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When outliers or other unusual estimates are included in the analysis, the use of alternative random effect distributions has previously been proposed. Instead of adopting the usual hierarchical approach to modelling between\u2010study variation, and so directly modelling the study specific true underling effects, we propose two new marginal distributions for modelling heterogeneous datasets. These two distributions are suggested because numerical integration is not needed to evaluate the likelihood. This makes the computation required when fitting our models much more robust. The properties of the new distributions are described, and the methodology is exemplified by fitting models to four datasets. \u00a9 2015 The Authors.\n                    <jats:italic>Research Synthesis Methods<\/jats:italic>\n                    published by John Wiley &amp; Sons, Ltd.\n                  <\/jats:p>","DOI":"10.1002\/jrsm.1191","type":"journal-article","created":{"date-parts":[[2015,11,27]],"date-time":"2015-11-27T03:43:03Z","timestamp":1448595783000},"page":"314-328","source":"Crossref","is-referenced-by-count":31,"title":["New models for describing outliers in meta\u2010analysis"],"prefix":"10.1002","volume":"7","author":[{"given":"Rose","family":"Baker","sequence":"first","affiliation":[{"name":"School of Business University of Salford City of Salford UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dan","family":"Jackson","sequence":"additional","affiliation":[{"name":"School of Business University of Salford City of Salford UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2015,11,27]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/jrsm.1065"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10729-007-9041-8"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1161\/01.RES.18.4.398"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/jrsm.1114"},{"issue":"1","key":"e_1_2_9_6_1","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","article-title":"Controlling the false discovery rate: a practical and powerful approach to multiple testing","volume":"57","author":"Benjamini Y","year":"1995","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.650"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0197-2456(86)90046-2"},{"key":"e_1_2_9_9_1","first-page":"16","article-title":"On Bayesian modelling of fat tails and skewness","volume":"130","author":"Fernandez C","year":"1998","journal-title":"Journal of the American Statistical Association 93, 359371. samples of measures of departure from normality, Proc. 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