Applying the Randomized Response Technique in Business Ethics Research: The Misuse of Information Systems Resources in the Workplace

Abstract

Mitigating response distortion in answers to sensitive questions is an important issue for business ethics researchers. Sensitive questions may be asked in surveys related to business ethics, and respondents may intend to avoid exposing sensitive aspects of their character by answering such questions dishonestly, resulting in response distortion. Previous studies have provided evidence that a surveying procedure called the randomized response technique (RRT) is useful for mitigating such distortion. However, previous studies have mainly applied the RRT to individual dichotomous questions (e.g., yes/no questions) in face-to-face survey settings. In this study, we focus on behavioral research examining the relationships between latent variables, which are unobserved variables measured by multiple items on Likert or bipolar scales. To demonstrate how the RRT can be applied to obtain valid answers from respondents answering a self-administered online questionnaire with Likert and bipolar scales, we build a behavioral model to study the effect of punishment severity on employees’ attitudes toward misuse of information systems resources in the workplace, which in turn influence misuse behavior. The survey findings meet our expectations. The respondents are generally more willing to disclose sensitive data about their attitudes and actual behavior related to misuse when the RRT is implemented. The RRT’s implications for causal modeling and the advantages and challenges of its use in online environments are also discussed.

Appendices

Appendix 1: An Example of the First Version of the RRT (with a 0.25 Probability of Answering the Sensitive Question)

Appendix 2

See Table 3.

Table 3 Literature review of empirical studies on unethical behavior in IS in the workplace

Appendix 3: Sample Formats of the Three Questionnaire Versions in the Current Study

Appendix 4: Technical Notes on the Implementation and Computation Involved in UQD in Our Study

• (i) Estimating the mean population response to a sensitive question under UQD

Suppose we are interested in the mean frequency of employees to install untrusted applications for personal purposes at work. This question is sensitive and respondents may not be willing to disclose honest answers. UQD is designed to reduce this type of bias. In UQD, the respondent is presented with two questions:

Question X: Installing untrusted applications for personal purposes at work, and

Question Y: Having dinner at home,

So that Questions X and Y are unrelated. Then, the respondent is asked to generate an outcome from a randomization device to determine which question (X or Y) he/she will answer, on a 7-point Likert scale (1 = never … 7 = very many times), without disclosing which question he/she actually answers. In this setting, the interviewer does not know which question the respondent answers, and hence the response to the sensitive question is hidden.

Define X and Y as the responses of a respondent to Questions X and Y, respectively, and Z as the observed response obtained from the randomization procedure. Let $\mu_{X}$, $\mu_{Y}$ and $\mu_{Z}$ be the population mean values of X, Y and Z, respectively, and let p be the probability that the respondent will answer Question X. Using the tree diagram in Fig. 4 to illustrate the randomization procedure, the mean response obtained from the randomization procedure, $\mu_{Z}$, can be derived as

$$ \mu_{Z} = p \mu_{X} + (1 - p)\mu_{Y} . $$

(1)

Fig. 4

Tree diagram of the randomization procedure for a single-randomized response

The whole sample is divided into two subsamples: Samples 1 and 2. They are assigned different probabilities of answering Question X. The probabilities for Samples 1 and 2 are denoted by $p_{\left( 1 \right)}$ and $p_{\left( 2 \right)}$, respectively. Thus, once the sample mean of the randomized response Z within Sample k (k = 1, 2), denoted by $\bar{Z}_{(k)}$, is available, we can replace p and $\mu_{Z}$ in Eq. (1) with $p_{\left( k \right)}$ and $\bar{Z}_{(k)}$, respectively. Then, the following simultaneous equations can be obtained

$$ \left\{ { \begin{array}{*{20}c} {\bar{Z}_{\left( 1 \right)} = p_{(1)} \hat{\mu }_{X} + (1 - p_{\left( 1 \right)} )\hat{\mu }_{Y} } \\ {\bar{Z}_{\left( 2 \right)} = p_{(2)} \hat{\mu }_{X} + \left( {1 - p_{\left( 2 \right)} } \right)\hat{\mu }_{Y} } \\ \end{array} } \right. , $$

