The one-sayers model for the Extended Crosswise design
The one-sayers model for the Extended Crosswise design
The Extended Crosswise design is a randomized response design characterized by a sensitive and an innocuous question and two sub-samples with complementary randomization probabilities of the innocuous question. The response categories are ‘One’ with two different answers and ‘Two’ with two answers that are the same. Due to the complementary randomization probabilities, ‘One’ is the incriminating response in one sub-sample, and ‘Two’ in the other. The use of two sub-samples generates a degree of freedom to test for response biases with a goodness-of-fit test, but this test is unable to detect bias resulting from self-protective respondents giving the non-incriminating response when the incriminating response was required. This raises the question what a significant goodness-of-fit test measures? In this paper, we hypothesize that respondents are largely unaware which response is associated with the sensitive characteristic, and intuitively perceive ‘One’ as the safer response. We present empirical evidence for one-saying in six surveys among a total of 4, 242 elite athletes, and present estimates of doping use corrected for it. Furthermore, logistic regression analyses are conducted to test the hypothesis that respondents who complete the survey in a short time are more likely to answer randomly, and therefore are less likely to be one-sayers.
cheating, doping, randomized response, response bias, self-protection
882-899
Cruyff, Maarten J.L.F.
7efbafcd-7831-48b4-bbea-9d95709b1235
Sayed, Khadiga H.A.
9f0ba98e-f5a6-41c1-8e29-9ef779803ff9
Petróczi, Andrea
8511a554-694d-45bc-9248-1ec7fcd63e34
van der Heijden, Peter G.M.
85157917-3b33-4683-81be-713f987fd612
October 2024
Cruyff, Maarten J.L.F.
7efbafcd-7831-48b4-bbea-9d95709b1235
Sayed, Khadiga H.A.
9f0ba98e-f5a6-41c1-8e29-9ef779803ff9
Petróczi, Andrea
8511a554-694d-45bc-9248-1ec7fcd63e34
van der Heijden, Peter G.M.
85157917-3b33-4683-81be-713f987fd612
Cruyff, Maarten J.L.F., Sayed, Khadiga H.A., Petróczi, Andrea and van der Heijden, Peter G.M.
(2024)
The one-sayers model for the Extended Crosswise design.
Journal of the Royal Statistical Society. Series A: Statistics in Society, 187 (4), .
(doi:10.1093/jrsssa/qnae009).
Abstract
The Extended Crosswise design is a randomized response design characterized by a sensitive and an innocuous question and two sub-samples with complementary randomization probabilities of the innocuous question. The response categories are ‘One’ with two different answers and ‘Two’ with two answers that are the same. Due to the complementary randomization probabilities, ‘One’ is the incriminating response in one sub-sample, and ‘Two’ in the other. The use of two sub-samples generates a degree of freedom to test for response biases with a goodness-of-fit test, but this test is unable to detect bias resulting from self-protective respondents giving the non-incriminating response when the incriminating response was required. This raises the question what a significant goodness-of-fit test measures? In this paper, we hypothesize that respondents are largely unaware which response is associated with the sensitive characteristic, and intuitively perceive ‘One’ as the safer response. We present empirical evidence for one-saying in six surveys among a total of 4, 242 elite athletes, and present estimates of doping use corrected for it. Furthermore, logistic regression analyses are conducted to test the hypothesis that respondents who complete the survey in a short time are more likely to answer randomly, and therefore are less likely to be one-sayers.
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More information
Accepted/In Press date: 12 January 2024
e-pub ahead of print date: 12 February 2024
Published date: October 2024
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Publisher Copyright:
© The Royal Statistical Society 2024.
Keywords:
cheating, doping, randomized response, response bias, self-protection
Identifiers
Local EPrints ID: 496717
URI: http://eprints.soton.ac.uk/id/eprint/496717
ISSN: 0964-1998
PURE UUID: a12cfd87-69a7-4cdf-b18f-7827705f6c08
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Date deposited: 07 Jan 2025 22:07
Last modified: 21 Jun 2025 01:48
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Contributors
Author:
Maarten J.L.F. Cruyff
Author:
Khadiga H.A. Sayed
Author:
Andrea Petróczi
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