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Prevalence of Substance Use Among Racial & Ethnic Subgroups in the U.S.
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Prevalence of Substance Use Among Racial & Ethnic Subgroups in the U.S. |
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The first four sections of this appendix discuss (1) sample weighting, (2) estimation of percentages (i.e., the method of statistical estimation used in Chapter 2-5), (3) statistical tests, and 4) suppression of estimates due to low precision. The final section presents standard errors for estimates presented in text tables of this report.
1. Sample weighting. The estimates of this report are based on sample survey data rather than on complete data for the population. This implies that the estimates must be weighted to take into account the complex sample design of the NHSDA. The basic sampling weights of each annual NHSDA are equal to the inverses of the probabilities of selection of sample respondents. In other words, the smaller a respondent's chance of entering the sample, the larger the weight of that respondent in the calculation of unbiased estimates for the target population. To obtain the final NHSDA weights, the basic sampling weights are adjusted to reflect household-level and individual-level nonresponse and further adjusted to ensure consistency with U.S. census population totals. (For details of NHSDA weighting, see SAMHSA, 1995c, Appendix D.)
The weight of the ith respondent, say wi, can be interpreted as the number of persons in the NHSDA target population that are represented by the ith respondent. The sum of the weights over all respondents estimates the size of the total target population, that is,
SUM FROM i w SUB i~ =~ Size~ of~ target~ population,~~~~~~~~~~(1)where the summation is over all NHSDA respondents in the survey year.
Given the near equivalence of sample designs and sample sizes of the 1991, 1992, and 1993 surveys, weights for the combined 1991-1993 file were calculated by dividing the final weight on each annual file by three. This yields a total sum of weights equal to about 205 million for the more than 87,000 respondents age 12 and older in the combined 1991-1993 NHSDAs.
All estimates presented in this report are weighted to take into account the complex sampling design of the NHSDA. Thus, the estimates presented in this report are unbiased estimates for the U.S. civilian, noninstitutionalized population aged 12 and older or for specified subgroups of that target population.
2. Estimation of percentages. Chapters 2 through 5 present estimates of the percentages of persons age 12 and older in the total NHSDA target population and in racial/ethnic and other demographic subgroups who used substances during the preceding 12-month period. Let pds denote the estimated percentage using substance 'd' in subgroup 's.' Then
p SUB {ds} ~=~100~{SUM FROM i`w SUB i~I SUB {di} `I SUB {si}} OVER {SUM FROM i` w SUB i ~ I SUB {si}}~,~~~~(2)where wi is the weight of sample respondent 'i,' Isi is a 0-1 variable which takes on the value 1 if and only if respondent 'i' belongs to subgroup 's,' Idi is a 0-1 variable which takes on the value 1 if and only if respondent 'i' reported using substance 'd' during the preceding 12-month period, and the summations are over all respondents to the 1991-93 NHSDAs who were age 12-17.
3. Statistical tests. We used statistical tests to determine the statistical significance, at the .05 level, of differences between subgroups that are reported in the text of this report. The statistical significance tests were standard difference-in-percentages tests, expressed as
Z~=~{LINE p_1~-~p_2 LINE} OVER
SQRT {SE(p_1) SUP 2~+~SE(p_2) SUP 2} ,~~~~~~~~~(3) where p1 is the estimated percentage of the first subgroup (e.g., the estimated percentage using cigarettes in the past year), p2 is the corresponding estimate of the second subgroup, SE(p1) is the standard error of p1, and SE(p2) is the standard error of p2.
The test statistic in (3) can be computed using the estimates reported in any text table and the standard errors reported in the corresponding standard error table of Appendix A. For example, Table 4.2 reports that the percentage of individuals age 12-to-17 using cigarettes in the past year equals 32.8 in Native American subgroup and 21.9 in the non-Hispanic white subgroup. Table A4.2 reports that the standard errors of these two rates are 6.2 and 0.6, respectively. From Eq. (3), it follows that Z = approximately 1.7, which is less than the critical value 1.96; hence, the difference between two percentages is not statistically significant at the .05 level. As a second example, Table 4.3 reports that, among males age 12 and older, the percentages using alcohol in the past year equal 65.0 among Central American Hispanics and 73.8 among Mexican Hispanics. From Table A4.3, the corresponding standard errors equal 2.4 and 1.0, respectively. From Eq. (3), Z = approximately 3.4, which is greater than 1.96; hence, the difference between the two percentages is statistically significant at the .05 level.
4. Suppression of low precision estimates. This report's estimates of the percentages of demographic subgroups using substances during the past year, dependent on alcohol, and in need of illicit drug abuse treatment were rounded to the nearest tenth of one percent and screened to confirm that they met a required level of statistical precision. Estimated percentages were considered to be of low precision if the standard error of the estimate was greater than 17.5 percent of the log transformation of the estimate. Low precision typically occurs for small subgroups when percents are close to zero or 100, but the large combined sample size of the 1991-93 NHSDAs ensured that few estimates had to be suppressed because of low precision. Estimates that were suppressed because of low precision are noted using asterisks in the text tables of this report.
