manova2 - © Gregory Carey, 1998 MANOVA II - 1 Multivariate...

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Unformatted text preview: © Gregory Carey, 1998 MANOVA II - 1 Multivariate Analysis of Variance (MANOVA) II: Practical Guide to ANOVA and MANOVA for SAS Terminology for ANOVA This chapter provides practical points in performing ANOVA and MANOVA. First, it is necessary to develop some terminology. Let us being with the Kurlu example. The structure of the data would look like this: Data Layout for the Kurlu Example Within Subjects Between Subjects Pretest Posttest Group Subject SI SF OA SI SF OA 1 (Control) 1 . . 1 (Control) 10 2 (Cognitive) 1 . . 2 (Cognitive) 10 3 (Behavioral) 1 . . 3 (Behavioral) 10 4 (Abreaction) 1 . . 4 (Abreaction) 10 The observations are the 40 patients who participated in the study. It is always recommended that the observations form the rows of the data matrix with one and only one row for an observation. For example, the data for the first observation in the Kurlu data set, Herkimer Schwatzbiggle, is given below. Name Group Sub- ject si_ pre sf_ pre oi_ pre si_ post sf_ post oi_ post Herkimer Schwatzbiggle Control 1 46 68 70 72 74 82 In entering data into a database or spreadsheet, it is entirely legitimate to make two rows for Herk, one for his pre-test scores and the second for the post-test scores. The data would then be structured like this: © Gregory Carey, 1998 MANOVA II - 2 Name Group Subject Time si sf oa Herkimer Schwatzbiggle Control 1 Pre 46 68 70 Herkimer Schwatzbiggle Control 1 Post 72 74 82 There is indeed nothing the matter with the structure in this table. One can perform ANOVAs and MANOVAs using this structure. However, setting up the ANOVA model for the structure in this table is much more difficult and error-prone than it is for the structure in the previous table. Consequently, for students learning these techniques, it is highly recommended to make certain that each row of the data matrix contains one and only one observational unit. Returning to the data, we notice that the observations are organized into groups corresponding to the four therapies. The analysis will use the variable Group as the independent variable or predictor variable. In ANOVA terms, an independent variable that classify individual observations into categories is called an ANOVA factor . The term “factor” in this sense should not be confused with a “factor” from factor analysis. In the Kurlu example, there is one and only one factor. When there is only one factor, the design is referred to as a oneway ANOVA. When there is more than a single ANOVA factor, the design is called a factorial design. For example, suppose that the patients in the Kurlu study were subdivided into those who had previous treatment for the disorder and those who had no previous treatment. If the ANOVA model then used the presence or absence of prior treatment as an independent variable, the design would look like that in the following table....
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This note was uploaded on 05/12/2010 for the course APPLIED ST 2010 taught by Professor Various during the Spring '10 term at Universidad Nacional Agraria La Molina.

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manova2 - © Gregory Carey, 1998 MANOVA II - 1 Multivariate...

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