Appendix C: Standard Errors and Design Effects

This appendix contains information on standard errors and design effects for the NLSY79 sample, briefly discussing how to use these two statistical factors. It then has tables for the first round (1979) and the latest available data, Round 21 (2004). Only a few intervening years have been included for space reasons; users interested in the intervening years should contact NLS User Services to obtain the NLSY79 Technical Sampling Report and Appendices.

Standard errors have been explicitly computed for a number of statistics based upon the entire NLSY79 sample (total, civilian, and military) and a number of sex and/or race subclasses. Standard errors for other statistics (defined over the entire sample or the subclasses) may be approximated with use of the DEFT factors given in the tables below. Users who examine the tables will note that CHRR has calculated standard errors for different variables over time.

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Approximate Standard Errors: Percentages

The following formula approximates a standard error of a percentage:

where:

se(P) = the approximate standard error for the percentage P

P = the sample percentage (ranging from 0 to 100)

n = the actual unweighted sample size for the demographic subclass from which the percentage was developed

DEFT = the appropriate DEFT factor for the particular demographic subclass and sample type from which the percentage was developed.

For example, for 1996 the appropriate DEFT factor for estimating a standard error of the percentage of Hispanic or Latino males who were high school dropouts is 1.17744 (see proportion column, row seven of Table C.2). Assuming the calculated sample (P) equals 22.19 percent and the unweighted sample estimate size is 946, then:

To approximate the standard error of the corresponding projected population total (NP/100), calculate:

where:

se(NP/100) = the approximate standard error of the projected population total corresponding to a percentage P within a particular demographic subclass and sample type.

N = the appropriate projected total population base for the particular demographic subclass and sample type.

For example, if the projected total population base for Hispanic or Latino males is 1,030,861, the projected number of civilian Hispanic or Latino male high school dropouts is equal to NP/100 or 1,030,861 * 22.19/100 = 228,748. Thus, the approximate standard error for the total number of Hispanic or Latino male high school dropouts is:

Note the 1.5907 came from the previous calculation.

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Approximate Standard Errors: Means

One can compute approximate standard errors for means as follows:

where:

se(X ) = the approximate standard error of the mean

DEFT = the appropriate DEFT factor for the particular demographic subclass and sample type from which the mean was developed

S2 = the weighted element variance computed for the demographic subclass and sample type from which the mean was developed

n = the unweighted sample size for the particular mean.

For example, for 1979 the DEFT factor for all Hispanics or Latinos is 1.45699 (see means column, row four of Table C.1). To approximate the standard error of the mean number of years of education completed by this subclass, where the weighted element variance is .72955 and the sample size is 77, compute:

Table C.1 Deft Factors for Round 1 (1979)

Proportions
Means

All Youth

 1.72547 1.71282

Males
1.46605
1.56808

Females
1.58029
1.49720

Hispanics or Latinos
1.44342
1.45699

Blacks
1.35303
1.43730

Non-black/non-Hispanics
1.58686
1.56996

Hispanic or Latino Males
1.24321
1.22329

Hispanic or Latino Females
1.40353
1.25095

Black Males
1.19457
1.21378

Black Females
1.24877
1.25243

Non-black/non-Hispanic Males
1.33775
1.45962

Non-black/non-Hispanic Females
1.46889
1.37581

Table C.2 Deft Factors for Round 17 (1996)
Proportions
Means

All Youth

 1.35848 1.967232

Males
1.28523
1.667333

Females
1.24536
1.621727

Hispanics or Latinos
1.28275
1.584298

Blacks
1.19735
1.423025

Non-black/non-Hispanics
1.19087
1.713184

Hispanic or Latino Males
1.17744
1.407125

Hispanic or Latino Females
1.13217
1.264911

Black Males
1.16541
1.174734

Black Females
1.13258
1.319091

Non-black/non-Hispanic Males
1.13217
1.456022

Non-black/non-Hispanic Females
1.09545
1.405347

Table C.3 Deft Factors for Round 18 (1998)