5. Standard error tables. The appendix tables present standard errors for all estimates that are presented in the text of this report. Like the estimates themselves, the standard errors of these estimates fully take into account the complex sampling design of the NHSDA. In particular, the variance estimation software (SUDAAN) used the method of Taylor Series linearization to adjust all standard errors for correlations between observations due to the multistage sample design of NHSDA. (See SAMHSA, 1995c, Appendices C and D, for details of the NHSDA sample design and variance estimation methodology.)
The standard error tables have the same formats as the text tables for which they provide statistical documentation. The appendix table presenting the standard errors for estimates shown in a specified text table has the same number as the text table except for the prefix "A." For example, appendix table A3.1 presents the standard errors for the estimates shown in text table 3.1.
1 Education, employment and marital status are calculated using respondents aged 18 and older.
Source: Office of Applied Studies, SAMHSA, National Household Survey on Drug Abuse, 1991-93.
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Table A3.2 Standard Errors for Percentage Distribution of Racial/Ethnic Groups by Sociodemographic Variables. Respondents Aged 12-17, 1991-1993. | ||||||||||||
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Total |
Native American |
Asian/Pacific Islander |
Hispanic: Caribbean |
Hispanic: Central American |
Hispanic: Cuban |
Hispanic: Mexican |
Hispanic: Puerto Rican |
Hispanic: South American |
Hispanic: other |
Non-Hispanic blacks |
Non-Hispanic whites | |
|
Gender: Male Female |
0.5 0.5 |
7.5 7.5 |
3.2 3.2 |
5.4 5.4 |
3.4 3.4 |
3.9 3.9 |
1.5 1.5 |
2.7 2.7 |
5.0 5.0 |
5.2 5.2 |
1.1 1.1 |
0.7 0.7 |
|
Region: Northeast North Central South West |
0.7 0.8 0.9 0.7 |
4.2 6.1 14.2 10.0 |
2.6 2.5 2.7 4.0 |
2.1 0.4 1.5 1.5 |
3.5 2.2 3.0 3.6 |
4.3 3.3 4.7 2.9 |
0.3 1.3 2.7 2.4 |
3.3 2.5 2.2 1.7 |
4.6 2.5 4.8 3.0 |
3.8 1.1 5.2 8.1 |
0.9 1.2 1.8 1.0 |
1.0 1.1 1.4 1.1 |
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Population Density: MSA >1million Other MSA Not in MSA |
1.4 2.3 2.0 |
8.0 9.1 14.0 |
4.1 4.3 1.6 |
4.9 4.9 0.0 |
3.9 3.2 2.7 |
5.2 4.9 2.4 |
2.4 2.1 2.8 |
4.2 4.5 1.5 |
5.5 4.5 4.4 |
10.0 5.7 14.4 |
2.7 3.1 2.5 |
1.5 2.7 2.5 |
|
Interview: Spanish English |
0.1 0.1 |
0.0 0.0 |
0.0 0.0 |
3.8 3.8 |
2.7 2.7 |
2.0 2.0 |
1.2 1.2 |
0.8 0.8 |
2.1 2.1 |
1.3 1.3 |
0.0 0.0 |
0.0 0.0 |
|
Family Income: <$20,000 $20-40,000 >$40,000 |
0.8 0.5 0.8 |
7.4 3.7 8.2 |
3.1 2.7 3.0 |
4.9 5.0 4.8 |
3.3 2.3 3.0 |
3.8 3.5 3.8 |
1.7 1.1 1.5 |
2.5 2.1 2.3 |
4.5 3.7 4.4 |
6.3 3.1 6.3 |
1.3 0.9 1.1 |
0.9 0.6 1.0 |
|
School Dropout: Yes No |
0.2 0.2 |
4.2 4.2 |
1.0 1.0 |
1.4 1.4 |
1.2 1.2 |
1.0 1.0 |
0.6 0.6 |
0.6 0.6 |
1.2 1.2 |
2.6 2.6 |
0.3 0.3 |
0.2 0.2 |
|
Family: Mother/Father Other |
0.6 0.6 |
6.9 6.9 |
2.9 2.9 |
4.8 4.8 |
3.4 3.4 |
3.9 3.9 |
1.3 1.3 |
2.7 2.7 |
4.1 4.1 |
4.0 4.0 |
1.0 1.0 |
0.7 0.7 |
|
Welfare Receipt: Yes No |
0.4 0.4 |
6.2 6.2 |
2.1 2.1 |
4.2 4.2 |
1.4 1.4 |
3.2 3.2 |
1.1 1.1 |
3.0 3.0 |
2.0 2.0 |
1.5 1.5 |
1.0 1.0 |
0.4 0.4 |
|
Insurance Coverage: Yes No |
0.5 0.5 |
8.0 8.0 |
1.9 1.9 |
3.9 3.9 |
3.4 3.4 |
3.2 3.2 |
1.3 1.3 |
1.8 1.8 |
3.8 3.8 |
3.0 3.0 |
1.1 1.1 |
0.6 0.6 |
|
Average Number of People in Household |
0.02 |
0.3 |
0.1 |
0.2 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.2 |
0.1 |
0.02 |
Source: Office of Applied Studies, SAMHSA, National Household Survey on Drug Abuse, 1991-93.
