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2002-2004 Sub State Report of Substance Use & Serious Psychological Distress |
Appendix:Highest and Lowest Prevalence Substate Regions within Each State and the Statistical Significance (p value) of Their Difference on Selected Variables:
Estimation Method: To test the difference between the prevalence of two substate regions, say region 1 (with the lowest estimate) and region 2 (with the highest estimate), in a particular State, let π1 and π2 denote the respective small area estimates. We want to test the hypothesis that π2 = π1 or equivalently test π2 - π1 = 0. The difference between π1 and π2 is defined in terms of the log-odds ratio (lor) as opposed to the simple difference because the posterior distribution of the lor is closer to Gaussian than the posterior distribution of the simple difference (π2 π1). The lor is defined as lor = log{[π2 /(1-π2)] ÷ [π1 /(1-π1)]}. So, the above hypothesis is now transformed to testing lor = 0. To compute the posterior variance of lor- v(lor), we define the log-odds ratio for each of the 1,250 Markov Chain Monte Carlo (MCMC) cycles as follows: li = log{[p2i) /(1-p2i)] ÷ [p1i /(1-p1i)]}, where i = 1, 2,...,1,250. In the definition of li above, p2i and p1i denote, respectively, the prevalence estimates of regions 2 and 1 for the i-th MCMC cycle. Then v(lor) is approximated by To calculate the p-value for testing the null hypothesis of no difference (lor = 0), it is assumed that the posterior distribution of lor is normal with mean = With the null value of lor = 0, the Bayes p-value or posterior probability of no difference is p-value = 2*P [Z ≥ abs(z)], where Z is a standard normal random variate,
Note that the unbenchmarked estimate of the prevalence was used in this significance testing. Also note that for States like New Hampshire, New York, and Texas, prevalences of the substate regions were tested rather than testing the prevalences of the aggregate regions presented on the map. Aggregate estimates for these States were calculated by combining several substate regions (the aggregate estimates are hence more centered, rather than being extreme). So, for the purpose of significance testing of the extreme (min, max) regions, we preferred to test the prevalences of the individual regions. Tables for past year cocaine use, past month marijuana use, and past month alcohol use are presented in this appendix. Our intent was to choose a few measures that have varying levels of the national prevalence estimates, from very low for cocaine to very high for alcohol use.
|
State | Lowest Prevalence Substate Region within State | Highest Prevalence Substate Region within State | p value | ||
---|---|---|---|---|---|
Substate Region Name | Estimate | Substate Region Name | Estimate | ||
Alabama | Region 1 | 1.93 | Region 2 | 2.52 | 0.153 |
Alaska | Rural | 1.80a | Southeast | 2.80 | 0.047 |
Arizona | Rural North | 2.94a | Pima | 4.28 | 0.041 |
Arkansas | Areas 2 and 3 | 1.55b | Area 9 | 2.24 | 0.059 |
California | Region 14 (Orange) | 2.18a | Region 4 | 3.63 | 0.010 |
Colorado | Region 4 | 3.00 | Regions 2 and 7 | 4.01 | 0.125 |
Connecticut | North Central | 2.03 | Eastern | 2.31 | 0.513 |
Delaware | Sussex | 2.25 | Wilmington City | 3.15 | 0.164 |
District of Columbia | Ward 8 | 2.76 | Ward 2 | 3.70 | 0.281 |
Florida | District 13 | 1.85a | District 10 (Broward) | 2.95 | 0.018 |
Georgia | Region 1 | 1.86 | Region 4 | 2.50 | 0.178 |
Hawaii | Kauai and Maui | 1.87 | Honolulu | 1.99 | 0.737 |
Idaho | Region 5 | 1.50 | Region 2 | 1.81 | 0.359 |
