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A Survey on Illicit Drug Use among University Students by Binary Randomized Response Technique: Crosswise Design

This paper aims to introduce Randomized Response Techniques (RRT’s) and show that how RRT’s are implemented in surveys in which sensitive behaviors are investigated. For this purpose, the most popular designs of the Binary RRT are summarized and an experimental study is conducted on drug use among dormitory students at a public university in Ankara, Turkey. Despite the wide applicability of the drug use studies in Turkey, surprisingly any applications using indirect questioning techniques are not observed in the literature. In this study, for the first time, drug use behavior is investigated with Crosswise design which is the most frequently used indirect questioning technique and indirect questioning method (Crosswise design) is compared with direct questioning method to evaluate the effectiveness of the RRT. Results revealed that when Crosswise design is provided on asking sensitive questions, considerably minor response refusals are happened and significantly higher drug-use estimates are observed.


INTRODUCTION
In natural and social sciences, some research topics are related sensitive behaviors such as mobbing, political view, tax evasion, illegal income Semitism, gambling, alcoholism, drug addiction, doping usage, sexual and physical abuse, homosexual activities, abortion, illegal hunting and many others. In surveys that collect data with direct techniques on sensitive topics, respondents often underreport on sensitive information, even they refuse answering. So, nonresponse on sensitive questions is normally higher than for other questions in a survey. In such surveys, a well-known technique to obtain valid and reliable information on sensitive questions is the Randomized Response Technique (RRT), introduced by [1]. The RRT is an effective indirect questioning technique that ensures privacy and may well succeed respondents' reluctance to express sensitive or probably illicit information. Therefore, respondents are more tend to collaborate and give true answers to sensitive questions. RRTs use a randomization device (a die, a deck of cards or a spinner) efficiently to reduce non-respondents rates resulting from sensitive, embarrassing or even illicit questions. In RRT, with usage of a randomization device, the respondent gives a randomized answer concerning his/her true status. Due to the interviewer is unknowing of the result of the randomization device, the use of these techniques protects the anonymity of answers of respondents. It also appeared that the results of the RRT's become more precise when the topic under investigation is more sensitive [2].
RRTs are sub classified as binary and quantitative RRTs. Binary RRT's are used to estimate the proportion of some sensitive behavior in a population. Quantitative RRTs are used to estimate the mean value of some behavior in a population [3]. In this study, the most popular Binary RRT's will introduce and real applications in literature will be given.
The paper is organized as: In section two, the most popular designs of the Binary RRT that have been proposed in the literature are summarized and reallife examples for each design will be given. Also, in this section, the crosswise design which is one of the most popular design used in recent studies is adapted to the stratified sampling. In section three, empirical studies on drug use in university students in Turkey are summarized. In section four, the application on drug use among dormitory students in a public university is described and the results are given. Section five concludes the paper.

