0.5 0.7 1.0 1.4 2.1 2.4
2,500 0.3 0.4 0.7 0.9 1.3 1.5
5,000 0.2 0.3 0.5 0.6 0.9 1.1
10,000 0.1 0.2 0.3 0.5 0.7 0.8
25,000 0.09 0.13 0.2 0.3 0.4 0.5
50,000 0.07 0.09 0.15 0.2 0.3 0.3
100,000 0.05 0.07 0.10 0.14 0.2 0.2
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table I.B.5 Standard Errors of Estimated Percentages or Persons Marital
Status, Household & Family Characteristics: March 1995
Total or White
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 4.4 6.1 9.6 13.2 19.0 21.9
50 3.1 4.3 6.8 9.3 13.4 15.5
100 2.2 3.1 4.8 6.6 9.5 11.0
250 1.4 1.9 3.0 4.2 6.0 6.9
500 1.0 1.4 2.1 2.9 4.3 4.9
1,000 0.7 1.0 1.5 2.1 3.0 3.5
2,500 0.4 0.6 1.0 1.3 1.9 2.2
5,000 0.3 0.4 0.7 0.9 1.3 1.6
10,000 0.2 0.3 0.5 0.7 1.0 1.1
25,000 0.14 0.19 0.3 0.4 0.6 0.7
50,000 0.10 0.14 0.2 0.3 0.4 0.5
100,000 0.07 0.10 0.15 0.2 0.3 0.3
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table I.B.6 Standard Errors of Estimated Percentages for Persons
Mobility Characteristics(Movers): Educational Attainment,
Labor Force, Marital Status, Household, Family, and
Income: March 1995
All
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 3.2 4.6 7.1 9.8 14.1 16.3
50 2.3 3.2 5.0 6.9 10.0 11.5
100 1.6 2.3 3.5 4.9 7.1 8.1
250 1.0 1.4 2.2 3.1 4.5 5.2
500 0.7 1.0 1.6 2.2 3.2 3.6
1,000 0.5 0.7 1.1 1.5 2.2 2.6
2,500 0.3 0.5 0.7 1.0 1.4 1.6
5,000 0.2 0.3 0.5 0.7 1.0 1.2
10,000 0.2 0.2 0.4 0.5 0.7 0.8
25,000 0.1 0.1 0.2 0.3 0.4 0.5
50,000 0.1 0.1 0.2 0.2 0.3 0.4
100,000 0.1 0.1 0.1 0.2 0.2 0.3
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table I.B.7 Standard Errors of Estimated Percentages for Persons
Mobility: U.S., County, State, Region or MSA: March 1995
All
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 5.3 7.5 11.7 16.1 23.2 26.8
50 3.8 5.3 8.3 11.4 16.4 19.0
100 2.7 3.8 5.8 8.1 11.6 13.4
250 1.7 2.4 3.7 5.1 7.4 8.5
500 1.2 1.7 2.6 3.6 5.2 6.0
1,000 0.8 1.2 1.8 2.5 3.7 4.2
2,500 0.5 0.8 1.2 1.6 2.3 2.7
5,000 0.4 0.5 0.8 1.1 1.6 1.9
10,000 0.3 0.4 0.6 0.8 1.2 1.3
25,000 0.2 0.2 0.4 0.5 0.7 0.8
50,000 0.1 0.2 0.3 0.4 0.5 0.6
100,000 0.1 0.1 0.2 0.3 0.4 0.4
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table I.B.8 Standard Errors of Estimated Percentages for Persons
Poverty: March 1995
All
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 6.2 8.7 13.5 18.6 26.8 30.9
50 4.4 6.1 9.5 13.1 18.9 21.9
100 3.1 4.3 6.7 9.3 13.4 15.5
250 1.9 2.7 4.3 5.9 8.5 9.8
500 1.4 1.9 3.0 4.1 6.0 6.9
1,000 1.0 1.4 2.1 2.9 4.2 4.9
2,500 0.6 0.9 1.3 1.9 2.7 3.1
5,000 0.4 0.6 1.0 1.3 1.9 2.2
10,000 0.3 0.4 0.7 0.9 1.3 1.5
25,000 0.2 0.3 0.4 0.6 0.8 1.0
50,000 0.1 0.2 0.3 0.4 0.6 0.7
100,000 0.1 0.1 0.2 0.3 0.4 0.5
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table I.B.9 Standard Errors of Estimated Percentages or Persons
Unemployment: March 1995
Total or White
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 3.1 4.4 6.8 9.4 13.6 15.7
50 2.2 3.1 4.8 6.7 9.6 11.1
100 1.6 2.2 3.4 4.7 6.8 7.9
250 1.0 1.4 2.2 3.0 4.3 5.0
500 0.7 1.0 1.5 2.1 3.0 3.5
1,000 0.5 0.7 1.1 1.5 2.1 2.5
2,500 0.3 0.4 0.7 0.9 1.4 1.6
5,000 0.2 0.3 0.5 0.7 1.0 1.1
10,000 0.2 0.2 0.3 0.5 0.7 0.8
25,000 0.1 0.1 0.2 0.3 0.4 0.5
50,000 0.1 0.1 0.2 0.2 0.3 0.4
100,000 0.0 0.1 0.1 0.1 0.2 0.2
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table II.A. Standard Errors of Estimated Numbers of Families, Households, or Unrelated Individuals for Selected Characteristics: March 1995 Size of Estimate (in thousands) Characteristic 25 50 100 250 500 1000 2500 5000 10000 15000 25000 50000 100000 150000 Income Tot or White 7 10 14 23 32 45 71 100 140 168 210 271 295 202 Black & Other 8 11 15 24 33 46 70 93 108 96 - - - - Hispanic Origin 8 11 15 24 33 46 67 83 71 - - - - - Marital Stat, Household & Family Tot or White 7 10 14 22 31 44 69 96 134 162 202 261 285 198 Black 7 9 13 21 29 41 62 83 101 100 - - - - Hispanic 7 9 13 21 29 40 59 71 55 - - - - - Poverty Tot or White 8 11 15 24 34 48 79 117 179 235 339 590 1080 1566 Black 8 11 15 24 34 48 79 117 179 235 339 590 1080 1566 Hispanic 8 11 15 24 34 48 79 117 179 235 339 590 1080 1566
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan.
