Crosswise model

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The Crosswise model is a type of question in the social sciences that tries to reduce bias on sensitive topics in surveys . In a symmetrical list of two statements, the question is asked whether none or both (as answer option A) of the statements apply or only one (option B). In individual cases, it is no longer possible to determine which of the questions, if any, received an affirmative answer. The Crosswise model is thus related to earlier methods that attempt to inquire into sensitive topics without assigning a meaning.

The main difference to other techniques is that anonymity can be created credibly. There are also no evasive or safe answer options (self-protective no answers), since each of the two answer options contains the sensitive element. The main point of criticism of the randomized response technique , which has the same objective, can therefore be eliminated here. The non-response (item nonresponse), the distorted statement because of social desirability or the complete refusal because of the sensitive survey can therefore be countered with the Crosswise model.

history

With methods such as lie detectors or the Bogus pipeline technique , with the help of an alleged machine in direct questioning situations, people can more often admit behavior that violates norms. With this ethically not unobjectionable method, it can be foreseen that the validity of the method will decrease or that the social expectations will be replaced by other answer errors . In addition, use in larger surveys (e.g. online surveys or telephone opinion polls) is excluded; anonymity cannot be guaranteed, which is why a low and not random willingness to participate can be expected. Another disadvantage is that in the case of extreme questions (about illegal behavior, for example), numerous interruptions can be foreseen even in a personal interview (or in the experimental design).

In the Crosswise method, an answer combination is recorded with an additional, non-sensitive question, the probability of which, however, is known. In this way, statistical conclusions (averaged over the observations) can be made about the proportion of the sample that has the sensitive feature sought: anonymity is retained in the individual case. This addition of a so-to-speak systematic noise (see also differential privacy ) in the context of the methods of the social sciences was first used in Warner's randomized response model , published in 1965 . The triangular method , from which the Crosswise model is derived (Yu, Tian and Tang 2008), is stochastically a modification of the same randomization as can be found in Warner and related models such as the item count technique . From an empirical point of view, the first findings are better for the Crosswise technique than for similar methods that have been in use for much longer.

Procedure

The aim of the survey is to collect correct values ​​for the proportion of people from a sample who display problematic behavior or behavior associated with social expectations , even for sensitive questions . The question type creates a credible and actual anonymity: Interviewers cannot with certainty assign or trace back the sensitive behavior to respondents. It is important that a known probability is used that the non-sensitive (or non-embarrassing) question applies (e.g. leap year as year of birth or certain months of birth of the respondents ). The proportional value can then be identified from the observed marginal distributions - provided the questions chosen do not correlate.

example

100 people are interviewed. A non-sensitive question is asked whether the grandmother's year of birth was a leap year (e.g. 1952 is a leap year, 1950 is not, 1948 is yes, etc.). The probability that affirmative statements are made here is 0.25. It is also asked whether taxes were deliberately evaded in the last 10 years. The answer should be identified according to the following combinations:

Answer A if neither or both apply

Answer B, if only one applies (it doesn't matter which one)

Only A or B should be given, the answers to the individual questions are not requested.

evaluation

72 people gave answer A, i.e. a percentage of 0.72. The sought-after proportion of tax evaders is calculated from û = (0.72 + 0.25 - 1) / (2 * 0.25 - 1) = -0.03 / -0.5 = 0.06 = 6%

Mind you: From the marginal distributions of the questions and thus the known distribution (¼ or 25%) it results that cross-over in the 2x2 contingency table of the answer combinations even if it is exactly 0% resp. 100% tax avoidance would exist in the sample, answer A would only give 75% or a minimum of 25% (with sufficiently large samples, see approximation ). If this is not the case, the calculation would result in negative probabilities (or greater than 1), which indicates an error in the answer, particularly to the question about the year.

criticism

As with most anonymization methods that work with special questioning techniques, it is only possible to carry out real validations of the method at considerable expense (which is probably why the randomized response technique (RRT) is not widely used, apart from special studies) . Often reference is therefore made to comparative studies that compare the methods with one another or in comparison to the direct standard question. Strictly speaking, the underlying more-is-better assumption (if, for example, a higher proportion of criminals is calculated than is determined via a direct question) for confirming the method is not valid as a validation.

Individual evidence

  1. ↑ Yu, J.-W., Tian, ​​G.-L. & Tang, M.-L. (2008). Two new models for survey sampling with sensitive characteristic: Design and analysis. Metrika, 67, 251-263. doi : 10.1007 / s00184-007-0131-x
  2. ↑ Barton, AH, 1958, Asking the Embarrassing Question, Public Opinion Quarterly 22 (1), 67-68. doi : 10.1086 / 266761 .
  3. ↑ Coutts, E., Jann, B., Krumpal, I. & Näher, A.-F., 2011, 'Plagiarism in Student Papers: Prevalence Estimates Using Special Techniques for Sensitive Questions', Yearbooks for Economics and Statistics 231 (5 -6), 756. doi : 10.1515 / jbnst-2011-5-612
  4. ↑ Krumpal, Ivar; Jann, Ben; Auspurg, Katrin; by Hermanni, Hagen (2015). Asking Sensitive Questions: A Critical Account of the Randomized Response Technique and Related Methods. In: Engel, Uwe; Jann, Ben; Lynn, Peter; Scherpenzeel, Annette; Sturgis, Patrick (eds.) Improving Survey Methods: Lessons from Recent Research (pp. 130-131). New York: Routledge. ISBN 978-0-415-81762-2
  5. ↑ Hoffmann, A .; Diedenhofen, B .; Verschuere, B .; Musch, J., 2016, 'A Strong Validation of the Crosswise Model Using Experimentally-Induced Cheating Behavior, Experimental Psychology (2015), 62, pp. 403-414. doi : 10.1027 / 1618-3169 / a000304
  6. ↑ Hoffmann, A. & Musch, J., 2016, 'Assessing the validity of two indirect questioning techniques: A Stochastic Lie Detector versus the Crosswise Model', Behavior research methods 48 (3), 1040-1043. doi : 10.3758 / s13428-015-0628-6 .