Illinois | Region II | 2.27 | Region I (Cook) | 2.85 | 0.101 |
Indiana | Southeast | 2.05 | Central | 2.75 | 0.128 |
Iowa | Northwest | 1.77 | Southeast | 2.22 | 0.236 |
Kansas | South Central | 1.82 | Wichita (Sedgwick) | 2.39 | 0.162 |
Kentucky | Adanta, Cumberland River, and Lifeskills | 2.19 | Bluegrass, Comprehend, and North Key | 2.80 | 0.180 |
Louisiana | Regions 7 and 8 | 2.16b | Region 1 | 3.45 | 0.056 |
Maine | Region 5 | 2.06b | Region 1 (Cumberland) | 2.94 | 0.062 |
Maryland | Montgomery | 1.41a | Baltimore City | 3.52 | 0.001 |
Massachusetts | Northeast | 2.50a | Boston | 3.70 | 0.047 |
Michigan | Western | 2.08a | Detroit City | 3.53 | 0.024 |
Minnesota | Region 7C | 2.09 | Region 7A (Hennepin) | 2.74 | 0.154 |
Mississippi | Region 1 | 1.61 | Region 6 | 2.17 | 0.183 |
Missouri | Southwest | 2.36b | Northwest (Jackson) | 3.44 | 0.053 |
Montana | Region 1 | 1.91 | Region 5 | 2.62 | 0.106 |
Nebraska | Region 4 | 1.63a | Region 6 | 2.45 | 0.041 |
Nevada | Rural | 1.77b | Washoe | 2.44 | 0.089 |
New Hampshire | Southern 1 (Rockingham) | 2.29a | Southern 2 | 3.35 | 0.039 |
New Jersey | Central | 2.03 | Southern | 2.21 | 0.679 |
New Mexico | Region 1 | 2.51a | Region 3 (Bernalillo) | 3.75 | 0.020 |
New York | Region 4 | 1.87a | Region 3 | 3.68 | 0.001 |
North Carolina | South Central | 1.97 | Western | 2.34 | 0.366 |
North Dakota | Lake Region and South Central | 1.48a | Southeast | 2.27 | 0.029 |
Ohio | Boards 3, 52, and 85 | 1.75a | Board 25 (Franklin) | 2.95 | 0.006 |
Oklahoma | East Central | 1.51a | Oklahoma County | 2.41 | 0.025 |
Oregon | Region 2 | 1.89a | Region 1 (Multnomah) | 3.10 | 0.009 |
Pennsylvania | Regions 21, 30, 32, and 49 | 1.84a | Region 18 (Philadelphia) | 3.46 | 0.001 |
Rhode Island | Kent | 3.27 | Washington | 3.74 | 0.471 |
South Carolina | Region 3 | 2.40 | Region 4 | 2.84 | 0.442 |
South Dakota | Region 6 | 1.48a | Region 3 (Minnehaha) | 2.18 | 0.042 |
Tennessee | Region 5 | 1.99a | Region 4 (Davidson) | 3.39 | 0.009 |
Texas | Region 3bc | 2.05a | Region 7a | 3.31 | 0.010 |
Utah | Central, Four Corners, San Juan, and Southwest | 1.56 | Salt Lake County | 2.04 | 0.161 |
Vermont | Rural Southeast | 2.27a | Champlain Valley | 3.70 | 0.005 |
Virginia | Region 2 | 2.10 | Region 5 | 2.53 | 0.387 |
Washington | Region 6 | 1.97 | Region 5 | 2.24 | 0.490 |
West Virginia | Eastern Highland | 2.05a | Northern C and D | 3.30 | 0.009 |
Wisconsin | Northern | 2.31 | Milwaukee | 3.11 | 0.152 |
Wyoming | Judicial District 8 | 1.68a | Judicial District 2 | 2.93 | 0.003 |
NOTE: p value: Bayes posterior probability of no difference. NOTE: Estimates are based on a survey-weighted hierarchical Bayes estimation approach. a Difference is statistically significant at the 0.05 level. b Difference is statistically significant at the 0.10 level. Source: SAMHSA, Office of Applied Studies, National Survey on Drug Use and Health, 2002, 2003, and 2004. |
State | Lowest Prevalence Substate Region within State | Highest Prevalence Substate Region within State | p value | ||
---|---|---|---|---|---|
Substate Region Name | Estimate | Substate Region Name | Estimate | ||
Alabama | Region 1 | 3.98 | Region 2 | 5.15 | 0.132 |
Alaska | Rural | 8.19 | Urban | 10.72 | 0.100 |
Arizona | Rural South | 4.69 | Pima | 6.41 | 0.108 |
Arkansas | Areas 2 and 3 | 4.64b | Area 9 | 6.75 | 0.056 |
California | Region 6 (Santa Clara) | 5.24a | Region 1 | 11.43 | 0.000 |
Colorado | Region 4 | 5.60a | Regions 2 and 7 | 8.58 | 0.013 |
Connecticut | Southwest | 4.96a | Northwestern | 8.88 | 0.003 |
Delaware | Sussex | 4.87a | Wilmington City | 7.46 | 0.022 |
