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We apply normalization techniques, such as variance stabilizing transformations, to ribonucleic acid sequencing data with varying sample sizes to assess their effectiveness in achieving symmetric data distributions. Our findings reveal that while normalization generally induces symmetry, some samples retain asymmetric distributions, challenging the conventional assumption of post-normalization symmetry. The Rp test, in particular, shows superior performance when there are variations in sample size and data distribution, making it a preferred tool for assessing symmetry when applied to genomic data. This finding underscores the importance of validating symmetry assumptions during data normalization, especially in genomic data, as overlooked asymmetries can lead to potential inaccuracies in downstream analyses. We analyze postmortem lateral temporal lobe samples to explore normal aging and Alzheimer\u2019s disease, highlighting the critical role of symmetry testing in the accurate interpretation of genomic data.<\/jats:p>","DOI":"10.3390\/stats7030059","type":"journal-article","created":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T05:59:08Z","timestamp":1725861548000},"page":"967-983","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Statistical Methodology for Evaluating Asymmetry after Normalization with Application to Genomic Data"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4755-3270","authenticated-orcid":false,"given":"V\u00edctor","family":"Leiva","sequence":"first","affiliation":[{"name":"Escuela de Ingenier\u00eda Industrial, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, Valpara\u00edso 2362807, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3730-7685","authenticated-orcid":false,"given":"Jimmy","family":"Corzo","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica, Facultad de Ciencias, Universidad Nacional de Colombia, Bogot\u00e1 111321, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1198-0051","authenticated-orcid":false,"given":"Myrian E.","family":"Vergara","sequence":"additional","affiliation":[{"name":"Escuela de Ciencias B\u00e1sicas y Aplicadas, Universidad de La Salle, Bogot\u00e1 110231, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9884-9090","authenticated-orcid":false,"given":"Raydonal","family":"Ospina","sequence":"additional","affiliation":[{"name":"Departamento de Estat\u00edstica, LInCa, Universidade Federal da Bahia, Salvador 40170-110, Brazil"},{"name":"Departamento de Estat\u00edstica, CASTLab, Universidade Federal da Pernambuco, Recife 50670-901, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9897-8186","authenticated-orcid":false,"given":"Cecilia","family":"Castro","sequence":"additional","affiliation":[{"name":"Centre of Mathematics, Universidade do Minho, 4710-057 Braga, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Garc\u00eda-Sancho, M., and Lowe, J. (2023). A History of Genomics across Species, Communities and Projects, Springer.","DOI":"10.1007\/978-3-031-06130-1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"583","DOI":"10.3390\/stats5030036","article-title":"Quantile regression approach for analyzing similarity of gene expressions under multiple biological conditions","volume":"5","author":"Deng","year":"2022","journal-title":"Stats"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhang, S. (2007). A comprehensive evaluation of SAM, the SAM R-package and a simple modification to improve its performance. BMC Bioinform., 8.","DOI":"10.1186\/1471-2105-8-230"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"550","DOI":"10.3390\/stats4030033","article-title":"A constrained generalized functional linear model for multi-loci genetic mapping","volume":"4","author":"Huang","year":"2021","journal-title":"Stats"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"10571","DOI":"10.48084\/etasr.5770","article-title":"Differential gene expression analysis of non-small cell lung cancer samples to classify candidate genes","volume":"13","author":"Hiremath","year":"2023","journal-title":"Eng. Technol. Appl. Sci. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"001724","DOI":"10.1099\/jgv.0.001724","article-title":"Differential gene expression reveals host factors for viral shedding variation in mallards (Anas platyrhynchos) infected with low-pathogenic avian influenza virus","volume":"103","author":"Dolinski","year":"2022","journal-title":"J. Gen. Virol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1584","DOI":"10.1038\/s41588-022-01217-6","article-title":"Improved RNA-seq normalization","volume":"5411","author":"Fletcher","year":"2022","journal-title":"Nat. Genet."