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A Note on Variance Components Model

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Bibliographic Details
Title: A Note on Variance Components Model
Language: English
Authors: Kshirsagar, Anant M., Radhakrishnan, R.
Source: International Journal of Mathematical Education in Science and Technology. Jan 2009 40(2):287-289.
Availability: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Physical Description: PDF
Page Count: 3
Publication Date: 2009
Document Type: Journal Articles
Reports - Descriptive
Descriptors: Statistical Analysis, Geometric Concepts, Mathematical Models, Structural Equation Models, Least Squares Statistics
DOI: 10.1080/00207390802276192
ISSN: 0020-739X
Abstract: In a balanced design (i.e. a design in which all cells have the same number of observations), if the effects in the linear model are random and normally distributed, the distribution of the ratio of any sum of squares (s.s.) in the ANOVA to the expected value of its mean square (m.s.) has a [chi][superscript 2]-distribution. In this note, we investigate the conditions under which this ratio is a [chi][superscript 2] if the design is not balanced.
Abstractor: As Provided
Number of References: 2
Entry Date: 2009
Accession Number: EJ829582
Database: ERIC
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Description
Abstract:In a balanced design (i.e. a design in which all cells have the same number of observations), if the effects in the linear model are random and normally distributed, the distribution of the ratio of any sum of squares (s.s.) in the ANOVA to the expected value of its mean square (m.s.) has a [chi][superscript 2]-distribution. In this note, we investigate the conditions under which this ratio is a [chi][superscript 2] if the design is not balanced.
ISSN:0020-739X
DOI:10.1080/00207390802276192