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The one-sayers model for the Extended Crosswise design

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Bibliographic Details
Title: The one-sayers model for the Extended Crosswise design
Authors: Maarten Cruyff, Khadiga H. A. Sayed, Andrea Petróczi, P.G.M. van der Heijden
Source: Journal of the Royal Statistical Society Series A: Statistics in Society. 187:882-899
Publisher Information: Oxford University Press (OUP), 2024.
Publication Year: 2024
Subject Terms: Response bias, Statistics and Probability, Survey Sampling, 05 social sciences, 01 natural sciences, 0504 sociology, Artificial Intelligence, Cheating, Physical Sciences, Multi-label Text Classification in Machine Learning, Computer Science, Doping, FOS: Mathematics, Self-protection, 0101 mathematics, Randomized response, Statistical Methods for Sensitive Survey Questions, Model-Based Clustering with Mixture Models, 10. No inequality, Mathematics
Description: 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.
Document Type: Article
Other literature type
Language: English
ISSN: 1467-985X
0964-1998
DOI: 10.1093/jrsssa/qnae009
DOI: 10.60692/x1wm3-1y891
DOI: 10.60692/wddzh-9t972
Rights: CC BY
Accession Number: edsair.doi.dedup.....253cc8a27e7c77e7c69e8c292738f76e
Database: OpenAIRE
Description
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.
ISSN:1467985X
09641998
DOI:10.1093/jrsssa/qnae009