THE MOST POPULAR DESIGNS IN BINARY RRT
In this section, the most popular designs in Binary RRT are summarized and instructions used in these designs are explained. The Binary RRT's will be described together with the equations to compute the population estimates and their variances. In each design, the equations are derived based on a probability distribution. Since the probability of distribution of the randomized design is known, the prevalence of the sensitive characteristic can be estimated on the basis of probability theory. In each design, the fundamental principle to compute prevalence estimate and its variance is establishing a probabilistic relationship between reported answers and unreported true scores [4]. On the other hand, some RRT procedures may confuse respondents and cause refusing answers. Many respondents hesitate that the RRT protects their sensitive behaviors even when they completely understand the instructions [5]. Therefore, for each design, the instructions are described clearly for successful implementation.
The most popular designs in Binary RRT classified into four types: randomization device (dice, coin or cards), whose outcome is unobserved by the interviewer. Let exemplify Warner [1] RRT with an example. For example, to estimate the "proportion of people who tried drug", two statements are written on the cards in a deck. The respondents are asked to answer one of two statements: 1. I tried drug (p). 2. I did not try drug ( 1-p) The respondent randomly picks a card, and simply responds "true" or "not true" to the statement without revealing to the interviewer which statement is selected. The respondent is simply responding to the statement shown on the randomly drawn card (see Figure 1) Elementary probability theory can then be used to get an unbiased estimate  ( ) of the prevalence of drug use in the population. So mathematically, π is the true proportion of the subjects with the sensitive characteristic, and p is the proportion of cards written on them with "I tried drug", (1-p) is the proportion of cards written on them with "I did not try drug". According to the Figure 1, the probability of a "yes" response, λ, is Solving for π, Warner [1] estimator is given as , p . p (2) Here,  is the observed proportion of "yes" answers in the sample:   1 n n (3) Note that the proportions p and 1 − p are known, as are the number of "yes" responses n1 and the sample size n. Hence, we can calculate the estimate values of π and sample variance.
The sample variance of Warner [1] estimator is As an early study of Warner design, Chaloupka [6] used this design to examine the illegal collection of shells in protected Great Barrier Reef in Australia. As a recent example, Gingerich [7] used this design to estimate the effect of a bureaucrat's partisan and electoral ambitions on participation in acts of political corruption in Bolivia, Brazil, and Chile.

Unrelated Question Design
Unrelated question design is developed by Greenberg et al. [9]. Unlike the Warner's design, in this design an unrelated question is used in order to increase respondents' adaptation with survey instructions. Thus, unlike Warner's technique from the previous section, at least some of the respondents would have the reassurance that they answered a wholly unrelated question, resulting in more respondent cooperation than Warner's technique. Under this design, there are two questions which one is sensitive and other one is unrelated, non-sensitive question. The randomization device assigns whether a respondent should answer a sensitive question or an unrelated, non-sensitive question. Let exemplify Greenberg et al. [9] RRT with an example. For example, to estimate the "proportion of people who tried drug". Two questions are written on the cards in a deck. The respondents are requested to answer one of two questions: 1. Have you ever tried drug in your lifetime? (Sensitive question is selected with p probability).

Is your mother born in January?'' (Nonsensitive question is selected with 1-p probability)
The respondent randomly picks a card, and simply responds "yes" or "no" to the question without expressing to the interviewer which question is selected. The respondent is simply responding to the question shown on the randomly drawn card (see Figure 2) Elementary probability theory can then be used to get an unbiased estimate  ( ) of the prevalence of drug use in the population. So mathematically, π is the true proportion of the subjects with the sensitive characteristic, and p is the proportion of cards written on them with sensitive question "Have you ever tried drug in your lifetime?"  u is the known population prevalence of unrelated, non-sensitive characteristic and (1-p) is the proportion of cards written on them non-sensitive question with "Is your mother born in January?". According to the Figure 2, the probability of a "yes" response, λ, is Solving for π, Greenberg et al. [9] estimator is given as Here,  is the observed proportion of "yes" answers in the sample: Note that the proportions p and 1 − p are known, as are the number of "yes" responses n1 and the sample size n and the prevalence of population of unrelated question. Hence variance of  is calculated under known parameters.
The sample variance of Greenberg et al. [9] estimator is For example, Lara et al. [10] applied the unrelated question design to study abortion rates in Mexico.
The instructions used in this study: Here is a folder, one colored red and the other green. The red folder contained a sheet of paper with a red dot and the following question: ''Did you ever interrupt a pregnancy?'' The words "yes" and "no" were printed below the question.
The green folder contained a sheet of paper with a green dot and the following question: ''Were you born in April?'' Again, the words "yes" and "no" were printed below. Then, fold the sheets of paper into the same shape, so that it is impossible to identify one from the other, and to place them in an opaque bag. Now, I shake the bag, please reach inside and select one folded sheet of paper and say your answer, either yes or no.
Here, the interviewer does not know which question the respondent had chosen and was answering. The respondent would then say her/his answer out loud, either yes or no. The interviewer then recorded the respondent's response.  (2), 377-388, 2020 As a recent example, Chen et al. [11] applied this design in the survey of issues relevant to commercial sex among men who have sex with men (MSM) in Beijing, China. Other applications of the unrelated question include abortion in Turkey [12], a criminology study of self-reported arrests in Philadelphia [13].

