Anova
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Analysis of Variance ANOVA Charles Quigley Liberty University
Definition A statistical technique for testing for differences in the means of several groups (Howell, 2008, p. 375)
(Varience.gif )
Components • Concepts/Models – Fixed – Random – Mixed
• Types – – – –
One-way ANOVA One-way ANOVA for repeated measures Factorial ANOVA Multivariate analysis of variance
Fixed-effects Models (I) Fixed-effect models are used to compare groups that are “identified by some characteristic that is repeatable and interesting” (McDonald, 2008, ¶ 2) – Impact of ambient temperature on mood – Paw-lick latency in novel environments – Variations in species in geographically isolated environments
Random-effects Models (II) The groups are chosen from a larger number of possible groups. And group means may be similar, but patterns of differences may be evident (McDonald, 2008).
Mixed-effects Models (III) Used when both fixed and random elements are present (Fredrick, 1999).
Types • • • •
One-way ANOVA One-way ANOVA for repeated measures Factorial ANOVA Multivariate analysis of variance
One-way ANOVA • Looking for differences between a groups – “For example, you might have data on student performance in non-assessed tutorial exercises as well as their final grading. You are interested in seeing if tutorial performance is related to final grade. ANOVA allows you to break up the group according to the grade and then see if performance is different across these grades” (Markham, 2000, ¶ 2).
One-way ANOVA for Repeated Measures • Used to compare repeated measurements of members of the same group (Markham, 2000). – Results from a pre, mid, and post test of a class can be used
Factorial ANOVA • “An experimental design in which every level of each variable is pare with every level of each other variable” (Howell, 2008, p. 419) In this illustration, each “object in the data set is exposed or characterized by a particular combination of the treatment variables” (McElroy, 2007). http://www.ext.vt.edu/departments/entomology/images/aphid.jpeg
Factorial Mixed-design ANOVA This is used when researchers have a mixture between groups and repeated variables (Field, 2008) – To find the best combination of medication and treatment models for various groups of students who display ADHD.
Multivariate analysis of variance (MANOVA) This is used when there is more than one dependent variable, for example: • • • • •
What are the main effects of the independent variables? What are the interactions among the independent variables? What is the importance of the dependent variables? What is the strength of association between dependent variables? What are the effects of covariates? How may they be utilized? (Conner, 2002 ).
Works Cited -- (N.D.) Aphid.jpeg. Retrieved November 8, 2008 from http://www.ext.vt.edu/departments/entomology/images/aphid.jpeg -- (N.D.) Varience.gif Retrieved November 8, 2008 from http://www.materresearch.org/ mrsc/Resources/StatCourse2006/pics/Variance.gif Conner, E. (2002). MANOVA. Retrieved November 8, 2008 from http://userwww.sfsu.edu/~efc/classes/biol710/manova/manovanew.htm Field, A. (2008). C8058 (Research Methods in Psychology): Mixed ANOVA using SPSS. Retrieved November 8, 2008 from http://www.statisticshell.com/mixed.pdf Fredrick, B. (1999). Fixed-, Random-, and Mixed-Effects ANOVA Models: A User-Friendly Guide for Increasing the Generalizability of ANOVA Results Paper presented at the Annual Meeting of the Southwest Educational Research Association (San Antonio, TX, January 21-23, 1999). Retrieved November 8, 2008 from http://eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/17/2c/5c.pdf Howell, T. (2008). Fundamental Statistics for the Behavioral Sciences. 6th Ed. Belmont, CA: Thomson Higher Education. Markham, S. (2000). Analysis of Variance (ANOVA). Retrieved November 8, 2008 from http://www.csse.monash.edu.au/~smarkham/resources/anova.htm McDonald, J. (2008). Handbook of Biological Statistics: Model I vs. Model II anova. Retrieved November 8, 2008 from http://udel.edu/~mcdonald/statanovamodel. html McElroy, D. (2007) Biology283.Lectures22 Retrieved November 8, 2008 from http://bioweb.wku.edu/faculty/McElroy/BIOL283/283lects22.htm
Definition A statistical technique for testing for differences in the means of several groups (Howell, 2008, p. 375)
(Varience.gif )
Components • Concepts/Models – Fixed – Random – Mixed
• Types – – – –
One-way ANOVA One-way ANOVA for repeated measures Factorial ANOVA Multivariate analysis of variance
Fixed-effects Models (I) Fixed-effect models are used to compare groups that are “identified by some characteristic that is repeatable and interesting” (McDonald, 2008, ¶ 2) – Impact of ambient temperature on mood – Paw-lick latency in novel environments – Variations in species in geographically isolated environments
Random-effects Models (II) The groups are chosen from a larger number of possible groups. And group means may be similar, but patterns of differences may be evident (McDonald, 2008).
