{"doi":"10.1111/opo.12399","title":"Recommendations for analysis of repeated‐measures designs: testing and correcting for sphericity and use of\n                    <scp>manova</scp>\n                    and mixed model analysis","abstract":"<jats:title>Abstract</jats:title>\n                  <jats:sec>\n                    <jats:title>Purpose</jats:title>\n                    <jats:p>\n                      A common experimental design in ophthalmic research is the repeated‐measures design in which at least one variable is a within‐subject factor. This design is vulnerable to lack of ‘sphericity’ which assumes that the variances of the differences among all possible pairs of within‐subject means are equal. Traditionally, this design has been analysed using a repeated‐measures analysis of variance (RM‐\n                      <jats:sc>anova</jats:sc>\n                      ) but increasingly more complex methods such as multivariate\n                      <jats:sc>anova</jats:sc>\n                      (\n                      <jats:sc>manova</jats:sc>\n                      ) and mixed model analysis (MMA) are being used. This article surveys current practice in the analysis of designs incorporating different factors in research articles published in three optometric journals, namely\n                      <jats:italic>Ophthalmic and Physiological Optics</jats:italic>\n                      (OPO),\n                      <jats:italic>Optometry and Vision Science</jats:italic>\n                      (OVS), and\n                      <jats:italic>Clinical and Experimental Optometry</jats:italic>\n                      (CXO), and provides advice to authors regarding the analysis of repeated‐measures designs.\n                    </jats:p>\n                  </jats:sec>\n                  <jats:sec>\n                    <jats:title>Recent findings</jats:title>\n                    <jats:p>\n                      Of the total sample of articles, 66% used a repeated‐measures design. Of those articles using a repeated‐measures design, 59% and 8% analysed the data using\n                      <jats:styled-content style=\"fixed-case\">RM</jats:styled-content>\n                      ‐\n                      <jats:sc>anova</jats:sc>\n                      or\n                      <jats:sc>manova</jats:sc>\n                      respectively and 33% used\n                      <jats:styled-content style=\"fixed-case\">MMA</jats:styled-content>\n                      . The use of\n                      <jats:styled-content style=\"fixed-case\">MMA</jats:styled-content>\n                      relative to\n                      <jats:styled-content style=\"fixed-case\">RM</jats:styled-content>\n                      ‐\n                      <jats:sc>anova</jats:sc>\n                      has increased significantly since 2009/10. A further search using terms to select those papers testing and correcting for sphericity (‘Mauchly's test’, ‘Greenhouse‐Geisser’, ‘Huynh and Feld’) identified 66 articles, 62% of which were published from 2012 to the present.\n                    </jats:p>\n                  </jats:sec>\n                  <jats:sec>\n                    <jats:title>Summary</jats:title>\n                    <jats:p>\n                      If the design is balanced without missing data then\n                      <jats:sc>manova</jats:sc>\n                      should be used rather than\n                      <jats:styled-content style=\"fixed-case\">RM</jats:styled-content>\n                      ‐\n                      <jats:sc>anova</jats:sc>\n                      as it gives better protection against lack of sphericity. If the design is unbalanced or with missing data then\n                      <jats:styled-content style=\"fixed-case\">MMA</jats:styled-content>\n                      is the method of choice. However,\n                      <jats:styled-content style=\"fixed-case\">MMA</jats:styled-content>\n                      is a more complex analysis and can be difficult to set up and run, and care should be taken first, to define appropriate models to be tested and second, to ensure that sample sizes are adequate.\n                    </jats:p>\n                  </jats:sec>","journal":"Ophthalmic and Physiological Optics","year":2017,"id":685073,"datarank":0.6798899239729885,"base_score":4.532599493153256,"endowment":4.532599493153256,"self_citation_contribution":0.6798899239729885,"citation_network_contribution":0.0,"self_endowment_contribution":0.6798899239729885,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":92,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1789831,"name":"Richard A. Armstrong","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Recommendations for analysis of repeated‐measures designs: testing and correcting for sphericity and use of\n                    <scp>manova</scp>\n                    and mixed model analysis","abstract":"<jats:title>Abstract</jats:title>\n                  <jats:sec>\n                    <jats:title>Purpose</jats:title>\n                    <jats:p>\n                      A common experimental design in ophthalmic research is the repeated‐measures design in which at least one variable is a within‐subject factor. This design is vulnerable to lack of ‘sphericity’ which assumes that the variances of the differences among all possible pairs of within‐subject means are equal. Traditionally, this design has been analysed using a repeated‐measures analysis of variance (RM‐\n                      <jats:sc>anova</jats:sc>\n                      ) but increasingly more complex methods such as multivariate\n                      <jats:sc>anova</jats:sc>\n                      (\n                      <jats:sc>manova</jats:sc>\n                      ) and mixed model analysis (MMA) are being used. This article surveys current practice in the analysis of designs incorporating different factors in research articles published in three optometric journals, namely\n                      <jats:italic>Ophthalmic and Physiological Optics</jats:italic>\n                      (OPO),\n                      <jats:italic>Optometry and Vision Science</jats:italic>\n                      (OVS), and\n                      <jats:italic>Clinical and Experimental Optometry</jats:italic>\n                      (CXO), and provides advice to authors regarding the analysis of repeated‐measures designs.