1997 National Household Survey on Drug Abuse

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Sample Design Effects and Generalized Standard Errors

var(p) = design-based variance estimate of p and
[p(1-p)/n] = simple random sample variance estimate of p .

Taking the log (base 10) of both sides of the above equation leads to the following log-linear model:


where

= regression coefficients for the intercept, log(p), log(1-p), and log(n), respectively.

Separate models were fit for the licit and illicit drug use estimates in the 1997 NHSDA. The design effects used to calculate the medians in Tables C.1 and C.2 were used to fit the licit and illicit drug use models for the 1997 NHSDA.

By substituting the fitted model into the definition of the design effect, a prediction equation for the approximate SE is obtained:


where

The index-i indicates whether the SE approximation is for a licit drug or illicit drug prevalence estimate.

After solving for the regression coefficients, the above approximation reduces to the following two prediction equations:


Tables C.3 and C.4 present generalized SEs for various percentages (from 1% to 99%) and sample sizes (from 100 to 24,505) for the 1997 NHSDA, predicted from Equations (C-2) and (C-3).
In summary, the user may obtain 1997 NHSDA SE estimates from the following recommended order of sources:
 

Once the variance estimates have been obtained, the user may apply the methods discussed in previous sections to compute confidence intervals or make statistical comparisons.
Table C.1 Median Design Effects of Illicit Drug Use Estimates, by Age Group and Demographic Characteristics: 1997 NHSDA Questionnaire
Note: These design effects apply to the following drugs: any illicit drug use; marijuana/hashish; cocaine; crack; inhalants; hallucinogens; lysergic acid diethylamide (LSD); phencyclidine (PCP); heroin; nonmedical use of any psychotherapeutics; nonmedical use of stimulants; nonmedical use of sedatives; nonmedical use of tranquilizers; nonmedical use of analgesics; and any illicit drug except marijuana.

N/A: Not applicable.

1The category "other" for race/ethnicity is not included.
2Data on adult education are not applicable for 12 to 17 year olds.
3Data on current employment are not applicable for 12 to 17 year olds.
4Retired, disabled, homemaker, student, or "other."

Source: Office of Applied Studies, SAMHSA, National Household Survey on Drug Abuse, 1997.

Table C.2 Median Design Effects of Licit Drug Use Estimates, by Age Group and Demographic Characteristics: 1997 NHSDA Questionnaire

Note: These design effects apply to the following drugs: cigarettes, alcohol, smokeless tobacco, binge drinking, and heavy drinking.

N/A: Not applicable.

1The category "other" for race/ethnicity is not included.
2Data on adult education are not applicable for 12 to 17 year olds.
3Data on current employment are not applicable for 12 to 17 year olds.
4Retired, disabled, homemaker, student, or "other."

Source: Office of Applied Studies, SAMHSA, National Household Survey on Drug Abuse, 1997.

Table C.3 Generalized Standard Errors for Estimated Percentages of Illicit Drug Use Estimates: 1997
Sample Size
for Base of
Percentage, n
Estimated Percentage (Proportion, p, Multiplied by 100)
1
2
3
5
10
20
30
40
50
60
70
80
90
95
97
98
99
100 0.38 0.67 0.93 1.40 2.41 3.98 5.13 5.93 6.40 6.50 6.22 5.44 3.96 2.73 2.04 1.62 1.07
300 0.24 0.43 0.60 0.90 1.54 2.55 3.29 3.81 4.11 4.17 3.99 3.49 2.54 1.75 1.31 1.04 0.69
500 0.20 0.35 0.49 0.73 1.26 2.08 2.68 3.10 3.34 3.40 3.25 2.84 2.07 1.43 1.07 0.84 0.56
700 0.17 0.31 0.42 0.64 1.10 1.81 2.34 2.71 2.92 2.97 2.83 2.48 1.80 1.24 0.93 0.74 0.49
900 0.16 0.28 0.38 0.58 0.99 1.64 2.11 2.44 2.63 2.68 2.56 2.24 1.63 1.12 0.84 0.67 0.44
1,000 0.15 0.26 0.37 0.55 0.95 1.57 2.03 2.34 2.53 2.57 2.45 2.15 1.56 1.08 0.81 0.64 0.42
1,250 0.14 0.24 0.34 0.51 0.87 1.43 1.85 2.14 2.31 2.35 2.24 1.96 1.43 0.98 0.74 0.58 0.39
1,500 0.13 0.22 0.31 0.47 0.81 1.33 1.72 1.99 2.14 2.18 2.08 1.82 1.33 0.91 0.68 0.54 0.36
2,000 0.11 0.20 0.28 0.42 0.72 1.19 1.53 1.77 1.91 1.94 1.86 1.62 1.18 0.81 0.61 0.48 0.32
2,500 0.10 0.18 0.25 0.38 0.66 1.08 1.40 1.62 1.74 1.77 1.70 1.48 1.08 0.74 0.56 0.44 0.29
3,000 0.10 0.17 0.24 0.36 0.61 1.01 1.30 1.50 1.62 1.65 1.57 1.38 1.00 0.69 0.52 0.41 0.27
4,000 0.09 0.15 0.21 0.32 0.54 0.90 1.16 1.34 1.44 1.47 1.40 1.23 0.89 0.62 0.46 0.36 0.24
5,000 0.08 0.14 0.19 0.29 0.50 0.82 1.06 1.22 1.32 1.34 1.28 1.12 0.82 0.56 0.42 0.33 0.22
7,500 0.07 0.12 0.16 0.25 0.42 0.70 0.90 1.04 1.12 1.14 1.09 0.95 0.69 0.48 0.36 0.28 0.19
10,000 0.06 0.10 0.15 0.22 0.38 0.62 0.80 0.92 1.00 1.01 0.97 0.85 0.62 0.43 0.32 0.25 0.17
15,000 0.05 0.09 0.12 0.19 0.32 0.53 0.68 0.79 0.85 0.86 0.82 0.72 0.52 0.36 0.27 0.21 0.14
18,000 0.05 0.08 0.11 0.17 0.30 0.49 0.63 0.73 0.79 0.80 0.76 0.67 0.49 0.34 0.25 0.20 0.13
24,5051 0.04 0.07 0.10 0.15 0.26 0.43 0.56 0.64 0.69 0.71 0.67 0.59 0.43 0.30 0.22 0.18 0.12