Mixed-effects Models (III) Used when both fixed and random elements are present (Fredrick, 1999).
Types • • • •
One-way ANOVA One-way ANOVA for repeated measures Factorial ANOVA Multivariate analysis of variance
One-way ANOVA • Looking for differences between a groups – “For example, you might have data on student performance in non-assessed tutorial exercises as well as their final grading. You are interested in seeing if tutorial performance is related to final grade. ANOVA allows you to break up the group according to the grade and then see if performance is different across these grades” (Markham, 2000, ¶ 2).
One-way ANOVA for Repeated Measures • Used to compare repeated measurements of members of the same group (Markham, 2000). – Results from a pre, mid, and post test of a class can be used
Factorial ANOVA • “An experimental design in which every level of each variable is pare with every level of each other variable” (Howell, 2008, p. 419) In this illustration, each “object in the data set is exposed or characterized by a particular combination of the treatment variables” (McElroy, 2007). http://www.ext.vt.edu/departments/entomology/images/aphid.jpeg
Factorial Mixed-design ANOVA This is used when researchers have a mixture between groups and repeated variables (Field, 2008) – To find the best combination of medication and treatment models for various groups of students who display ADHD.
Multivariate analysis of variance (MANOVA) This is used when there is more than one dependent variable, for example: • • • • •
What are the main effects of the independent variables? What are the interactions among the independent variables? What is the importance of the dependent variables? What is the strength of association between dependent variables? What are the effects of covariates? How may they be utilized? (Conner, 2002 ).
Works Cited -- (N.D.) Aphid.jpeg. Retrieved November 8, 2008 from http://www.ext.vt.edu/departments/entomology/images/aphid.jpeg -- (N.D.) Varience.gif Retrieved November 8, 2008 from http://www.materresearch.org/ mrsc/Resources/StatCourse2006/pics/Variance.gif Conner, E. (2002). MANOVA. Retrieved November 8, 2008 from http://userwww.sfsu.edu/~efc/classes/biol710/manova/manovanew.htm Field, A. (2008). C8058 (Research Methods in Psychology): Mixed ANOVA using SPSS. Retrieved November 8, 2008 from http://www.statisticshell.com/mixed.pdf Fredrick, B. (1999). Fixed-, Random-, and Mixed-Effects ANOVA Models: A User-Friendly Guide for Increasing the Generalizability of ANOVA Results Paper presented at the Annual Meeting of the Southwest Educational Research Association (San Antonio, TX, January 21-23, 1999). Retrieved November 8, 2008 from http://eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/17/2c/5c.pdf Howell, T. (2008). Fundamental Statistics for the Behavioral Sciences. 6th Ed. Belmont, CA: Thomson Higher Education. Markham, S. (2000). Analysis of Variance (ANOVA). Retrieved November 8, 2008 from http://www.csse.monash.edu.au/~smarkham/resources/anova.htm McDonald, J. (2008). Handbook of Biological Statistics: Model I vs. Model II anova. Retrieved November 8, 2008 from http://udel.edu/~mcdonald/statanovamodel. html McElroy, D. (2007) Biology283.Lectures22 Retrieved November 8, 2008 from http://bioweb.wku.edu/faculty/McElroy/BIOL283/283lects22.htm