where $\hat{\mu }_{X}$ and $\hat{\mu }_{Y}$, denoting the estimates of $\mu_{X}$ and $\mu_{Y}$, are unknowns in the above two equations. Provided that $p_{\left( 1 \right)} \ne p_{\left( 2 \right)}$, we can solve the two equations and get $\hat{\mu }_{X} = \frac{{\left( {1 - p_{\left( 2 \right)} } \right)\bar{Z}_{\left( 1 \right)} - \left( {1 - p_{\left( 1 \right)} } \right)\bar{Z}_{\left( 2 \right)} }}{{p_{\left( 1 \right)} - p_{\left( 2 \right)} }}$ and $\hat{\mu }_{Y} = \frac{{p_{\left( 1 \right)} \bar{Z}_{\left( 2 \right)} - p_{\left( 2 \right)} \bar{Z}_{\left( 1 \right)} }}{{p_{\left( 1 \right)} - p_{\left( 2 \right)} }}$. Note that the whole estimation involves only the sample mean of the randomized responses, $\bar{Z}_{\left( 1 \right)}$ and $\bar{Z}_{\left( 2 \right)}$, and that the responses of individual respondents to Question X are kept confidential throughout the estimation. Take the result of our survey as an example. The mean randomized responses from Samples 1 and 2 ($\bar{Z}_{\left( 1 \right)}$ and $\bar{Z}_{\left( 2 \right)}$) are equal to 4.200 and 3.733, respectively. $p_{\left( 1 \right)}$ is set to 1/3 while $p_{\left( 2 \right)}$ is set to 2/3 in our survey. Using the formula above, the estimated population mean of X, $\hat{\mu }_{X}$, is equal to 3.266.

• (ii) Estimating the covariance matrix of responses to both sensitive and direct questions under UQD

In this section, we discuss three cases on how to estimate (a) the variance of a sensitive response, (b) the covariance of two sensitive responses, and (c) the covariance of a sensitive response and a direct response. The full covariance matrix of responses to both sensitive and direct questions can be estimated provided that the estimates of the above variance/covariance terms are available.

• (a) Variance of a sensitive response

As in part (i), the respondent is presented with two questions:

Question X₁: Installing untrusted applications for personal purposes at work, and

Question Y₁: Having dinner at home.

Then, he/she is asked to respond to either one of them based on a 7-point Likert scale (1 = never … 7 = very many times) according to an outcome from a randomization device which assigns the respondent with probability p to answer Question X₁. Let X₁ and Y₁ be the response of the respondent to Questions X₁ and Y₁, respectively. Let Z₁ be the response obtained from the randomization procedure. In addition, let $\sigma_{X11}$, $\sigma_{Y11}$ and $\sigma_{Z11}$ be the variances of X₁, Y₁, and Z₁, respectively. Without loss of generality, assume that the means of X₁, Y₁, and Z₁ are all 0. As such, $\sigma_{X11}$, $\sigma_{Y11}$ and $\sigma_{Z11}$ are equal to the means of the square of X₁, Y₁, and Z₁ or, in mathematical notation, $E\left[ {X_{1}^{2} } \right]$,$E\left[ {Y_{1}^{2} } \right]$ and $E\left[ {Z_{1}^{2} } \right]$, respectively. Thus, the rationale of deriving Eq. (1) is still applicable, and we can simply replace $\mu_{X}$, $\mu_{Y}$ and $\mu_{Z}$ with $\sigma_{X11}$, $\sigma_{Y11}$ and $\sigma_{Z11}$, respectively, to obtain

$$ \sigma_{Z11} = p \sigma_{X11} + \left( {1 - p} \right)\sigma_{Y11} . $$

Following part (i), the whole sample is divided into two subsamples: Samples 1 and 2. They are then assigned different probabilities of responding to Question X₁, denoted by $p_{\left( 1 \right)}$ and $p_{\left( 2 \right)}$, respectively. Provided that the sample means of $Z_{1}^{2}$ in both Samples 1 and 2, denoted by $\bar{Z}_{1\left( 1 \right)}^{2}$ and $\bar{Z}_{1\left( 2 \right)}^{2}$, respectively, are available, we can replace $\sigma_{Z11}$ with $\bar{Z}_{1\left( k \right)}^{2}$ and $p$ with $p_{\left( k \right)}$, respectively (k = 1, 2) to obtain

$$ \left\{ { \begin{array}{*{20}c} {\bar{Z}_{1\left( 1 \right)}^{2} = p_{(1)} \hat{\sigma }_{X11} + (1 - p_{\left( 1 \right)} )\hat{\sigma }_{Y11} } \\ {\bar{Z}_{1\left( 2 \right)}^{2} = p_{(2)} \hat{\sigma }_{X11} + \left( {1 - p_{\left( 2 \right)} } \right)\hat{\sigma }_{Y11} } \\ \end{array} } \right. , $$