- Not applicable.
Table II.B.1 Standard Errors of Estimated Percentages for Families,
Households, or Unrelated Individuals Income: March 1995
All
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 2.9 4.0 6.3 8.6 12.5 14.4
50 2.0 2.8 4.4 6.1 8.8 10.2
100 1.4 2.0 3.1 4.3 6.2 7.2
250 0.9 1.3 2.0 2.7 3.9 4.6
500 0.6 0.9 1.4 1.9 2.8 3.2
1,000 0.5 0.6 1.0 1.4 2.0 2.3
2,500 0.3 0.4 0.6 0.9 1.2 1.4
5,000 0.2 0.3 0.4 0.6 0.9 1.0
10,000 0.1 0.2 0.3 0.4 0.6 0.7
25,000 0.1 0.1 0.2 0.3 0.4 0.5
50,000 0.1 0.1 0.1 0.2 0.3 0.3
100,000 0.0 0.1 0.1 0.1 0.2 0.2
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table II.B.2 Standard Errors of Estimated Percentages for Families,
Households, or Unrelated Individuals Marital Status,
Household, & Family Characteristics & Educational Attainment:
March 1995
Total or White
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 2.8 3.9 6.0 8.3 12.0 13.8
50 1.9 2.7 4.3 5.9 8.5 9.8
100 1.4 1.9 3.0 4.1 6.0 6.9
250 0.9 1.2 1.9 2.6 3.8 4.4
500 0.6 0.9 1.3 1.9 2.7 3.1
1,000 0.4 0.6 1.0 1.3 1.9 2.2
2,500 0.3 0.4 0.6 0.8 1.2 1.4
5,000 0.2 0.3 0.4 0.6 0.8 1.0
10,000 0.1 0.2 0.3 0.4 0.6 0.7
25,000 0.1 0.1 0.2 0.3 0.4 0.4
50,000 0.1 0.1 0.1 0.2 0.3 0.3
100,000 0.0 0.1 0.1 0.1 0.2 0.2
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table II.B.3 Standard Errors of Estimated Percentages for
Poverty: March 1995
Total or White
Base of 1 or 2 or 5 or 10 or 25 or 50
Percentage 99 98 95 90 75
(thousands)
25 3.0 4.2 6.5 9.0 13.0 15.0
50 2.1 3.0 4.6 6.4 9.2 10.6
100 1.5 2.1 3.3 4.5 6.5 7.5
250 0.9 1.3 2.1 2.9 4.1 4.8
500 0.7 0.9 1.5 2.0 2.9 3.4
1,000 0.5 0.7 1.0 1.4 2.1 2.4
2,500 0.3 0.5 0.7 0.9 1.3 1.5
5,000 0.2 0.3 0.5 0.6 0.9 1.1
10,000 0.1 0.2 0.3 0.5 0.7 0.8
25,000 0.1 0.1 0.2 0.3 0.4 0.5
50,000 0.1 0.1 0.1 0.2 0.3 0.3
100,000 0.0 0.1 0.1 0.1 0.2 0.2
NOTE: Multiply these standard errors by 1.5 when tabulating by nonmetropolitan. See Table III for factors to be applied to these standard errors for Black and Other Races and Hispanic Origin.
Table III. Factors to be Applied to Tables I.B.1 through I.B.9 and
II.B.1 through II.B.