Forced Response Design
Forced response design is developed by Boruch [14]. Under Boruch design, randomization device assigns whether a respondent truthfully answers the sensitive question or simply replies with an automatic (forced) answer, `yes'or `no" response regardless of the true answer to the sensitive question. The result of the randomizing device is known only to the respondent, not to the interviewers. In Boruch [14] design, each respondent's answer provided with a randomization device, such as a die or a deck of cards. There are three statements in this design: (i) report "yes" (ii) report "no", (iii) report the true answer of the sensitive variable, say "yes" or "no" with proportion p1, p2 and p3 respectively.
So mathematically, π is the true proportion of the subjects with the sensitive characteristic, and p1 is the proportion of "yes" reports, p2 is the proportion of "no" reports and p3 is the proportion of cards written on them with sensitive question "Have you ever tried drug in your lifetime?". According to the Figure 3, the probability of a "yes" response, λ, is Solving for π, Boruch [14] estimator is given as Here,  is the observed proportion of "yes" answers in the sample: Note that the proportions p1 and p2 are known, as are the number of "yes" responses n1 and the sample size n. Hence variance of  is calculated under known parameters.
The sample variance of Boruch [14]  For example, a study of xenophobia and anti-Semitism in Germany [15]. Krumpal [15] used coin flip method for this design.
The instructions are reproduced here, "Now we would like to know your personal opinion on different segments of the population. One of these segments is foreigners living in Germany. We are aware of the fact that many people are very hesitant about giving their personal opinion on topics like this because they are very private. With this in mind, the University of Leipzig has developed a novel question technique that guarantees your privacy and makes the interview more comfortable.
When answering the following questions, you can keep your personal opinion secret by flipping a coin. This might sound a bit unusual, however, I would like to ask you to help us and try out this -If you flip tails 3 times, please always answer "yes".
-If you flip heads 3 times, please always answer "no".
-If you flip a combination of heads and tails, for example tails 2 times and heads 1 time, please always tell your true personal opinion.
As you can see, coincidence will decide whether you answer the question truthfully or whether you give a predetermined answer. This way your privacy will always be protected. I will not know the result of your coin flip and therefore I will never know why your answer is "yes" or "no". Did you understand the coin-flip method? (…) Sometimes you will answer "yes" or "no" due to the result of your coin flip, even though this is not your real personal opinion. Please do not worry about that. You are doing the right thing if you follow the rules of the coin-flip method and always answer according to the result of the coin-flip.
I will now read out aloud some statements to you which you might have heard at some point before. Please tell me each time, according to your coin flip, whether or not you would somewhat agree with the statement. We will now start with the first statement. (…) Please flip your three coins now without telling me the result. According to your coin flip, would you somewhat agree with the following statement? "There are too many foreigners in Germany" (...)." This design is popular among applied researchers and there are numerous examples.
A study of fabrication in job applications [16], social security fraud in Netherland [17], use of performance enhancing drugs [18] and vote choice regarding a Mississippi abortion referendum [19].