District of Columbia | Ward 4 | 6.13a | Ward 2 | 9.60 | 0.019 |
Florida | District 13 | 3.92a | District 2 | 9.21 | 0.000 |
Georgia | Region 1 | 3.87a | Region 3 | 6.62 | 0.003 |
Hawaii | Honolulu | 5.89a | Kauai and Maui | 10.86 | 0.001 |
Idaho | Region 7 | 3.82a | Region 2 | 6.24 | 0.022 |
Illinois | Region IV | 4.48a | Region I (Cook) | 6.38 | 0.007 |
Indiana | Northeast | 4.70b | Central | 6.67 | 0.073 |
Iowa | Northwest | 3.72 | Southeast | 4.85 | 0.198 |
Kansas | West | 3.48a | Kansas City Metro | 5.65 | 0.015 |
Kentucky | Adanta, Cumberland River, and Lifeskills | 4.40a | Seven Counties | 8.40 | 0.001 |
Louisiana | Regions 5 and 6 | 4.32a | Region 1 | 7.32 | 0.009 |
Maine | Region 7 | 6.74b | Region 1 (Cumberland) | 9.22 | 0.075 |
Maryland | Western | 4.30a | Baltimore City | 6.96 | 0.008 |
Massachusetts | Metrowest | 6.70a | Boston | 9.66 | 0.025 |
Michigan | Western | 5.83a | Genesee | 9.23 | 0.027 |
Minnesota | Region 7C | 5.10a | Region 7A (Hennepin) | 7.58 | 0.022 |
Mississippi | Region 1 | 3.77b | Region 7 | 5.51 | 0.063 |
Missouri | Southeast | 4.73a | Northwest (Jackson) | 7.71 | 0.014 |
Montana | Region 3 | 6.89a | Region 5 | 9.66 | 0.037 |
Nebraska | Regions 1 and 2 | 4.06a | Region 6 | 6.16 | 0.027 |
Nevada | Rural | 6.29a | Washoe | 9.02 | 0.037 |
New Hampshire | Central 1 | 8.18b | Southern 2 | 10.71 | 0.058 |
New Jersey | Northern | 4.41 | Central | 5.15 | 0.365 |
New Mexico | Region 4 | 6.66b | Region 3 (Bernalillo) | 9.22 | 0.061 |
New York | Region 4 | 5.13a | Region 3 | 10.73 | 0.000 |
North Carolina | Eastern | 4.52a | Western | 6.69 | 0.021 |
North Dakota | Badlands and West Central | 4.55a | Southeast | 6.87 | 0.012 |
Ohio | Boards 20, 32, 54, and 69 | 4.19a | Board 57 (Montgomery) | 9.55 | 0.000 |
Oklahoma | East Central | 3.86a | Oklahoma County | 6.76 | 0.009 |
Oregon | Region 5 | 7.16a | Region 1 (Multnomah) | 11.08 | 0.014 |
Pennsylvania | Regions 17, 24, 27, 43, and 47 | 4.12a | Region 1 (Allegheny) | 7.56 | 0.000 |
Rhode Island | Kent | 8.26a | Washington | 12.01 | 0.023 |
South Carolina | Region 3 | 4.91 | Region 4 | 5.66 | 0.454 |
South Dakota | Region 6 | 3.72a | Region 2 | 6.87 | 0.004 |
Tennessee | Region 5 | 3.75a | Region 4 (Davidson) | 6.78 | 0.003 |
Texas | Region 11c (Hidalgo) | 3.41a | Region 7a | 7.51 | 0.000 |
Utah | Central, Four Corners, San Juan, and Southwest | 2.79a | Salt Lake County | 5.08 | 0.003 |
Vermont | Rural Southeast | 8.37b | Champlain Valley | 10.96 | 0.065 |
Virginia | Region 4 | 5.09 | Region 3 | 5.84 | 0.449 |
Washington | Region 2 | 5.66 | Region 4 (King) | 7.30 | 0.171 |
West Virginia | South Central I | 4.62b | Northern C and D | 6.49 | 0.072 |
Wisconsin | Western | 4.87a | Milwaukee | 7.25 | 0.035 |
Wyoming | Judicial District 8 | 3.89a | Judicial District 2 | 7.21 | 0.002 |
NOTE: p value: Bayes posterior probability of no difference. NOTE: Estimates are based on a survey-weighted hierarchical Bayes estimation approach. a Difference is statistically significant at the 0.05 level. b Difference is statistically significant at the 0.10 level. Source: SAMHSA, Office of Applied Studies, National Survey on Drug Use and Health, 2002, 2003, and 2004. |
State | Lowest Prevalence Substate Region within State | Highest Prevalence Substate Region within State | p value | ||
---|---|---|---|---|---|
Substate Region Name | Estimate | Substate Region Name | Estimate | ||
Alabama | Region 1 | 35.60 | Region 2 | 40.26 | 0.116 |
Alaska | Rural | 34.24a | Southeast | 52.56 | 0.000 |
Arizona | Rural South | 43.56a | Pima | 53.22 | 0.015 |
Arkansas | Areas 4 and 7 | 32.50a | Area 9 | 45.55 | 0.000 |