Factors
Characteristic
Total or Black and Hispanic
White Other Races Origin
PERSONS
Educational Attainment 1.00 1.16 1.16
Employment 1.00 1.02 1.09
Persons by Family Income 1.00 1.07 1.07
Income 1.00 1.07 1.07
Marital Status, Household and
Family Characteristics 1.00 1.20 1.20
Mobility Characteristics(Movers)
Educational Attainment, Labor
Force, Marital Status, Household,
Family and Income 1.00 1.00 1.00
U.S., County, State, Regional or MSA 1.00 1.00 1.00
Poverty 1.00 1.00 1.00
Unemployment 1.00 1.03 1.05
FAMILIES, HOUSEHOLDS, OR
UNRELATED INDIVIDUALS
Income 1.00 1.04 1.04
Marital Status, Household and
Family Characteristics,
Educational Attainment,
Population by Age and/or Sex 1.00 0.95 0.95
Poverty 1.00 1.00 1.00
Table IV. a and b Parameters for Standard Error Estimates for Persons and
Families: March 1995
Characteristic Total or White Black Hispanic
a b a b a b
PERSONS
Educational Attainment -0.000013 2549 -0.000148 3454 -0.000189 3454
Employment Characteristics -0.000016 2488 -0.000113 2613 -0.000113 2613
Persons by Family -0.000024 4531 -0.000240 5188 -0.000305 5188
Income -0.000011 2269 -0.000112 2598 -0.000142 2598
Marital Status, Household
& Family Characteristics -0.000024 4818 -0.000297 6921 -0.000378 6921
Mobility Characteristics
(Movers) Educational
Attainment, Labor Force
Marital Status, Household
Family, and Income -0.000010 2653 -0.000083 2653 -0.000100 2653
US, County, State, Region
or MSA -0.000028 7203 -0.000224 7203 -0.000272 7203
Poverty -0.000048 9566 -0.000410 9566 -0.000523 9566
Unemployment -0.000016 2465 -0.000191 2622 -0.000191 2622
FAMILIES, HOUSEHOLDS,
OR UNRELATED
INDIVIDUALS
Income -0.000012 2072 -0.000110 2262 -0.000176 2262
Marital Status, Household
and Family Characteristics
Educational Attainment,
Population by Age and/or Sex -0.000011 1912 -0.000071 1730 -0.000143 1730
Poverty 0.000094 2258 0.000094 2258 0.000094 2258
NOTE: Multiply a and b parameters by 1.5 when tabulating nonmetropolitan. If the characteristic of interest is total state population, not subtotaled by race or ethnic origin, the a and b parameters are zero.
Table V. Factors for State Standard Errors and Parameters and State Populations (March 1995 Adjusted 16+ Civilian Noninstitutional Control Totals) State f f2 Population Alabama 1.07 1.15 3,250,000 Alaska 0.36 0.13 416,000 Arizona 1.03 1.06 3,100,000 Arkansas 0.81 0.66 1,882,000 California 1.12 1.25 23,545,000 Colorado 1.03 1.06 2,807,000 Connecticut 1.10 1.20 2,503,000 Delaware 0.48 0.23 547,000 District of Columbia 0.48 0.23 462,000 Florida 0.95 0.90 11,011,000 Georgia 1.33 1.78 5,357,000 Hawaii 0.59 0.35 862,000 Idaho 0.51 0.26 849,000 Illinois 0.96 0.93 8,891,000 Indiana 1.30 1.70 4,402,000 Iowa 0.87 0.76 2,148,000 Kansas 0.81 0.66 1,890,000 Kentucky 1.03 1.06 2,947,000 Louisiana 1.14 1.29 3,185,000 Maine 0.61 0.37 956,000 Maryland 1.23 1.52 3,834,000 Massachusetts 0.70 0.49 4,689,000 Michigan 0.85 0.73 7,156,000 Minnesota 1.14 1.31 3,416,000 Mississippi 0.81 0.66 1,996,000 Missouri 1.25 1.57 3,985,000 Montana 0.47 0.22 648,000 Nebraska 0.64 0.41 1,203,000 Nevada 0.60 0.36 1,151,000 New Hampshire 0.64 0.41 877,000 New Jersey 0.78 0.61 6,073,000 New Mexico 0.64 0.41 1,225,000 New York 0.89 0.80 13,976,000 North Carolina 0.70 0.49 5,445,000 North Dakota 0.40 0.16 471,000 Ohio 0.91 0.83 8,438,000 Oklahoma 0.94 0.88 2,432,000 Oregon 0.97 0.95 2,419,000 Pennsylvania 0.95 0.90 9,282,000 Rhode Island 0.59 0.35 763,000 South Carolina 0.90 0.81 2,785,000 South Dakota 0.40 0.16 524,000 Tennessee 1.13 1.28 4,026,000 Texas 1.12 1.26 13,728,000 Utah 0.68 0.46 1,342,000 Vermont 0.45 0.20 454,000 Virginia 1.18 1.39 4,981,000 Washington 1.17 1.37 4,073,000 West Virginia 0.72 0.52 1,447,000 Wisconsin 1.11 1.23 3,840,000 Wyoming 0.42 0.18 355,000
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