{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T15:03:49Z","timestamp":1773414229353,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T00:00:00Z","timestamp":1743984000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T00:00:00Z","timestamp":1743984000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100012320","name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100012320","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Brain Inf."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Bipolar psychometric scale data play a crucial role in psychological healthcare and health economics, such as in psychotherapeutic profiling and setting standards. Creating an accurate psychological profile not only benefits the patient but also saves time and costs. The quality of psychotherapeutic measures directly impacts grant funding decisions, influencing managerial choices. Moreover, the accuracy of consumer data analyses affects costs, profits, and the long-term sustainability of decisions. Considering psychometric bipolar scale data as compositional data can enhance the statistical power of well-known paired and unpaired two-sample t-tests, supporting managerial decision-making and the development or implementation of health interventions. This increase in statistical power is observed when the central limit theorem (CLT) holds true in statistics. Through stochastic simulation, this study explores the impact of violating the CLT on statistical power of the unpaired t-test under heavy-tailed data generating processes (DGPs) with finite variance. The findings reveal a reduction in statistical power based on specific parameters like the psychometric limit of quantification, the number of items in a questionnaire, the response scale used, and the dispersion of the DGP.<\/jats:p>","DOI":"10.1186\/s40708-025-00253-2","type":"journal-article","created":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T19:13:44Z","timestamp":1744053224000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Breakdown of the compositional data approach in psychometric Likert scale big data analysis: about the loss of statistical power of two-sample t-tests applied to heavy-tailed big data"],"prefix":"10.1186","volume":"12","author":[{"given":"Ren\u00e9","family":"Lehmann","sequence":"first","affiliation":[]},{"given":"Bodo","family":"Vogt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,7]]},"reference":[{"key":"253_CR1","volume":"12","author":"MU Tariq","year":"2021","unstructured":"Tariq MU, Babar M, Poulin M, Khattak AS, Alshehri MD, Kaleem S (2021) Human behavior analysis using intelligent big data analytics. Front Psychol 12:686610","journal-title":"Front Psychol"},{"key":"253_CR2","first-page":"738","volume":"7","author":"MW-L Cheung","year":"2016","unstructured":"Cheung MW-L, Jak S (2016) Analyzing big data in psychology: a split\/analyze\/meta-analyze approach. Front Psychol 7:738","journal-title":"Front Psychol"},{"issue":"4","key":"253_CR3","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1027\/2151-2604\/a000348","volume":"226","author":"MW-L Cheung","year":"2018","unstructured":"Cheung MW-L, Jak S (2018) Challenges of big data analyses and applications in psychology. Zeitschrift f\u00fcr Psychologie 226(4):209\u2013211","journal-title":"Zeitschrift f\u00fcr Psychologie"},{"key":"253_CR4","doi-asserted-by":"crossref","unstructured":"Lehmann, R. and Vogt, B. (2023b). Reconsidering bipolar scales data as compositional data improves psychometric healthcare data analytics. In Proceedings of the 56th Hawaii International Conference on System Sciences, pages 2380\u20132389","DOI":"10.24251\/HICSS.2023.349"},{"key":"253_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-4109-0","volume-title":"The statistical analysis of compositional data","author":"J Aitchison","year":"1986","unstructured":"Aitchison J (1986) The statistical analysis of compositional data. Chapman and Hall"},{"key":"253_CR6","doi-asserted-by":"crossref","first-page":"6100","DOI":"10.1016\/j.scitotenv.2009.08.008","volume":"407","author":"P Filzmoser","year":"2009","unstructured":"Filzmoser P, Hron K, Reimann C (2009) Univariate statistical analysis of environmental (compositional) data: problems and possibilities. Sci Total Environ 407:6100\u20136108","journal-title":"Sci Total Environ"},{"key":"253_CR7","doi-asserted-by":"crossref","unstructured":"Aitchison, J. (2003b). The statistical Analysis of Compositional Data. Blackburn Press, reprint of 1986 containing additional