Source: Office of Applied Studies, SAMHSA, National Household Survey on Drug Abuse, 1991-93.
| Table A3.4 Standard Errors for Percentage Distribution of Racial/Ethnic Groups by Sociodemographic Variables. Respondents Aged 26-34, 1991-1993. | ||||||||||||
|
Total |
Native American |
Asian/Pacific Islander |
Hispanic: Caribbean |
Hispanic: Central American |
Hispanic: Cuban |
Hispanic: Mexican |
Hispanic: Puerto Rican |
Hispanic: South American |
Hispanic: other |
Non-Hispanic blacks |
Non-Hispanic whites | |
|
Gender: Male Female |
0.5 0.5 |
6.4 6.4 |
3.5 3.5 |
4.4 4.4 |
3.0 3.0 |
3.8 3.8 |
1.3 1.3 |
2.6 2.6 |
4.7 4.7 |
5.5 5.5 |
1.1 1.1 |
0.6 0.6 |
|
Region: Northeast North Central South West |
0.8 0.8 0.9 0.8 |
2.3 5.7 16.1 12.4 |
3.7 2.0 3.4 4.1 |
3.4 0.9 3.0 1.6 |
2.8 1.3 3.0 3.6 |
4.3 1.6 5.1 3.2 |
0.3 0.9 2.4 2.2 |
2.9 2.0 2.0 1.8 |
5.2 1.1 4.3 3.7 |
3.9 2.8 2.9 6.8 |
1.1 1.4 2.0 0.8 |
1.0 1.0 1.2 1.0 |
|
Population Density: MSA >1million Other MSA Not in MSA |
1.4 2.2 1.7 |
9.9 11.4 17.0 |
4.4 4.7 1.5 |
4.2 3.8 2.0 |
3.0 2.8 1.2 |
2.6 2.6 0.0 |
2.5 2.2 2.5 |
3.4 3.6 2.3 |
3.6 3.7 0.2 |
7.8 7.1 13.2 |
2.7 2.8 2.2 |
1.6 2.6 2.1 |
|
Interview: Spanish English |
0.1 0.1 |
0.0 0.0 |
0.0 0.0 |
3.2 3.2 |
3.5 3.5 |
3.1 3.1 |
1.6 1.6 |
1.3 1.3 |
2.8 2.8 |
2.0 2.0 |
0.0 0.0 |
0.0 0.0 |
|
Family Income: <$20,000 $20-40,000 >$40,000 |
0.7 0.5 0.7 |
8.1 2.3 8.4 |
3.2 2.3 3.4 |
4.7 4.4 4.2 |
3.2 3.0 3.4 |
3.1 1.5 3.4 |
1.6 1.1 1.6 |
2.8 2.2 3.2 |
3.1 4.5 4.4 |
5.3 4.5 6.2 |
1.2 0.9 1.3 |
0.9 0.7 0.9 |
|
Education: (1) 0-8 years 9-11 years High school grad > High school |
0.2 0.4 0.6 0.8 |
2.2 5.2 7.2 6.0 |
0.8 0.8 3.0 3.6 |
4.2 3.8 4.9 4.4 |
2.7 2.3 3.1 3.3 |
0.7 1.9 3.3 3.6 |
1.3 1.0 1.2 1.2 |
1.0 2.1 2.9 3.1 |
1.1 1.7 4.0 4.3 |
1.7 2.9 6.8 5.3 |
0.2 0.8 1.1 1.3 |
0.3 0.5 0.8 1.0 |
|
Marital Status: (1) Married Widowed/div/sep Never married |
0.6 0.4 0.5 |
6.6 6.6 3.4 |
3.4 1.7 3.4 |
5.5 4.7 4.0 |
3.0 1.5 2.9 |
4.0 2.3 4.2 |
1.2 0.6 1.0 |
3.0 1.7 2.5 |
4.6 2.6 4.2 |
3.9 2.0 3.9 |
1.2 0.7 1.1 |
0.7 0.5 0.6 |
|
Employment (1) Employed Unemployed Not in labor force |
0.5 0.3 0.4 |
7.6 5.4 9.9 |
3.0 1.2 2.8 |
4.5 3.1 3.8 |
3.1 1.0 3.1 |
3.0 1.4 2.6 |
1.2 0.7 1.0 |
2.5 1.7 1.9 |
4.3 2.3 2.9 |
3.9 3.2 2.4 |
0.9 0.7 0.7 |
0.7 0.4 0.5 |
|
Number of Own Children: None 1 or more |
0.6 0.6 |
7.2 7.2 |
3.3 3.3 |
4.9 4.9 |
3.4 3.4 |
5.3 5.3 |
1.2 1.2 |
2.6 2.6 |
4.2 4.2 |
4.7 4.7 |
1.2 1.2 |
0.8 0.8 |