California | Region 8 | 42.74a | Region 4 | 59.91 | 0.000 |
Colorado | Region 4 | 49.19a | Region 3 | 61.80 | 0.002 |
Connecticut | South Central | 58.18 | Northwestern | 63.27 | 0.127 |
Delaware | Sussex | 44.66a | New Castle (excluding Wilmington city) | 57.72 | 0.000 |
District of Columbia | Ward 8 | 42.60a | Ward 3 | 74.68 | 0.000 |
Florida | District 14 | 45.50a | District 8 | 58.73 | 0.000 |
Georgia | Region 1 | 36.50a | Region 3 | 52.43 | 0.000 |
Hawaii | Honolulu | 47.30 | Kauai and Maui | 49.53 | 0.483 |
Idaho | Region 7 | 36.31a | Region 4 | 55.78 | 0.000 |
Illinois | Region III | 47.17a | Region II | 55.81 | 0.000 |
Indiana | Southeast | 41.01a | West | 51.72 | 0.005 |
Iowa | Southwest | 52.70 | Northeast | 56.49 | 0.271 |
Kansas | West | 42.51a | Kansas City Metro | 53.86 | 0.001 |
Kentucky | Kentucky River, Mountain, and Pathways | 30.06a | Seven Counties | 48.55 | 0.000 |
Louisiana | Regions 7 and 8 | 40.66a | Region 10 (Jefferson) | 53.28 | 0.000 |
Maine | Region 7 | 42.91a | Region 1 (Cumberland) | 59.30 | 0.000 |
Maryland | Prince George's | 44.28a | Montgomery | 60.84 | 0.000 |
Massachusetts | Central | 55.29a | Metrowest | 65.24 | 0.004 |
Michigan | Detroit City | 39.44a | Washtenaw | 62.52 | 0.000 |
Minnesota | Regions 1 and 2 | 52.93a | Region 7C | 64.67 | 0.001 |
Mississippi | Region 2 | 30.75a | Region 7 | 43.40 | 0.000 |
Missouri | Southeast | 41.89a | Eastern (St. Louis City and County) | 57.53 | 0.000 |
Montana | Region 1 | 50.44a | Region 4 | 60.57 | 0.005 |
Nebraska | Region 4 | 48.90a | Region 6 | 56.23 | 0.026 |
Nevada | Clark | 47.31a | Washoe | 53.80 | 0.034 |
New Hampshire | Central 1 | 57.30b | Southern 1 (Rockingham) | 63.43 | 0.078 |
New Jersey | Southern | 53.51a | Central | 62.30 | 0.009 |
New Mexico | Region 4 | 40.52a | Region 3 (Bernalillo) | 55.12 | 0.000 |
New York | Region 1 | 41.05a | Region 5 | 62.56 | 0.000 |
North Carolina | Eastern | 36.48a | Western | 43.18 | 0.021 |
North Dakota | Lake Region and South Central | 49.91a | Southeast | 64.79 | 0.000 |
Ohio | Boards 27, 71, and 73 | 37.28a | Board 25 (Franklin) | 55.49 | 0.000 |
Oklahoma | East Central | 35.36a | Tulsa County | 48.46 | 0.001 |
Oregon | Region 5 | 51.38b | Region 1 (Multnomah) | 57.87 | 0.094 |
Pennsylvania | Regions 5, 20, 26, 28, and 40 | 44.00a | Region 1 (Allegheny) | 58.90 | 0.000 |
Rhode Island | Providence | 56.72a | Washington | 66.23 | 0.004 |
South Carolina | Region 3 | 40.23 | Region 4 | 45.44 | 0.136 |
South Dakota | Region 6 | 53.58a | Region 3 (Minnehaha) | 61.99 | 0.014 |
Tennessee | Region 6 | 29.93a | Region 4 (Davidson) | 43.77 | 0.000 |
Texas | Region 11c (Hidalgo) | 33.90a | Region 7a | 57.73 | 0.000 |
Utah | Utah County | 19.75a | Salt Lake County | 35.14 | 0.000 |
Vermont | Rural Northeast | 53.95a | Champlain Valley | 62.39 | 0.004 |
Virginia | Region 3 | 42.15a | Region 2 | 58.68 | 0.000 |
Washington | Region 2 | 46.26a | Region 4 (King) | 59.78 | 0.000 |
West Virginia | Southern II | 27.56a | Northern A and B | 41.51 | 0.000 |
Wisconsin | Milwaukee | 58.03 | Southeastern | 62.77 | 0.175 |
Wyoming | Judicial District 3 | 46.95a | Judicial District 2 | 55.75 | 0.014 |
NOTE: p value: Bayes posterior probability of no difference. NOTE: Estimates are based on a survey-weighted hierarchical Bayes estimation approach. a Difference is statistically significant at the 0.05 level. b Difference is statistically significant at the 0.10 level. Source: SAMHSA, Office of Applied Studies, National Survey on Drug Use and Health, 2002, 2003, and 2004. |
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