The University of Southampton
University of Southampton Institutional Repository

The one-sayers model for the Extended Crosswise design

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
0964-1998
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
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), 882-899. (doi:10.1093/jrsssa/qnae009).

Record type: Article

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.

This record has no associated files available for download.

More information

Accepted/In Press date: 12 January 2024
e-pub ahead of print date: 12 February 2024
Published date: October 2024
Additional Information: 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
ORCID for Peter G.M. van der Heijden: ORCID iD orcid.org/0000-0002-3345-096X

Catalogue record

Date deposited: 07 Jan 2025 22:07
Last modified: 21 Jun 2025 01:48

Export record

Altmetrics

Contributors

Author: Maarten J.L.F. Cruyff
Author: Khadiga H.A. Sayed
Author: Andrea Petróczi

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×