2021-2022 National Survey on Drug Use and Health: Comparison of Population Percentages from the United States, Census Regions, States, and the District of Columbia (Documentation for CSV and Excel Files)

Documentation for CSV and Excel Files

Description of the CSV File Type

Files with a comma-separated value (*.csv) extension are in plain text. They contain characters stored in a flat, nonproprietary format and can be opened by most computer programs. Each *.csv file contains a set of tabular data, with each record delineated by a line break and each field within a record delineated by a comma. A field that contains commas as part of its content has the additional delineation of a quote mark character before and after the field’s contents. When a quote mark character is part of a field’s content, it is included as two consecutive ""quote mark"" characters.

Computers with Microsoft Excel installed open *.csv files in Excel by default, with the fields automatically arranged appropriately in columns. Other database programs also open *.csv files with the fields appropriately arranged.

The 168 *.csv files (i.e., “P Value Table#.csv”) reflect the 168 Excel tables, and they contain the table title, table notes, column headings, and data. The webpage at https://www.samhsa.gov/data/report/2021-2022-nsduh-substate-region-estimates-p-value-tables for the 2021-2022 National Survey on Drug Use and Health (NSDUH) state p value tables includes a hyperlinked table of contents on the first sheet of the Excel file that combines all of the Excel tables, as well as a ZIP file containing all of the individual *.csv files. Additionally, the ZIP file includes a text file with a list of the table numbers and titles.

How to Use the P Value Tables

The p values contained in these tables for each outcome and age group can be used to test the null hypothesis of no difference between population percentages for the following types of comparisons:

total United States versus census region (within the table, to find the p value, go to the census region row, then to the Total U.S. column),
total United States versus state (within the table, to find the p value, go to the state row, then to the Total U.S. column),
census region versus census region (within the table, to find the p value, go to the census region with the higher order number, then navigate to the column of the other region [“Order” is the first column in the excel tables and includes values 1 (Total U.S.) to 56 (Wyoming)]),
census region versus state (within the table, to find the p value, go to the state row, then navigate to the census region column), and
state versus state (within the table, to find the p value, go to the state row with the higher order number, then navigate to the column of the other state [“Order” is the first column in the excel tables and includes values 1 (Total U.S.) to 56 (Wyoming)]).

In general, to find the p value when testing any two geographic areas, navigate to the row of the area with the higher order number, then navigate to the column of the other area. For example, within any given table, by scrolling across Alabama’s state row to the South’s census region column, the p value found will determine whether Alabama’s state population percentage and the South’s census region population percentage are significantly different for a particular outcome of interest. Note that the tests included here are for a given outcome and age group produced using 2021 and 2022 data.¹ Beginning in 2021, suppression is applied to unreliable state estimates (see Section A.4 of 2021-2022 National Survey on Drug Use and Health: Guide to State Tables and Summary of Small Area Estimation Methodology at https://www.samhsa.gov/data/report/2021-2022-nsduh-guide-state-tables-and-summary-sae-methodology). If a state estimate is suppressed, then the corresponding p value is also suppressed.

For example, Table 2.3 contains p values for past year marijuana use among people aged 18 to 25. The p value for testing the null hypothesis of no difference between Alabama and the South region population percentages for past year marijuana use among people aged 18 to 25 is 0.003. Thus, the hypothesis of no difference (Alabama population percentage = South region population percentage) is rejected at the 1 percent level of significance, meaning that the two population percentages are statistically different. Note that the Alabama and South region estimates for past year marijuana use among people aged 18 to 25 are 25.93 and 32.35 percent, respectively.²

Comparison between Two Small Area Population Percentages

To produce state, census region, and national small area estimates, the 2021-2022 NSDUH data³ were modeled using the method discussed in Section B.1 of the 2021-2022 Guide to State Tables and Summary of SAE Methodology document at https://www.samhsa.gov/data/report/2021-2022-nsduh-guide-state-tables-and-summary-sae-methodology. This modeling results in 1,250 Markov Chain Monte Carlo (MCMC) samples that are used here to calculate p values for testing the null hypothesis of no difference between two small area population percentages.