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Corchete, L.A., Rojas, E.A., Alonso-L\u00f3pez, D., De Las Rivas, J., Guti\u00e9rrez, N.C., and Burguillo, F.J. (2020). Systematic comparison and assessment of RNA-seq procedures for gene expression quantitative analysis. Sci. Rep., 10.","DOI":"10.1038\/s41598-020-76881-x"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Concha-Aracena, M.S., Barrios-Blanco, L., Elal-Olivero, D., da Silva, P.H.F., and Nascimento, D.C.D. (2022). Extending normality: A case of unit distribution generated from the moments of the standard normal distribution. Axioms, 11.","DOI":"10.3390\/axioms11120666"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Dubois, E., Galindo, A.N., Dayon, L., and Cominetti, O. (2022). Assessing normalization methods in mass spectrometry-based proteome profiling of clinical samples. Biosystems, 215.","DOI":"10.1016\/j.biosystems.2022.104661"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ghandi, M., and Beer, M.A. (2012). Group normalization for genomic data. PLoS ONE, 7.","DOI":"10.1371\/journal.pone.0038695"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF02481082","article-title":"Normalizing and variance stabilizing transformations for intraclass correlations","volume":"37","author":"Konishi","year":"1985","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1038\/s41576-021-00431-y","article-title":"Computational analysis of cancer genome sequencing data","volume":"23","author":"Gulhan","year":"2022","journal-title":"Nat. Rev. Genet."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1016\/j.csda.2008.04.012","article-title":"On the glog-normal distribution and its association with the gene expression problem","volume":"53","author":"Leiva","year":"2009","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Abrams, Z.B., Johnson, T.S., Huang, K., Payne, P.R., and Coombes, K. (2019). A protocol to evaluate RNA sequencing normalization methods. BMC Bioinform., 20.","DOI":"10.1186\/s12859-019-3247-x"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2354","DOI":"10.1080\/02664763.2013.811480","article-title":"On a variance stabilizing model and its application to genomic data","volume":"40","author":"Vilca","year":"2013","journal-title":"J. Appl. Stat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1186\/s12936-022-04104-x","article-title":"Leveraging Mann\u2013Whitney U test on large-scale genetic variation data for analysing malaria genetic markers","volume":"21","author":"Tai","year":"2022","journal-title":"Malar. J."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Hafemeister, C., and Satija, R. (2019). Normalization and variance stabilization of single-cell RNA-sequencing data using regularized negative binomial regression. Genome Biol., 20.","DOI":"10.1186\/s13059-019-1874-1"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1515\/sagmb-2012-0030","article-title":"A new variance stabilizing transformation for gene expression data analysis","volume":"12","author":"Kelmansky","year":"2013","journal-title":"Stat. Appl. Genet. Mol. Biol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1186\/s40035-022-00315-z","article-title":"A review of brain imaging biomarker genomics in Alzheimer\u2019s disease: Implementation and perspectives","volume":"11","author":"Li","year":"2022","journal-title":"Transl. Neurodegener."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"295","DOI":"10.11144\/Javeriana.SC24-2.artf","article-title":"A runs test for the hypothesis of symmetry with one sided alternative","volume":"24","year":"2019","journal-title":"Univ. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"984","DOI":"10.1080\/00949655.2011.647026","article-title":"A modified runs test for symmetry","volume":"83","author":"Corzo","year":"2013","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Luecken, M.D., and Theis, F.J. (2019). Current best practices in single-cell RNA-seq analysis: A tutorial. Mol. Syst. Biol., 15.","DOI":"10.15252\/msb.20188746"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1038\/s41576-023-00586-w","article-title":"Best practices for single-cell analysis across modalities","volume":"24","author":"Heumos","year":"2023","journal-title":"Nat. Rev. Genet."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1038\/s41592-023-01911-1","article-title":"Expansion spatial transcriptomics","volume":"20","author":"Fan","year":"2023","journal-title":"Nat. Methods"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Love, M.I., Huber, W., and Anders, S. (2014). Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome Biol., 15.","DOI":"10.1186\/s13059-014-0550-8"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1093\/bioinformatics\/btp616","article-title":"edgeR: A Bioconductor package for differential expression analysis of digital gene expression data","volume":"26","author":"Robinson","year":"2010","journal-title":"Bioinformatics"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4062","DOI":"10.1093\/bioinformatics\/btac498","article-title":"DiffChIPL: A differential peak analysis method for high-throughput sequencing data with biological replicates based on Limma","volume":"38","author":"Chen","year":"2022","journal-title":"Bioinformatics"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"McManus, C. (2022). Cerebral polymorphisms for lateralisation: Modelling the genetic and phenotypic architectures of multiple functional modules. Symmetry, 14.","DOI":"10.3390\/sym14040814"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v028.i03","article-title":"lawstat: An R package for law, public policy and biostatistics","volume":"28","author":"Hui","year":"2008","journal-title":"J. Stat. Softw."},{"key":"ref_31","unstructured":"Gastwirth, J.L., Gel, Y.R., Hui, W.W., Lyubchich, V., Miao, W., Noguchi, K., and Lyubchich, M.V. (2019). Package \u2018Lawstat\u2019, R Foundation for Statistical Computing."