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This hypothesis is tested against the alternatives (i) \u03c332&amp;gt;\u03c312+\u03c322, (ii) \u03c332&amp;lt;\u03c312+\u03c322 and (iii) \u03c332\u2260\u03c312+\u03c322. The test procedures satisfy the property that the size or the Type I error does not exceed the preassigned level \u03b1. Optimum properties of the tests and their size and power functions are also investigated. The generalization of the procedures to the case involving more than three variances is also discussed.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1974.tb01002.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T05:14:50Z","timestamp":1544159690000},"page":"243-257","source":"Crossref","is-referenced-by-count":0,"title":["On Some Procedures for Testing a Linear Relation Among Variances"],"prefix":"10.1093","volume":"36","author":[{"given":"Umesh D.","family":"Naik","sequence":"first","affiliation":[{"name":"University of Sheffield"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920472718700_rssb01002-cit-0001","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1214\/aoms\/1177728786","article-title":"Some theorems on quadratic forms applied in the study of analysis of variance problems I. Effect of inequality of variance in one-way classification","volume":"25","author":"Box","year":"1954","journal-title":"Ann. Math. 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