Let pi sub 1 a and pi sub 2 a denote the population percentages of two areas (e.g., state 1 versus state 2 or state 1 versus national) for age group-a. The difference between and is defined in terms of the log-odds ratio, the log-odds ratio, lor sub a, is defined as the natural logarithm of the ratio of two quantities; the numerator of the ratio is pi sub 2 a divided by 1 minus pi sub 2 a. The denominator of the ratio is pi sub 1 a divided by 1 minus pi sub 1 a , where ln denotes the natural logarithm, as opposed to the simple difference ( pi sub 2 a minus pi sub 1 ), because the posterior distribution of the log-odds ratio is closer to Gaussian than the posterior distribution of the simple difference.

An estimate, lor hat sub a , of lor sub a is given by the average of the 1,250 MCMC sample-based log‑odds ratios. Let lor i sub a denote the log-odds ratio for the i-th MCMC sample. That is,

The log-odds ratio, lor i sub a, is defined as the natural logarithm of the ratio of two quantities. The numerator of the ratio is pi i sub 2 a divided by 1 minus pi i sub 2 a. The denominator of the ratio is pi i sub 1 a, divided by 1 minus pi i sub 1 a. The value i in the equation takes on values 1 to 1250. .

Then lor hat sub a is defined as the ratio of two quantities. The numerator is the sum over 1,250 values of lor i sub a. The denominator of the ratio is 1,250. and the variance of is given by the following:

The variance of lor hat sub a is defined as the ratio of two quantities. The numerator is the sum over 1,250 values of the square of the difference between lor i sub a and lor hat sub a. The denominator is 1,250. .

To calculate the p value for testing the null hypothesis of no difference, ( Log-odds ratio, lor sub a, is equal to zero. ), it is assumed that the posterior distribution of is normal with estimated Mean is equal to the estimate of the log-odds ratio, lor hat sub a. and Variance is equal to the variance v of the estimate of the log-odds ratio, lor hat sub a. . The Bayesian p value or significance level for the null hypothesis of no difference, ( Log-odds ratio, lor sub a, is equal to zero ), is The p value is equal to 2 times the probability of realizing a standard normal variate greater than or equal to the absolute value of a quantity z. , where capital Z is a standard normal random variate, Quantity z is the estimate of the log-odds ratio, lor hat sub a, divided by the square root of the variance of lor hat sub a. , and absolute value of quantity z denotes the absolute value of . This Bayesian significance level (or p value) for the null value of log-odds ratio lor sub a , say log-odds ratio lor sub zero , is defined following Rubin (1987)⁴ as the posterior probability for the collection of the values that are less likely or have smaller posterior density, d of the log-odds ratio lor , than the null (no change) value, . That is,

The p value of log-odds ratio lor sub zero is equal to the probability of d of the log-odds ratio lor when it is less than or equal to d of the log-odds ratio lor sub zero. .

With the posterior distribution of log-odds ratio lor sub a approximately normal, the p value of log-odds ratio lor sub zero is given by the above expression. If the p value is less than 0.01, for example, then it can be stated that the population percentages of two areas are statistically different from each other at the 1 percent level of significance.

End Notes

¹ The outcomes in these tables focus on illicit drug use, alcohol use, tobacco use, perception of great risk of harm from substance use, substance use disorder, substance use treatment, any mental illness, serious mental illness, mental health treatment, major depressive episode, and suicidal thoughts and behavior. The age groups include people aged 12 or older, youths aged 12 to 17, young adults aged 18 to 25, adults aged 26 or older, and adults aged 18 or older. Alcohol use outcomes are also provided for people aged 12 to 20 (i.e., underage people). Note that not all outcomes have data broken out by all age groups. Estimates for youths aged 12 to 17 are not available for past year heroin use because past year heroin use was extremely rare among youths aged 12 to 17 in the 2021 and 2022 NSDUHs. As a result, estimates for people aged 12 or older are also not produced. Thus, p value tables for these two age groups for past year heroin use are not available. For the three substance use treatment outcomes and one mental health treatment outcome, only 2022 NSDUH data were used.

² See Table 2 of 2021-2022 National Survey on Drug Use and Health: Model-Based Prevalence Estimates (50 States and the District of Columbia) at https://www.samhsa.gov/data/report/2021-2022-nsduh-state-prevalence-estimates.

³ For the three substance use treatment outcomes and one mental health treatment outcome, only 2022 NSDUH data were used.

⁴ See the following reference: Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys (Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics). John Wiley & Sons.