Crosswise Design
Crosswise design (CD) is developed by Yu et al. [20]. This design is like unrelated question design. In this design, the sensitive question is asked together with a non-sensitive question that has a known population distribution (such as whether one's mother's birthday occurs in certain months). In this design, respondents are requested to give a joint answer to two questions rather than responding directly to the sensitive questions. The respondents are asked to indicate only whether their answers to two questions are the same (both "yes" and both "no") or different (one answer is "yes" and the other answer is "no"). In this design, the probability distribution of the non-sensitive question should be known and unequal to 0.5 for prevalence estimation of sensitive characteristic. In addition to this, provided that the answer to the unrelated question is unknown, the respondent's answer to the sensitive question remains confidential. The respondents could easily understand that the crosswise design protects their privacy because the interviewer is unaware of the possible answers, "the same" or "different". Furthermore no one is forced to give a "yes" or "no" answer.
So mathematically, π is the true proportion of the subjects with the sensitive characteristic, and p is the known population prevalence of non-sensitive question. According to the Figure 4, the probability of a "same" response, λs, is Solving for π, Yu et.al. [20] Crosswise design estimator is given as . p (12) Here, ˆs is the observed proportion of "same" answers in the sample.  (13) Note that the crosswise design is formally equal to the Warner [1] original design. However, it follows a different logic than the Warner's design.
In crosswise design, the respondents have to answer two questions simultaneously and they don't have to give directly "yes" or "no" answer. Recent studies have pointed out that the CD successfully reduces under-reporting of socially undesirable behavior. This design is also popular among applied researchers and there are numerous examples, recently. [21] conducted CD between Swiss and Germany university students to estimate plagiarism prevalence. [22] conducted a study to investigate drug use prevalence, especially anabolic steroids, among bodybuilding athletes in Iran. [23] implemented CD to estimate prevalence of illicit drug use among the students of Tehran University of Medical Sciences. [24] used this design to investigate illicit drug use prevalence among students studying at Universities in Shahroud (Northeast of Iran). Other CD studies are summarized as, tax evasion [25], sexual behavior [26], attitudes towards Muslims [27], organ donation [28].

Stratified Crosswise design
In this section, crosswise design is suggested in stratified sampling. Let the population be divided into L non-overlapping homogeneous strata with Nh units in the h th stratum and nh be the number of units drawn by SRSWR from the h th stratum. is the stratum weight. An individual respondent in the sample from h th stratum is instructed to report a joint answer to two questions. the probability of a "same" response in h. stratum λsh, is Solving for πh, crosswise design estimator in h. stratum is Crosswise design estimator in stratified sampling is given as 1,2,..., (16) The sample variance of crosswise design estimator in stratified sampling is Here, ˆs h is the observed proportion of "same" answers in the h. stratum, ph is the known population prevalence of non-sensitive question in h.stratum.

DRUG USE IN UNIVERSITY STUDENTS IN TURKEY
Empirical studies on university students in Turkey are based on direct questioning about socially undesirable behavior such as drug use. Altındağ et al. [29] investigated the prevalence of illicit drug, smoking and alcohol use in fist year students of Harran University (n=253) and lifetime illicit drug use prevalence was identified as 2.3%. Akvardar et al. [30] investigated the prevalence of illicit drug, smoking and alcohol use in medical students from three different medical schools in Turkey (n=447) and they found that 4% of the students reported using illicit drugs (cannabis, ecstasy, cocaine) at least once in their lifetime. Mayda [31] studied to determine the prevalence of substance, cigarette, alcohol use in students of Forestry Faculty of Düzce University (n=398) and he found that the substance use among students is 9.3%. Turhan et al. [32] made a cross-sectional study in students of Mustafa Kemal University (n=396) and lifetime illicit drug use were identified as 9.6%. Ulukoca et al. [33] researched the prevalence of cigarette, alcohol, and substance use among the students of Kırklareli University (n=902) and 10.4% of students had tried using substances at least once in their life, with marijuana (4.1%) and solvents (3.2%) reported as the substances most commonly tried. Yüncü and Atlam [34] evaluated the relationship between cigarette, alcohol, substance experience among gender, faculty, class, living environment, substance use of families among students of Ege university (n=1522). 13.4% of students had tried using substances at least once in their life with cannabis (12.5%), ecstasy (MDMA) (2%), cocaine (0.6%) and heroin (0.1%) were mostly used illegal drugs. They found that the illicit drug use prevalence is significantly different among men (22.2%) a women student (7.6%). Türk and Yavuz [35] investigated the meaning of penal sanctions with regards to substance use on students from different universities in Turkey (n=227). In the study, the students reported they used the below substances at least once; 17.9% marijuana, 3.4% heroine, 4.5% cocaine, 2.6% LSD, 4.5% ecstasy, 3% bonsai. The current study on drug use was carried on by Coşkun et al. [36]. They determined the change on alcohol and drug use among the first and last year university students of Gaziantep University (n=2217) and they found that 8.6% of the men and 2.1% of the women had used drug at least once. 8.3% of the last year students had used drug at least once while 4.6% of the first-year students had used drug at least once.