Proportions Means

All Youth

 1.38301 1.96469

Males

 1.30836 1.66433

Females

 1.28311 1.60000

Hispanics or Latinos

 1.21917 1.52807

Blacks

 1.19164 1.40890

Non-black/non-Hispanics

 1.17937 1.67481

Hispanic or Latino Males

 1.19248 1.37659

Hispanic or Latino Females

 1.13418 1.25100

Black Males

 1.14336 1.12694

Black Females

 1.12088 1.31529

Non-black/non-Hispanic Males

 1.18195 1.43353

Non-black/non-Hispanic Females

 1.11028 1.37133

Table C.4 Deft Factors for Round 19 (2000)

 Proportions Means

All Youth

 1.36423 1.90919

Males

 1.26007 1.61864

Females

 1.21244 1.58588

Hispanics or Latinos

 1.24544 1.48492

Blacks

 1.19954 1.42127

Non-black/non-Hispanics

 1.20052 1.62327

Hispanic or Latino Males

 1.19722 1.31909

Hispanic or Latino Females

 1.09240 1.22474

Black Males

 1.20277 1.18322

Black Females

 1.08282 1.34907

Non-black/non-Hispanic Males

 1.12750 1.39462

Non-black/non-Hispanic Females

 1.13908 1.34907

Table C.5 Deft Factors for Round 20 (2002)

Proportions Means
All Youth 1.34578 1.82757
Males 1.29701 1.58430
Females 1.18181 1.52807
Hispanics or Latinos 1.24097 1.47986
Blacks 1.20692 1.35647
Non-black/non-Hispanics 1.15085 1.56844
Hispanic or Latino Males 1.12450 1.28841
Hispanic or Latino Females 1.09479 1.21861
Black Males 1.20830 1.12694
Black Females 1.18743 1.33604
Non-black/non-Hispanic Males 1.20468 1.37659
Non-black/non-Hispanic Females 1.06829 1.30958

Table C.6 Deft Factors for Round 21 (2004)

Proportions Means
All Youth 1.38789 1.83712
Males 1.27377 1.55563
Females 1.23592 1.55081
Hispanics or Latinos 1.30336 1.46969
Blacks 1.14782 1.35831
Non-black/non-Hispanics 1.18163 1.57003
Hispanic or Latino Males 1.27083 1.31149
Hispanic or Latino Females 1.12750 1.19164
Black Males 1.14455 1.10454
Black Females 1.02896 1.37113
Non-black/non-Hispanic Males 1.09373 1.35647
Non-black/non-Hispanic Females 1.08224 1.32098
Notes:  Users are cautioned that the figures in the proportion column for the last six categories are becoming much less relevant over time. The proportion DEFT column is based on education, training, marriage, and employment variables. Over time categories, such as black females, have only a few respondents in school or training, which causes the DEFT factors to change from survey to survey. Broader categories, like "All Youth," "Males," and "Females" are more accurate to use.

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Table C.7 Standard Errors For Round 1 (1979)
All
Male
Female
Hispanic or Latino
Black
Non-black, non-Hisp.
Male
H or L
Female
H or L
Male Black
Female Black
Male NB/NH
Female NB/NH

Prop. HS dropout
0.00471
0.00627
0.00545
0.01385
0.00835
0.00527
0.01744
0.01814
0.01232
0.00928
0.00710
0.00619

Prop. attending HS
0.00735
0.00893
0.01006
0.01554
0.01151
0.00904
0.02176
0.02146
0.01460
0.01628
0.01085
0.01233

Prop attending college
0.00597
0.00729
0.00778
0.01037
0.00784
0.00710
0.01230
0.01460
0.00919
0.01119
0.00862
0.00947

Prop. HS graduate
0.00658
0.00776
0.00905
0.01277
0.01033
0.00785
0.01440
0.01957
0.01217
0.01448
0.00926
0.01094