where $\hat{\sigma }_{X11}$ and $\hat{\sigma }_{Y11}$ are the estimates of $\sigma_{X11}$ and $\sigma_{Y11}$, respectively. Solving the above two equations, we obtain $\hat{\sigma }_{X11} = \frac{{\left( {1 - p_{\left( 2 \right)} } \right)\bar{Z}_{1\left( 1 \right)}^{2} - \left( {1 - p_{\left( 1 \right)} } \right)\bar{Z}_{1\left( 2 \right)}^{2} }}{{p_{\left( 1 \right)} - p_{\left( 2 \right)} }}$ and $\hat{\sigma }_{Y11} = \frac{{p_{\left( 1 \right)} \bar{Z}_{1\left( 2 \right)}^{2} - p_{\left( 2 \right)} \bar{Z}_{1\left( 1 \right)}^{2} }}{{p_{\left( 1 \right)} - p_{\left( 2 \right)} }}$. Again, the whole estimation involves only the sample mean of the squared randomized responses $\bar{Z}_{1\left( 1 \right)}^{2}$ and $\bar{Z}_{1\left( 2 \right)}^{2}$. The responses of individual respondents to Question X₁ are kept confidential and unknown to interviewers.

• (b) Covariance of two sensitive responses

In addition to Questions X₁ and Y₁ in case (a), we introduce another pair of unrelated sensitive and non-sensitive questions:

Question X₂: Using untrusted network (e.g., Internet) for data transmission at work, and

Question Y₂: Taking public transportation.

Under UQD, Questions X₂ and Y₂ are shown simultaneously to the respondent, and he/she is asked to respond to either one of them on a 7-point Likert scale (1 = never … 7 = very many times) according to an outcome from a randomization device which assigns the respondent with probability p to answer Question X₂. The responses to Questions X₂ and Y₂ are denoted by X₂ and Y₂, respectively, and the response collected under the randomization procedure is denoted by Z₂. In this case, we would like to estimate the covariance of X₁ and X₂, i.e., the covariance of two sensitive responses.

Define $\sigma_{X12}$, $\sigma_{Y12}$, $\sigma_{X1Y2}$, $\sigma_{X2Y1}$ and $\sigma_{Z12}$ as the covariance of X₁ and X₂, Y₁ and Y₂, X₁ and Y₂, X₂ and Y₁, and Z₁ and Z₂, respectively. Without loss of generality, assume that the means of X₁, Y₁, X₂, Y₂, Z₁, and Z₂ are all zero. Under this assumption, the covariance of any pair of those variables is equal to the mean of their product. In other words, $\sigma_{X12} = E[X_{1} X_{2} ]$, $\sigma_{Y12} = E[Y_{1} Y_{2} ]$, $\sigma_{X1Y2} = E[X_{1} Y_{2} ]$, $\sigma_{X2Y1} = E[X_{2} Y_{1} ]$ and $\sigma_{Z12} = E[Z_{1} Z_{2} ]$. Moreover, as Questions X₁ and X₂ are unrelated to Questions Y₁ and Y₂, we can further impose an assumption that $\sigma_{X1Y2}$ and $\sigma_{X2Y1}$ are equal to 0. Thus, based on the tree diagram shown in Fig. 5a, we can derive the following equation

$$ \begin{array}{*{20}c} {\sigma_{Z12} = p^{2} \sigma_{X12} + p \left( {1 - p} \right)\sigma_{X1Y2} + \left( {1 - p} \right)p \sigma_{X2Y1} + \left( {1 - p} \right)^{2} \sigma_{Y12} } \\ { = p^{2} \sigma_{X12} + \left( {1 - p} \right)^{2} \sigma_{Y12} . } \\ \end{array} $$

Fig. 5

Tree diagram of the randomization procedure for multiple randomized response

Similar to the process in part (i) and case (a), we divide the whole sample into two subsamples and assign them with different probability, $p_{\left( 1 \right)}$ and $p_{\left( 2 \right)}$, to respond to the sensitive questions. In this way, we can derive that $\sigma_{X12}$ and $\sigma_{Y12}$ can be estimated by $\hat{\sigma }_{X12} = \frac{{\left( {1 - p_{\left( 2 \right)} } \right)^{2} \bar{Z}_{12\left( 1 \right)} - \left( {1 - p_{\left( 1 \right)} } \right)^{2} \bar{Z}_{12\left( 2 \right)} }}{{\left( {p_{\left( 1 \right)} + p_{\left( 2 \right)} - 2p_{\left( 1 \right)} p_{\left( 2 \right)} } \right) (p_{\left( 1 \right)} - p_{\left( 2 \right)} )}}$ and $\hat{\sigma }_{Y12} = \frac{{p_{\left( 1 \right)}^{2} \bar{Z}_{12\left( 2 \right)} - p_{\left( 2 \right)}^{2} \bar{Z}_{12\left( 1 \right)} }}{{\left( {p_{\left( 1 \right)} + p_{\left( 2 \right)} - 2p_{\left( 1 \right)} p_{\left( 2 \right)} } \right) (p_{\left( 1 \right)} - p_{\left( 2 \right)} )}}$, respectively, by formulating the following two simultaneous equations as in estimating the variance of a sensitive response,