APPLICATION
This study aims to introduce binary RRTs and show the real application of RRTs in Turkey. By this aim, a RRT application is carried out in Ankara, Turkey. The survey's target population included the dormitory students at a public university in Ankara, Turkey. First of all, a pretest (n= 60) was conducted to students in order to with which binary RRT, they would feel safe and comfortable. The binary RRTs which are introduced in section 2 were presented to the students with instructions. After the presentation, the students were asked "which RRT design do you feel safe and comfortable for answering your sensitive behaviors?". Most of the students (%78) reported that they would be more confident when Crosswise design (CD) is conducted. After pretest result, crosswise design was implemented to estimate illicit drug use prevalence. To evaluate crosswise design (CD) ensures better estimates of illicit drug use than direct questioning (DQ) method, two different questionnaires: a directquestioning version and a CD version were conducted on dormitory students. The private dormitory has 1980 students. Students were selected using stratified random sampling method. The survey is conducted with 712 students with 0.03 margin of error. The sample is consisting of %46 women and %54 men.
Students were randomly selected using a ratio of 3 for the CD (n=534) to 1 for DQ (n=178). For both techniques, the students were selected with stratified random sampling method which has two stratum and the stratum is gender.
Due to the sensitive research topic, for both conditions, the students were all informed about the aims of the study.
In the 'direct questioning' technique, a confidentiality assurance was read out loud to the respondent. " We are aware of the fact that many people are very hesitant about revealing their sensitive behaviors because they are very private. With this in mind, we would like to assure you that all answers given will be kept confidential and will not be passed on to anyone else. I will now read aloud a question to you. Please answer the question by simply telling us 'Yes' and 'No'. Now, I read the question. "Have you ever tried illicit drug in your lifetime?" The instructions used in the CD technique: We are aware of the fact that many people are very hesitant about revealing their sensitive behaviors because they are very private. With this in mind to ensure the protection of your personal rights, we will use an indirect questioning technique that guarantees that your answers will be totally anonymous.
Therefore, you will not be requested to answer any question directly, but rather, you will be asked" two questions at the same time by simply telling us whether the answers to the questions are (a) the same or (b) different.
The questions:

CONCLUSION
This study introduces the Binary RRTs and shows the real application of a RRT design in Turkey.

Nilgün Özgül
A Survey on Illicit Drug Use among University Students by Binary Randomized Response Technique: Cross... The randomizing procedure is crucial for the success of the RRT, as it shows the answers of the respondents are protected by probability theory. In this study, Crosswise design is preferred in estimation of the prevalence of illicit drug use. It has seen that crosswise design provides more secure for respondents and easier to apply to the other designs. The present study compared indirect and direct questioning techniques in estimating illicit drug use and with crosswise design, considerably minor response refusals are obtained and significantly higher drug-use estimates are observed by gaining more privacy in the data collection process. So, it can be concluded that Crosswise design gives the most efficient statistical estimation compared to alternative RRT designs. Moreover, the present research will provide to extend the recognition of the RRTs in sensitive surveys and encourage researchers to study on sensitive topics in Turkey. Future studies can be extended for analyzing all sociodemographic characteristic of the students and can be replicated for all university students in Turkey.