material edition","DOI":"10.1007\/978-94-009-4109-0_11"},{"key":"253_CR8","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s11004-007-9141-5","volume":"40","author":"P Filzmoser","year":"2008","unstructured":"Filzmoser P, Hron K (2008) Outlier detection for compositional data using robust methods. Mathematical Geosci 40:233\u2013248","journal-title":"Mathematical Geosci"},{"issue":"1","key":"253_CR9","doi-asserted-by":"crossref","first-page":"4149","DOI":"10.1007\/s10661-014-4149-z","volume":"187","author":"R Lehmann","year":"2014","unstructured":"Lehmann R (2014) A new approach for assessing the state of environment using isometric log-ratio transformation and outlier detection for computation of mean pcdd\/f patterns in biota. Environ Monitor Assess 187(1):4149","journal-title":"Environ Monitor Assess"},{"key":"253_CR10","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1007\/s11004-008-9196-y","volume":"41","author":"P Filzmoser","year":"2009","unstructured":"Filzmoser P, Hron K (2009) Correlation analysis for compositional data. Mathematical Geosci 41:905\u2013919","journal-title":"Mathematical Geosci"},{"key":"253_CR11","volume-title":"Increasing the power of two-sample t-tests in health psychology using a compositional data approach","author":"R Lehmann","year":"2023","unstructured":"Lehmann R, Vogt B (2023) Increasing the power of two-sample t-tests in health psychology using a compositional data approach. Cham, Springer Nature Switzerland"},{"key":"253_CR12","doi-asserted-by":"crossref","unstructured":"Lehmann, R. and Vogt, B. (2024a). Compositional data statistics improves smart tourism data analytics: profound managerial decisions through reduced statistical bias and increased power. In Proceedings of the 57th Hawaii International Conference on System Sciences","DOI":"10.24251\/HICSS.2024.214"},{"issue":"1","key":"253_CR13","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1186\/s40708-024-00232-z","volume":"11","author":"R Lehmann","year":"2024","unstructured":"Lehmann R, Vogt B (2024) Improving likert scale big data analysis in psychometric health economics: reliability of the new compositional data approach. Brain Infor 11(1):19","journal-title":"Brain Infor"},{"key":"253_CR14","doi-asserted-by":"crossref","unstructured":"Lehmann, R. and Vogt, B. (2024d). Increasing normal approximation in psychometric health care data analyses using a compositional data approach. In Proceedings of the 57th Hawaii International Conference on System Sciences","DOI":"10.24251\/HICSS.2024.194"},{"key":"253_CR15","doi-asserted-by":"crossref","unstructured":"Lehmann, R. and Vogt, B. (2024g). Shifting psychometric bipolar scales data towards the normal distribution. In Proceedings of the 57th Hawaii International Conference on System Sciences","DOI":"10.24251\/HICSS.2024.400"},{"issue":"29","key":"253_CR16","first-page":"19","volume":"12","author":"J Murphy","year":"2021","unstructured":"Murphy J, Valli\u00e8res F, Bentall RP, Shevlin M, McBride O, Hartman TK, McKay R, Bennett K, Mason L, Gibson-Miller J, Levita L, Martinez AP, Stocks TVA, Karatzias T, Hyland P (2021) Psychological characteristics associated withcovid-19 vaccine hesitancy and resistancein ireland and the united kingdom. Nat Commun 12(29):19","journal-title":"Nat Commun"},{"issue":"7855","key":"253_CR17","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1038\/s41586-021-03344-2","volume":"592","author":"G Pennycook","year":"2021","unstructured":"Pennycook G, Epstein Z, Mosleh M, Arechar AA, Eckles D, Rand DG (2021) Shifting attention to accuracy can reduce misinformation online. Nature 592(7855):590\u2013595","journal-title":"Nature"},{"key":"253_CR18","first-page":"106","volume":"3","author":"J Carifio","year":"2007","unstructured":"Carifio J, Perla RJ (2007) Ten common misunderstandings, misconceptions, persistent myths and urban legends about likert scales and likert response formats and their antidotes. J Soc Sci 3:106\u2013116","journal-title":"J Soc Sci"},{"key":"253_CR19","doi-asserted-by":"crossref","first-page":"1150","DOI":"10.1111\/j.1365-2923.2008.03172.x","volume":"42","author":"J Carifio","year":"2008","unstructured":"Carifio J, Perla RJ (2008) Resolving the 50 year debate around using and misusing likert scales. Med Educ 42:1150\u20131152","journal-title":"Med Educ"},{"issue":"140","key":"253_CR20","first-page":"5","volume":"22","author":"R Likert","year":"1932","unstructured":"Likert R (1932) A technique for the measurement of attitudes. Archiv Psychol 