Mean yrs. of school completed
0.02900
0.04000
0.03800
0.08200
0.05700
0.03400
0.10000
0.10500
0.06100
0.07400
0.04600
0.04400

Mean yrs. of school expected
0.04600
0.05900
0.04700
0.10800
0.06400
0.05500
0.12500
0.11700
0.07900
0.07900
0.07100
0.05500

Prop. living in south
0.02286
0.02353
0.02324
0.05641
0.04264
0.02544
0.04973
0.06060
0.04555
0.04084
0.02610
0.02601

Mean #'s of children expected
0.02400
0.02700
0.03200
0.05800
0.04600
0.02800
0.06500
0.07000
0.05600
0.05500
0.03100
0.03700

Prop. married
0.00454
0.00365
0.00686
0.01023
0.00533
0.00570
0.00923
0.01646
0.00440
0.00884
0.00448
0.00855

Table C.8 Standard Errors For Round 17 (1996)
All
Male
Female
Hispanic or Latino
Black
Non-black, non-Hisp.
Male
H or L
Female
H or L
Male Black
Female Black
Male NB/NH
Female NB/NH

Prop. not on active duty
0.001
0.003
0.001
0.005
0.004
0.002
0.009
0.001
0.007
0.003
0.003
0.001

Prop. high school dropouts
0.006
0.008
0.006
0.014
0.009
0.007
0.018
0.016
0.012
0.010
0.009
0.007

Prop. in high school or less
0.000
0.001
0.001
0.002
0.001
0.001
0.002
0.002
0.001
0.002
0.001
0.000

Prop. attending college
0.003
0.003
0.005
0.006
0.005
0.004
0.008
0.009
0.005
0.007
0.004
0.005

Prop. high school graduate
0.006
0.007
0.006
0.015
0.009
0.007
0.018
0.016
0.012
0.010
0.009
0.007

Prop. living in south
0.034
0.034
0.036
0.052
0.046
0.039
0.049
0.059
0.046
0.048
0.038
0.041

Prop. currently married
0.007
0.010
0.010
0.016
0.013
0.008
0.020
0.021
0.018
0.017
0.011
0.011

Prop. employed at present
0.006
0.007
0.009
0.015
0.009
0.007
0.017
0.020
0.014
0.013
0.007
0.010

Prop. unemployed
0.002
0.003
0.003
0.006
0.005
0.003
0.007
0.009
0.008
0.008
0.004
0.004

Prop. in labor force
0.005
0.005
0.008
0.013
0.008
0.006
0.015
0.018
0.012
0.012
0.006
0.010

Prop. government training
0.001
0.001
0.001
0.003
0.002
0.001
0.003
0.003
0.002
0.004
0.001
0.001

Average number of children
0.023
0.027
0.030
0.054
0.035
0.028
0.067
0.065
0.040
0.050
0.033
0.036

Average highest grade completed
0.060
0.074
0.063
0.109
0.065
0.073
0.137
0.119
0.074
0.081
0.091
0.077

Prop. currently enrolled
0.003
0.004
0.005
0.006
0.005
0.004
0.008
0.008
0.005
0.007
0.004
0.006

Table C.9 Standard Errors For Round 18 (1998)

 All Male Female Hispanic or Latino Black Non-black, non-Hisp. Male
H or L		 Female
H or L		 Male Black Female Black Male NB/NH Female NB/NH

