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Week 11 Multivariate Statistics

# Week 11 Multivariate Statistics - 1 SAN JOS STATE...

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1 SAN JOSÉ STATE UNIVERSITY College of Social Work S. W. 242 Spring 2009 Edward Cohen Week 11 April 3, 2009 Review of statistical tests so far Labs 2b & 3 Bivariate and Multivariate Linear Regression Review of Analysis Plan for Final Paper Concepts you should know: Bivariate linear regression Multivariate statistics Multivariate (or multiple) linear regression Multivariate model Control variables R 2 and adjusted R 2 Analysis of variance in linear regression F ratio in linear regression Regression coefficient (B coefficient) Standardized coefficient (Beta coefficient) t -test in linear regression I. Review—what statistical procedure would answer the research question? A. Does a group case management intervention result in fewer overall costs than an individual case management intervention? B. For decisions about those eligible vs. not eligible for SSI (Supplemental Social Security Income), does ethnicity of applicant matter? C. For caseworkers in a child welfare agency, is there a relationship between average caseload size and the number of families that reunify in a two-year period? D. Does the change in a living skills scale score vary by type of treatment: individual therapy, individual therapy with case management, or case management without therapy? E. What effect does the initial motivation for treatment have on improvement in a depression scale, controlling for age, gender, and seriousness of initial symptoms? multivariate regression II. Bivariate and Multivariate (or multiple) linear regression

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2 A. What is “regression”? Regression is a form of correlation analysis; it can be either bivariate or multivariate. Bivariate regression predicts the value of a dependent (or outcome) variable from an observed independent (or predictor) variable. The dependent variable must be continuous. The independent variable is most often continuous. (Bivariate regression is not used much—instead use correlation for two continuous variables. Use t -tests or ANOVA if the IV is categorical.) Multivariate (or multiple) regression predicts the value of a dependent (or outcome) variable from two or more observed independent (or predictor) variables. The independent variables (or control variables) may be continuous or categorical. B. You can say ““The IV is predictive of the DV, controlling for other IVs” C. Controlling for a variable (e.g. gender) means 1. We collect data on that variable 2. We include that variable in the list of independent variables in our model 3. The regression analysis separates out the effects of each attribute (male, female) 4. You can interpret the resulting statistics for all other variables as if by saying “regardless of gender” 5. So you can say about any independent variable, “controlling for the effects of all other variables…” D. Bivariate example 1. Null and Alternative Hypotheses y H A : For children in residential care, the number of strength-based comments by staff is
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Week 11 Multivariate Statistics - 1 SAN JOS STATE...

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