\n                    </jats:p>\n                  </jats:sec>\n                  <jats:sec>\n                    <jats:title>Recent findings</jats:title>\n                    <jats:p>\n                      Of the total sample of articles, 66% used a repeated‐measures design. Of those articles using a repeated‐measures design, 59% and 8% analysed the data using\n                      <jats:styled-content style=\"fixed-case\">RM</jats:styled-content>\n                      ‐\n                      <jats:sc>anova</jats:sc>\n                      or\n                      <jats:sc>manova</jats:sc>\n                      respectively and 33% used\n                      <jats:styled-content style=\"fixed-case\">MMA</jats:styled-content>\n                      . The use of\n                      <jats:styled-content style=\"fixed-case\">MMA</jats:styled-content>\n                      relative to\n                      <jats:styled-content style=\"fixed-case\">RM</jats:styled-content>\n                      ‐\n                      <jats:sc>anova</jats:sc>\n                      has increased significantly since 2009/10. A further search using terms to select those papers testing and correcting for sphericity (‘Mauchly's test’, ‘Greenhouse‐Geisser’, ‘Huynh and Feld’) identified 66 articles, 62% of which were published from 2012 to the present.\n                    </jats:p>\n                  </jats:sec>\n                  <jats:sec>\n                    <jats:title>Summary</jats:title>\n                    <jats:p>\n                      If the design is balanced without missing data then\n                      <jats:sc>manova</jats:sc>\n                      should be used rather than\n                      <jats:styled-content style=\"fixed-case\">RM</jats:styled-content>\n                      ‐\n                      <jats:sc>anova</jats:sc>\n                      as it gives better protection against lack of sphericity. If the design is unbalanced or with missing data then\n                      <jats:styled-content style=\"fixed-case\">MMA</jats:styled-content>\n                      is the method of choice. However,\n                      <jats:styled-content style=\"fixed-case\">MMA</jats:styled-content>\n                      is a more complex analysis and can be difficult to set up and run, and care should be taken first, to define appropriate models to be tested and second, to ensure that sample sizes are adequate.\n                    </jats:p>\n                  </jats:sec>","is_dataset_classified":null,"base_score":4.532599493153256,"endowment":4.532599493153256,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"28726257","pmcid":null,"openalex_id":"https://openalex.org/W2737460962","authors":[],"funders":[],"total_grants":0,"fwci":2.6168,"citation_percentile":0.90276878,"influential_citations":0,"citation_trend":[{"year":2017,"count":1},{"year":2018,"count":2},{"year":2019,"count":4},{"year":2020,"count":9},{"year":2021,"count":11},{"year":2022,"count":12},{"year":2023,"count":9},{"year":2024,"count":15},{"year":2025,"count":19},{"year":2026,"count":10}],"oa_status":"bronze","license":"http://onlinelibrary.wiley.com/termsAndConditions#vor","oa_locations":[{"url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/opo.12399","host_type":"journal"},{"url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/opo.12399","host_type":"publisher"},{"url":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fopo.12399","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/pdf/10.1111/opo.12399","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/full-xml/10.1111/opo.12399","host_type":"publisher"},{"url":"https://doi.org/10.1111/opo.12399","host_type":"journal"},{"url":"https://pubmed.ncbi.nlm.nih.gov/28726257","host_type":"repository"},{"url":"https://publications.aston.ac.uk/view/author/b688ed7dac988bb59e703b38c19badee.html>","host_type":"repository"},{"url":"https://publications.aston.ac.uk/id/eprint/31454/1/Testing_and_correcting_for_sphericity_and_use_of_manova_and_mixed_model_analysis.pdf","host_type":"repository"}],"fields_of_study":["Ophthalmology and Visual Impairment Studies","Corneal surgery and disorders","Glaucoma and retinal disorders","Biomedical Research","Humans","Models, Statistical","Optometry"],"mesh_terms":["Humans","Optometry","Models, Statistical","Biomedical Research"],"keywords":["Multivariate analysis of variance","Sphericity","Repeated measures design","Analysis of variance","Mixed-design analysis of variance","Statistics","Variance (accounting)","Multivariate statistics","Mathematics","Multivariate analysis","Computer science","Mixed Model Analysis","Greenhouse-geisser","Huynh-feldt","Mauchly's Test","Repeated-measures Design"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-08-18T15:41:21.139305Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}