$$ \left\{ { \begin{array}{*{20}c} {\bar{Z}_{12\left( 1 \right)}^{{}} = p_{(1)}^{2} \hat{\sigma }_{X12} + (1 - p_{\left( 1 \right)} )^{2} \hat{\sigma }_{Y12} } \\ {\bar{Z}_{12\left( 2 \right)}^{{}} = p_{(2)}^{2} \hat{\sigma }_{X12} + \left( {1 - p_{\left( 2 \right)} } \right)^{2} \hat{\sigma }_{Y12} } \\ \end{array} } \right. , $$

where $\bar{Z}_{12\left( 1 \right)}$ and $\bar{Z}_{12\left( 2 \right)}$ are the sample means of Z₁Z₂ in Samples 1 and 2, respectively. Take the result of our survey as an example. The sample mean products of randomized responses Z₁Z₂ in Samples 1 and 2 (after being subtracted by the mean), $\bar{Z}_{12\left( 1 \right)}$ and $\bar{Z}_{12\left( 2 \right)}$, are equal to 0.315 and 0.640, respectively. Hence, the formula above implies that the estimated covariance of X₁ and X₂, $\hat{\sigma }_{X12}$, is equal to 1.346. The responses of individual respondents to Questions X₁ and X₂ are kept confidential throughout the estimation.

• (c) Covariance of a sensitive response and a direct response

In addition to the pair of sensitive and non-sensitive questions, Questions X₁ and Y₁, in case (a), we consider an additional direct question

Question D: I would probably be caught eventually, after engaging in IS resource misuse.

The respondent is just asked to directly answer the question on a 7-point Likert scale (1 = strongly disagree … 7 = strongly agree), instead of going through the randomization procedure. Let D be the response to Question D. What we are interested is the covariance of X₁ and D, which is the covariance of a sensitive response and a direct response. Recall that Z₁ is the randomized response corresponding to Questions X₁ and Y₁. Let $\sigma_{X1D}$, $\sigma_{Y1D}$ and $\sigma_{Z1D}$ be the covariances of X₁ and D, Y₁ and D, and Z₁ and D, respectively. Without loss of generality, assume that the population means of X₁, Y₁, Z₁, and D are 0. Again, under this assumption, $\sigma_{X1D} = E[X_{1} D]$, $\sigma_{Y1D} = E[Y_{1} D]$ and $\sigma_{Z1D} = E[Z_{1} D]$. Moreover, as Question Y₁ and Question D are unrelated, we can further assume that $\sigma_{Y1D} = 0$. Based on the tree diagram shown in Fig. 5b, we derive that

$$ \sigma_{Z1D} = p \sigma_{X1D} + \left( {1 - p} \right)\sigma_{Y1D} = p \sigma_{X1D} . $$

Using two samples under UQD and going through the sample process mentioned in cases (a) and (b), we can derive that the estimate of $\sigma_{X1D}$ given by $\hat{\sigma }_{X1D} = \frac{{\overline{{Z_{1} D}}_{\left( 1 \right)} + \overline{{Z_{2} D}}_{\left( 2 \right)} }}{{p_{\left( 1 \right)} + p_{\left( 2 \right)} }}$, where $\overline{{Z_{1} D}}_{\left( 1 \right)}$ and $\overline{{Z_{1} D}}_{\left( 2 \right)}$ are the sample mean of Z₁D in Samples 1 and 2.

Remarks

If the means of the variables are not 0, we can subtract each entry of the data by the corresponding sample mean, so that the method introduced above is still applicable.

Moreover, the estimation method introduced above provides a way to estimate the variance of a sensitive response, the covariance of two sensitive responses and the covariance of a sensitive response and a direct response. Thus, we can estimate the full covariance matrix of all of the sensitive and direct responses. The estimated covariance matrix can then be inputted into statistical software like SPSS Amos, to obtain the estimated paths of the designed SEM.

Appendix 5: R Code to Compute the Estimated Mean and Covariance of the Randomized Data Under the UQD Framework

Dat1:

The data matrix of Sample 1, with row representing an observation and column representing an attribute (the columns of all attributes under direct questioning should be on the left of those under randomized questioning)

Dat2:

The data matrix of Sample 2, with row representing an observation and column representing an attribute (the order of attributes in Dat2 is required to be the same as that in Dat1)

p1:

The probability for respondent in Sample 1 to answer a sensitive question

p2:

The probability for respondent in Sample 2 to answer a sensitive question

ns:

Number of direct questions

nz:

Number of randomized questions