22(140):5\u201355","journal-title":"Archiv Psychol"},{"issue":"4","key":"253_CR21","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1037\/0022-3514.54.4.580","volume":"54","author":"J James","year":"1988","unstructured":"James J, Wood G (1988) The effects of incomplete information on the formation of attitudes toward behavioral alternatives. J Person Soc Psychol 54(4):580\u2013591","journal-title":"J Person Soc Psychol"},{"issue":"3","key":"253_CR22","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/0167-4870(89)90028-7","volume":"10","author":"WH Loke","year":"1989","unstructured":"Loke WH (1989) The effects of framing and incomplete information on judgments. J Econ Psychol 10(3):329\u2013341","journal-title":"J Econ Psychol"},{"key":"253_CR23","doi-asserted-by":"crossref","first-page":"135","DOI":"10.3389\/fpsyg.2016.00135","volume":"7","author":"A Romano","year":"2016","unstructured":"Romano A, Mosso C, Merlone U (2016) The role of incomplete information and others\u2019 choice in reducing traffic: a pilot study. Front Psychol 7:135","journal-title":"Front Psychol"},{"key":"253_CR24","unstructured":"Aitchison, J. (2003a). A Concise Guide to Compositional Data Analysis. Department of Statistics University of Glasgow"},{"key":"253_CR25","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1007\/s11004-005-7383-7","volume":"37","author":"J Aitchison","year":"2005","unstructured":"Aitchison J, Egozcue JJ (2005) Compositional data analysis: where are we and where should we be heading? Mathema Geol 37:829\u2013850","journal-title":"Mathema Geol"},{"key":"253_CR26","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1023\/B:MATG.0000002983.12476.89","volume":"35","author":"J Aitchison","year":"2003","unstructured":"Aitchison J, Mateu-Figueras G, Ng K (2003) Characterization of distributional forms for compositional data and associated distributional tests. Mathematical Geol 35:667\u2013680","journal-title":"Mathematical Geol"},{"key":"253_CR27","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1023\/B:MATG.0000002983.12476.89","volume":"35","author":"J Aitchison","year":"2003","unstructured":"Aitchison J, Mateu-Figueras G, Ng KW (2003) Characterization of distributional forms for compositional data and associated distributional tests. Mathematical Geol 35:667\u2013680","journal-title":"Mathematical Geol"},{"key":"253_CR28","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1016\/j.cageo.2004.11.013","volume":"31","author":"P Filzmoser","year":"2005","unstructured":"Filzmoser P, Garrett RG, Reimann C (2005) Multivariate outlier detection in exploration geochemistry. Compu Geosci 31:579\u2013587","journal-title":"Compu Geosci"},{"key":"253_CR29","doi-asserted-by":"crossref","DOI":"10.4324\/9780203771587","volume-title":"Statistical Power Analysis for the Behavioral Sciences","author":"J Cohen","year":"2013","unstructured":"Cohen J (2013) Statistical Power Analysis for the Behavioral Sciences. Routledge"},{"key":"253_CR30","doi-asserted-by":"crossref","first-page":"863","DOI":"10.3389\/fpsyg.2013.00863","volume":"4","author":"D Lakens","year":"2013","unstructured":"Lakens D (2013) Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and anovas. Front Psychol 4:863","journal-title":"Front Psychol"},{"key":"253_CR31","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1007\/s10459-010-9222-y","volume":"15","author":"G Norman","year":"2010","unstructured":"Norman G (2010) Likert scales, levels of measurementand the laws of statistics. Adv Health Sci Educ 15:625\u2013632","journal-title":"Adv Health Sci Educ"},{"key":"253_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-87857-7","volume-title":"A History of the Central Limit Theorem","author":"H Fischer","year":"2011","unstructured":"Fischer H (2011) A History of the Central Limit Theorem. Springer"},{"key":"253_CR33","volume-title":"Econometric Theory","author":"J Davidson","year":"2001","unstructured":"Davidson J (2001) Econometric Theory. Blackwell Publishing, Oxford"},{"key":"253_CR34","doi-asserted-by":"crossref","unstructured":"Yee, T. (2006). Vgam: Vector generalized linear and additive models","DOI":"10.32614\/CRAN.package.VGAM"},{"key":"253_CR35","doi-asserted-by":"crossref","unstructured":"Lehmann, R., Bengart, P., and Vogt, B. (2025). Discovering careless response behavior in psychometric data. In Proceedings of the 58th Hawaii International Conference on System Sciences","DOI":"10.24251\/HICSS.2025.400"},{"key":"253_CR36","doi-asserted-by":"crossref","unstructured":"Lehmann R, Vogt B (2024e) Robustness of the compositional data approach in bipolar psychometric likert scales big bimodal data analysis. In: Proceedings of the 10th IEEE International Conference on Engineering and Emerging Technologies (ICEET 2024). IEEE Xplore (in press)","DOI":"10.1109\/ICEET65156.2024.10913870"},{"key":"253_CR37","unstructured":"Lehmann, R. and Vogt, B. (2024f). Robustness of the compositional data approach in bipolar psychometric likert scales big skewed data analysis. In Proceedings of the 23rd IEEE\/WIC International Conference on Web Intelligence and Intelligent Agent Technology (WI-IAT). IEEE WIC"},{"key":"253_CR38","doi-asserted-by":"crossref","DOI":"10.4135\/9781412986038","volume-title":"Summated Rating Scale Construction","author":"P Spector","year":"1992","unstructured":"Spector P (1992) Summated Rating Scale Construction. SAGE Publications Inc, London"},{"issue":"5","key":"253_CR39","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1509\/jmr.11.0368","volume":"49","author":"B Weijters","year":"2012","unstructured":"Weijters B, Baumgartner H (2012) Misresponse to reversed and negated items in surveys: a review. J Mark Res 49(5):737\u2013747","journal-title":"J Mark Res"},{"issue":"1","key":"253_CR40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0001-6918(99)00050-5","volume":"104","author":"CC Preston","year":"2000","unstructured":"Preston CC, Colman AM (2000) Optimal number of response categories in rating scales: reliability, validity, discriminating power, and respondent preferences. Acta Psychol 104(1):1\u201315","journal-title":"Acta Psychol"},{"key":"253_CR41","volume-title":"Computer Methods for Mathematical Computations","author":"GE Forsythe","year":"1977","unstructured":"Forsythe GE, Malcolm MA, Moler CB (1977) Computer Methods for Mathematical Computations. Wiley"},{"key":"253_CR42","unstructured":"Lehmann R, Vogt B (2024) Empirical insights into the value of a novel compositional data approach for analyzing bipolar Likert scale data. Lecture Notes in Computer Science, vol. 15541, chapter 27, ISSN 978-981-96-3293-0, Springer Nature Switzerland (in press)"},{"key":"253_CR43","unstructured":"Rammstedt, B., Kemper, C.\u00a0J., Klein, M.\u00a0C., Beierlein, C., and Kovaleva, A. (2014). Big five inventory (bfi-10). Zusammenstellung sozialwissenschaftlicher Items und Skalen (ZIS)"},{"key":"253_CR44","unstructured":"Beierlein, C., Kovaleva, A., Kemper, C.\u00a0J., and Rammstedt, B. (2015). Kurzskala zur erfassung der risikobereitschaft (r-1). Zusammenstellung sozialwissenschaftlicher Items und Skalen (ZIS)"},{"key":"253_CR45","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1093\/biomet\/52.3-4.591","volume":"52","author":"SS Shapiro","year":"1965","unstructured":"Shapiro SS, Wilk MB (1965) An analysis of variance test for normality (complete samples). Biometrika 52:591\u2013611","journal-title":"Biometrika"},{"issue":"2","key":"253_CR46","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1002\/sim.4780120209","volume":"12","author":"P Royston","year":"1993","unstructured":"Royston P (1993) A pocket-calculator algorithm for the shapiro-francia test for non-normality: an application to medicine. Statis Med 12(2):181\u2013184","journal-title":"Statis Med"},{"key":"253_CR47","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1080\/01621459.1954.10501232","volume":"49","author":"TW Anderson","year":"1954","unstructured":"Anderson TW, Darling DA (1954) A test of goodness-of-fit. J Am Statis Assoc 49:765\u2013769","journal-title":"J Am Statis Assoc"}],"container-title":["Brain Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40708-025-00253-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s40708-025-00253-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40708-025-00253-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T19:15:55Z","timestamp":1744053355000},"score":1,"resource":{"primary":{"URL":"https:\/\/braininformatics.springeropen.com\/articles\/10.1186\/s40708-025-00253-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,7]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["253"],"URL":"https:\/\/doi.org\/10.1186\/s40708-025-00253-2","relation":{},"ISSN":["2198-4018","2198-4026"],"issn-type":[{"value":"2198-4018","type":"print"},{"value":"2198-4026","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,7]]},"assertion":[{"value":"18 July 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"All authors consent to the publication of this article.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"9"}}