Share with your friends










Submit

Analytics Magazine

The Five-Minute Analyst: Drug tests for needy families

July/August 2011

CLICK HERE TO GO TO THE DIGITAL VERSION OF THIS ARTICLE

New Florida bill requires welfare applicants to take a drug test to continue receiving benefits. Will the policy save the state money?

Harrison Schramm, CAPBy Harrison Schramm

The state of Florida has signed into law a bill that requires welfare applicants to take a drug test to continue receiving benefits [1, 2]. A twist to this law is that applicants will pay for the drug test out of pocket. If they pass the drug test, their fee ($10-$25) [3] will be reimbursed, and they will continue to receive benefits under the Temporary Assistance for Needy Families program (TANF) for six months. The value of this benefit is $300 per month. Approximately 4,000 persons apply for the benefit each month.

Will this policy save money for Florida? Let’s examine the policy mathematically from four points of view:

A. The state’s point of view: perfect drug testing

Let:
Drug tests for needy families

The cost of the program with no drug screening is: NB=$7.2 million

The cost of the program with drug screening is:  Drug tests for needy families

Assuming 10 percent applicant drug use, the cost of the program with perfect drug testing is $6.5 million, with a net savings to the taxpayers of $700,000. Drug testing will be cost effective [4] if the proportion of drug users who apply for aid is greater than 1 percent.

Consider now an imperfect drug test — one that is susceptible to both false positives [5] and false negatives [6]. A ‚”decision tree‚” for an imperfect drug test is shown in Figure 1:

Figure 1: Imperfect drug test decision tree.
Figure 1: Imperfect drug test decision tree.

B. The drug user’s decision

A drug user is interested in the outcome ‚”drug user, tests negative,‚” and specifically in the rate of false positives that make the benefit of assistance (weighted by his probability of getting it) equals his potential loss paying for the test [7]. A drug user should take the test if it has a false-negative rate ? .5 percent. As a policy implication, drug users will want the state to choose the most inexpensive test available, as it makes the price of entering the ‚”lottery‚” cheaper. An inexpensive drug test may also have a higher false positive rate.

C. The non-drug user’s decision

An applicant who does not use drugs should not use an expected value model for their decision; the assistance program is not a lottery to them but rather a means to survive. Assuming the refund for the test is timely, non drug-users will want the state to have the test that will have the lowest false positive rate Imperfect drug test regardless of expense.

D. The state’s decision — revisited

The state may be interested in the probability that a person using drugs is receiving the benefit. We can solve this by reversing the conditioning and applying Bayes Theorem [8]. Reducing the population from ‚”everyone‚” to ‚”everyone who tests negative for drugs‚” may be thought of as: ‚”drug users who test negative‚” divided by ‚”everyone who tests negative‚” [9].

If the state were to use a drug test with draug test and 1 percent of the applicants use drugs, then the probability a drug user is receiving assistance is less than 1 in 10,000. If 10 percent of the applicants use drugs, then the probability a drug user is receiving assistance remains less than 1 in 1,000.

In conclusion, a drug test for welfare applicants is a mathematically defensible policy. This is not the end of the debate on this issue but rather the beginning.  Armed with statistical reasoning, we may now ask the real question: How do the savings under this policy compare with the significant ethical and legal issues it raises?

Harrison Schramm (harrison.schramm@gmail.com) is a military instructor in the Operations Research Department at the Naval Postgraduate School in Monterey, Calif.

References

  1. www.economist.com/node/18805970
  2. www.reuters.com/article/2011/05/31/us-florida-welfare-drugs-idUSTRE74U6W320110531
  3. http://gantdaily.com/2011/06/01/florida-governor-signs-controversial-drug-test-bill-into-law/
  4. We set drug tests and solve for drug tests
  5. Reporting the presence of drugs where there are none
  6. Reporting the absence of drugs when they are present
  7. drug test
  8. Wolcott and Smith have an excellent, accessible discussion of Bayes Theorem in ‚”The Cartoon Guide to Statistics,‚” p.46-50.
  9. The formula is: drug tests

CLICK HERE TO GO TO THE DIGITAL VERSION OF THIS ARTICLE

Analytics Blog

Electoral College put to the math test


With the campaign two months behind us and the inauguration of Donald Trump two days away, isn’t it time to put the 2016 U.S. presidential election to bed and focus on issues that have yet to be decided? Of course not.


Headlines

What you like in a CEO candidate may not deliver results

Attributes that often get someone hired as CEO may not be the ones that drive success once they are at the helm of the company. That’s one of many provocative insights in a study by consulting firm ghSMART. The study, recently featured in Harvard Business Review, identifies characteristics that differentiate the most effective leaders. Read more →

Paying for online reviews backfires among socially influential

Online user reviews have become an essential tool for consumers who increasingly rely on them to evaluate products and services before purchase. The business models of online review platforms such as Yelp and TripAdvisor and e-commerce sites such as Amazon and Expedia critically depend on them. Should such sites pay users to encourage them to write reviews? Read more →

UPCOMING ANALYTICS EVENTS

INFORMS-SPONSORED EVENTS

CONFERENCES

2017 INFORMS Healthcare Conference
July 26-28, 2017, Rotterdam, the Netherlands

CAP® EXAM SCHEDULE

CAP® Exam computer-based testing sites are available in 700 locations worldwide. Take the exam close to home and on your schedule:


 
For more information, go to 
https://www.certifiedanalytics.org.