Prop. not on active duty

 0.001 0.003 0.001 0.005 0.003 0.002 0.008 0.002 0.006 0.003 0.003 0.001

Prop. high school dropouts

 0.005 0.007 0.006 0.014 0.009 0.006 0.017 0.016 0.012 0.010 0.009 0.007

Prop. in high school or less

 0.000 0.000 0.001 0.000 0.001 0.000 0.000 0.001 0.001 0.001 0.000 0.001

Prop. attending college

 0.003 0.003 0.005 0.005 0.005 0.003 0.005 0.008 0.005 0.007 0.004 0.005

Prop. high school graduate

 0.005 0.007 0.006 0.014 0.009 0.006 0.017 0.016 0.012 0.010 0.009 0.007

Prop. living in south

 0.035 0.034 0.037 0.051 0.045 0.039 0.047 0.058 0.044 0.047 0.039 0.041

Prop. currently married

 0.008 0.010 0.011 0.015 0.012 0.008 0.021 0.021 0.018 0.016 0.011 0.010

Prop. employed at present

 0.006 0.007 0.009 0.014 0.009 0.007 0.017 0.020 0.012 0.014 0.008 0.011

Prop. unemployed

 0.002 0.003 0.003 0.005 0.005 0.002 0.007 0.008 0.007 0.007 0.003 0.003

Prop. in labor force

 0.005 0.006 0.009 0.013 0.008 0.006 0.016 0.019 0.011 0.011 0.006 0.011

Prop. government training

 0.001 0.001 0.001 0.002 0.002 0.001 0.003 0.004 0.003 0.004 0.001 0.001

Average number of children

 0.024 0.028 0.030 0.050 0.036 0.028 0.061 0.065 0.042 0.050 0.033 0.035

Average highest grade completed

 0.061 0.077 0.063 0.114 0.066 0.073 0.147 0.121 0.074 0.082 0.09. 0.074

Prop. currently enrolled

 0.003 0.003 0.004 0.005 0.005 0.003 0.005 0.008 0.005 0.007 0.004 0.005

Table C.10 Standard Errors For Round 19 (2000)

 All Male Female Hispanic or Latino Black Non-black, non-Hisp. Male
H or L		 Female
H or L		 Male Black Female Black Male NB/NH Female NB/NH

Prop. not on active duty

 0.001 0.002 0.000 0.003 0.003 0.001 0.006 0.001 0.005 0.002 0.003 0.000

Prop. high school dropouts

 0.005 0.007 0.006 0.014 0.009 0.006 0.017 0.015 0.013 0.010 0.009 0.006

Prop. in high school or less

 0.000 0.000 0.000 0.001 0.001 0.000 0.001 0.002 0.002 0.000 0.000 0.000

Prop. attending college

 0.003 0.003 0.004 0.006 0.004 0.003 0.008 0.009 0.004 0.007 0.003 0.005

Prop. high school graduate

 0.005 0.007 0.006 0.014 0.009 0.006 0.017 0.015 0.013 0.010 0.009 0.006

Prop. living in south

 0.035 0.034 0.037 0.052 0.043 0.039 0.049 0.059 0.044 0.046 0.038 0.041

Prop. currently married

 0.008 0.010 0.010 0.014 0.012 0.008 0.022 0.021 0.018 0.015 0.011 0.010

Prop. employed at present

 0.006 0.006 0.009 0.012 0.009 0.007 0.014 0.018 0.014 0.012 0.007 0.010

Prop. government training

 0.001 0.001 0.001 0.003 0.002 0.001 0.003 0.004 0.003 0.003 0.001 0.001

Average number of children

 0.024 0.029 0.030 0.048 0.037 0.027 0.061 0.064 0.046 0.051 0.034 0.035

Average highest grade completed

 0.061 0.076 0.065 0.114 0.069 0.074 0.146 0.118 0.078 0.089 0.092 0.078

Prop. currently enrolled

 0.003 0.003 0.004 0.006 0.004 0.003 0.008 0.009 0.005 0.007 0.003 0.005
Notes:  Users are cautioned that by round 17 cohort changes have made some categories much less relevant.  In particular, the extremely small subsample sizes for "Proportion government training participant" and "Proportion in high school or less" make these categories statistically suspect.  They have been kept in the table for historical continuity.