Note: Generalized standard errors are predicted from the following equation: SE = 100*[ 1.1032p(.8264)*(1-p)(.6002)/n(.4036)].

1The total sample size for the 1997 NHSDA is 24,505.

Source: Office of Applied Studies, SAMHSA, National Household Survey on Drug Abuse, 1997.

Table C.4 Generalized Standard Errors for Estimated Percentages of Licit Drug Use Estimates: 1997
Sample Size
for Base of
Percentage, n
Estimated Percentage (Proportion, p, Multiplied by 100)
1
2
3
5
10
20
30
40
50
60
70
80
90
95
97
98
99
100 0.98 1.46 1.85 2.47 3.62 5.10 6.02 6.55 6.75 6.64 6.19 5.35 3.90 2.73 2.08 1.67 1.14
300 0.64 0.96 1.21 1.62 2.36 3.33 3.93 4.28 4.41 4.34 4.05 3.49 2.55 1.79 1.36 1.09 0.75
500 0.52 0.78 0.99 1.33 1.94 2.73 3.22 3.51 3.62 3.56 3.32 2.87 2.09 1.47 1.12 0.90 0.61
700 0.46 0.69 0.87 1.16 1.70 2.40 2.83 3.08 3.17 3.12 2.91 2.52 1.83 1.29 0.98 0.79 0.54
900 0.42 0.63 0.79 1.06 1.54 2.18 2.57 2.79 2.88 2.83 2.64 2.28 1.66 1.17 0.89 0.71 0.49
1,000 0.40 0.60 0.76 1.01 1.48 2.09 2.46 2.68 2.76 2.72 2.54 2.19 1.60 1.12 0.85 0.68 0.47
1,250 0.37 0.55 0.70 0.93 1.36 1.92 2.26 2.46 2.53 2.49 2.33 2.01 1.46 1.03 0.78 0.63 0.43
1,500 0.34 0.51 0.65 0.87 1.27 1.79 2.11 2.29 2.36 2.32 2.17 1.87 1.36 0.96 0.73 0.59 0.40
2,000 0.31 0.46 0.58 0.77 1.13 1.60 1.88 2.05 2.11 2.08 1.94 1.67 1.22 0.86 0.65 0.52 0.36
2,500 0.28 0.42 0.53 0.71 1.04 1.46 1.73 1.88 1.94 1.91 1.78 1.54 1.12 0.79 0.60 0.48 0.33
3,000 0.26 0.39 0.50 0.66 0.97 1.36 1.61 1.75 1.81 1.78 1.66 1.43 1.04 0.73 0.56 0.45 0.31
4,000 0.23 0.35 0.44 0.59 0.87 1.22 1.44 1.57 1.61 1.59 1.48 1.28 0.93 0.65 0.50 0.40 0.27
5,000 0.21 0.32 0.41 0.54 0.79 1.12 1.32 1.44 1.48 1.46 1.36 1.17 0.86 0.60 0.46 0.37 0.25
7,500 0.18 0.27 0.35 0.46 0.68 0.96 1.13 1.23 1.27 1.24 1.16 1.00 0.73 0.51 0.39 0.31 0.21
10,000 0.16 0.25 0.31 0.42 0.61 0.86 1.01 1.10 1.13 1.11 1.04 0.90 0.65 0.46 0.35 0.28 0.19
15,000 0.14 0.21 0.27 0.35 0.52 0.73 0.86 0.94 0.97 0.95 0.89 0.77 0.56 0.39 0.30 0.24 0.16
18,000 0.13 0.20 0.25 0.33 0.48 0.68 0.80 0.87 0.90 0.89 0.83 0.71 0.52 0.37 0.28 0.22 0.15
24,5051 0.12 0.17 0.22 0.29 0.43 0.60 0.71 0.78 0.80 0.79 0.73 0.63 0.46 0.32 0.25 0.20 0.14

Note: Generalized standard errors are predicted from the following equation: SE = 100*[.8911p(.5910)*(1-p)(.5569)/n(.3876)].

1The total sample size for the 1997 NHSDA is 24,505.

Source: Office of Applied Studies, SAMHSA, National Household Survey on Drug Abuse, 1997.

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This page was last updated on December 30, 2008.