},{"key":"ref_32","unstructured":"R Core Team (2023). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Nayak, D.S.K., Das, J., and Swarnkar, T. (2021). Quality control pipeline for next generation sequencing data analysis. Proceedings of Intelligent and Cloud Computing, Springer.","DOI":"10.1007\/978-981-16-9873-6_20"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"349","DOI":"10.2307\/3315744","article-title":"A simple test of symmetry about an unknown median","volume":"24","author":"Cabilio","year":"1996","journal-title":"Can. J. Stat."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1080\/02664769921963","article-title":"Distribution-free test for symmetry based on Bonferroni\u2019s measure","volume":"26","author":"Mira","year":"1999","journal-title":"J. Appl. Stat."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Miao, W., Gel, Y., and Gastwirth, J. (2006). A new test of symmetry about an unknown median. Random Walk, Sequential Analysis and Related Topics\u2014A Festschrift in Honor of Yuan-Shih Chow, World Scientific.","DOI":"10.1142\/9789812772558_0013"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1038\/s41588-020-0696-0","article-title":"An integrated multi-omics approach identifies epigenetic alterations associated with Alzheimer disease","volume":"52","author":"Nativio","year":"2020","journal-title":"Nat. Genet."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1262","DOI":"10.1111\/biom.13214","article-title":"Operating characteristics of the rank-based inverse normal transformation for quantitative trait analysis in genome-wide association studies","volume":"76","author":"McCaw","year":"2020","journal-title":"Biometrics"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1080\/02664769822765","article-title":"Hybrid test for the hypothesis of symmetry","volume":"25","author":"Modarres","year":"1998","journal-title":"J. Appl. Stat."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1093\/bib\/bbs046","article-title":"A comprehensive evaluation of normalization methods for Illumina high-throughput RNA sequencing data analysis","volume":"14","author":"Dillies","year":"2013","journal-title":"Brief. Bioinform."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"The Cancer Genome Atlas Research Network (2013). Genomic and epigenomic landscapes of adult de novo acute myeloid leukemia. N. Engl. J. Med., 368, 2059\u20132074.","DOI":"10.1056\/NEJMoa1301689"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"SEQC\/MAQC-III Consortium (2014). A comprehensive assessment of RNA-seq accuracy, reproducibility and information content by the Sequencing Quality Control Consortium. Nat. Biotechnol., 32, 903\u2013914.","DOI":"10.1038\/nbt.2957"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Conesa, A., Madrigal, P., Tarazona, S., Gomez-Cabrero, D., Cervera, A., McPherson, A., Szcze\u015bniak, M.W., Gaffney, D.J., Elo, L.L., and Zhang, X. (2016). A survey of best practices for RNA-seq data analysis. Genome Biol., 17.","DOI":"10.1186\/s13059-016-0881-8"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Yu, L., Fernandez, S., and Brock, G. (2017). Power analysis for RNA-seq differential expression studies. BMC Bioinform., 18.","DOI":"10.1186\/s12859-017-1648-2"},{"key":"ref_45","unstructured":"McCaw, Z. (2024, August 25). RNOmni: Rank Normal Transformation Omnibus Test. Version 1.0.1.2. Available online: https:\/\/CRAN.R-project.org\/package=RNOmni."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1038\/nmeth.1315","article-title":"mRNA-Seq whole-transcriptome analysis of a single cell","volume":"6","author":"Tang","year":"2009","journal-title":"Nat. Methods"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41596-020-00409-w","article-title":"Tutorial: Guidelines for the computational analysis of single-cell RNA sequencing data","volume":"16","author":"Andrews","year":"2021","journal-title":"Nat. Protoc."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1002\/asmb.2556","article-title":"Birnbaum-Saunders quantile regression and its diagnostics with application to economic data","volume":"37","author":"Sanchez","year":"2021","journal-title":"Appl. Stoch. Model. Bus. Ind."},{"key":"ref_49","first-page":"1","article-title":"Air contaminant statistical distributions with application to PM10 in Santiago, Chile","volume":"223","author":"Marchant","year":"2013","journal-title":"Rev. Environ. Contam. Toxicol."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Palacios, C.A., Reyes-Suarez, J.A., Bearzotti, L.A., Leiva, V., and Marchant, C. (2021). Knowledge discovery for higher education student retention based on data mining: Machine learning algorithms and case study in Chile. Entropy, 23.","DOI":"10.3390\/e23040485"}],"container-title":["Stats"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2571-905X\/7\/3\/59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:51:54Z","timestamp":1760111514000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2571-905X\/7\/3\/59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,9]]},"references-count":50,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["stats7030059"],"URL":"https:\/\/doi.org\/10.3390\/stats7030059","relation":{},"ISSN":["2571-905X"],"issn-type":[{"type":"electronic","value":"2571-905X"}],"subject":[],"published":{"date-parts":[[2024,9,9]]}}}