Table C.11 Standard Errors For Round 20 (2002)

All Male Female Hispanic or Latino Black Non-black, non-Hisp. Male
H or L		 Female
H or L		 Male Black Female Black Male NB/NH Female NB/NH
Prop. not on active duty 0.001 0.002 0.000 0.002 0.002 0.001 0.004 0.000 0.004 0.002 0.003 0.000
Prop. high school dropouts 0.005 0.007 0.005 0.015 0.008 0.006 0.018 0.016 0.011 0.010 0.009 0.006
Prop. in high school or less 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.001 0.001 0.001 0.000
Prop. attending college 0.002 0.003 0.004 0.004 0.004 0.002 0.005 0.006 0.005 0.006 0.003 0.004
Prop. high school graduate 0.005 0.007 0.005 0.015 0.008 0.006 0.018 0.016 0.011 0.010 0.009 0.006
Prop. living in south 0.035 0.034 0.036 0.053 0.042 0.039 0.050 0.060 0.043 0.045 0.039 0.041
Prop. currently married 0.009 0.010 0.011 0.015 0.013 0.009 0.023 0.022 0.018 0.015 0.011 0.012
Prop. employed at present 0.007 0.007 0.009 0.012 0.011 0.008 0.016 0.015 0.016 0.014 0.008 0.011
Prop. government training 0.002 0.002 0.002 0.004 0.004 0.002 0.006 0.006 0.006 0.006 0.002 0.002
Average number of children 0.023 0.028 0.028 0.051 0.037 0.026 0.062 0.067 0.048 0.053 0.034 0.034
Average highest grade completed 0.061 0.077 0.065 0.120 0.066 0.074 0.150 0.125 0.073 0.091 0.094 0.078
Prop. currently enrolled 0.002 0.003 0.003 0.004 0.004 0.002 0.005 0.006 0.005 0.006 0.003 0.004
Notes:  Users are cautioned that by round 17 cohort changes have made some categories much less relevant.  In particular, the extremely small subsample sizes for "Proportion government training participant" and "Proportion in high school or less: make these categories statistically suspect.  They have been kept in the table for historical continuity.

Table C.12 Standard Errors For Round 21 (2004)

All Male Female Hispanic or Latino Black Non-black, non-Hisp. Male
H or L		 Female
H or L		 Male Black Female Black Male NB/NH Female NB/NH
Prop. not on active duty 0.001 0.002 0.000 0.002 0.002 0.001 0.004 0.001 0.003 0.002 0.002 0.000
Prop. high school dropouts 0.005 0.007 0.005 0.014 0.009 0.006 0.019 0.015 0.013 0.010 0.009 0.006
Prop. in high school or less 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Prop. attending college 0.002 0.002 0.003 0.006 0.003 0.003 0.006 0.009 0.004 0.006 0.002 0.004
Prop. high school graduate 0.005 0.007 0.005 0.014 0.009 0.006 0.019 0.015 0.012 0.010 0.009 0.006
Prop. living in south 0.034 0.034 0.036 0.053 0.044 0.039 0.051 0.059 0.044 0.045 0.039 0.041
Prop. currently married 0.008 0.010 0.011 0.014 0.012 0.008 0.021 0.020 0.018 0.014 0.010 0.012
Prop. employed at present 0.007 0.007 0.010 0.014 0.009 0.008 0.018 0.018 0.012 0.013 0.008 0.012
Prop. government training 0.001 0.002 0.002 0.003 0.003 0.001 0.003 0.006 0.004 0.003 0.002 0.002
Average number of children 0.024 0.029 0.031 0.053 0.037 0.028 0.069 0.065 0.049 0.051 0.035 0.036
Average highest grade completed 0.061 0.076 0.065 0.115 0.069 0.074 0.149 0.119 0.074 0.096 0.093 0.077
Prop. currently enrolled 0.002 0.002 0.003 0.006 0.003 0.003 0.006 0.009 0.004 0.006 0.002 0.004
Notes:  Users are cautioned that cohort changes over time have made some categories much less relevant. In particular, the extremely small subsample sizes for education related variables such as "Proportion in high school or less," "Proportion government training participant," "Proportion currently enrolled," and "Proportion attending college" make these categories statistically suspect. They have been kept in the table for historical continuity.

 

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