# Discriminant Analysis

While regression analysis evaluates the ability of multiple predictor variables to predict values on a single continuous variable, discriminant analysis evaluates the ability of multiple predictor variables to predict classification on a single categorical variable. Discriminant analysis can also be viewed as the reverse of a MANOVA: In MANOVA, the IVs are the groups and the DVs are the predictors. In DA, the IVs are the predictors and the DVs are the groups. (In order to avoid semantic confusion, it’s easier to refer to IVs as the predictors—or discriminating variables—and to DVs as the grouping variables.)

The emphases of MANOVA and DA are different. While MANOVA seeks to find a linear combination of variables that will maximize the test statistic, DA is used to establish the linear combination of dependent variables that maximally discriminates among groups. DA is used to predict membership in naturally occurring groups and to determine if a combination of variables can reliably predict group membership. Several variables are included in a study to see which ones best contribute to the discrimination between groups.

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As with factor analysis, discriminant functions are identified through the analysis, but it remains for the researcher to provide a meaningful interpretation and labeling of these.

Use the Discussion Area to ask for help in completing the tasks from your classmates and the facilitator; likewise, offer your suggestions to those asking for help. Participating in this community of scholars will help you clarify processes, solve problems, and gain the immediate reinforcement you need to quickly solidify gains that you’re making in working with multiple variables and advanced statistics.

Open the Statistical Package for the Social Sciences (SPSS) data file created in M6: Assignment 1. Use the following variables:

Create a Grouping Criterion Variable: Using the continuous data for Number of Previous Hospitalizations, transform this into categorical data by assigning patients to different categorical groups. You will add a new variable to your data file, which indicates which group each case falls into. For example, use the descriptive statistics and frequency information for the number of hospitalizations to decide your cut-offs for scores to define each group and then to assign patients to a group such as Group 1 (lower number of hospitalizations), Group 2 (medium number of hospitalizations), and Group 3 (higher number of hospitalizations) or you may consider quartiles, a median split, and dividing by standard deviation units. Justify your method.

Select five (or more, if justified) continuous variables to use as predictor variables for your analysis. Briefly justify your choices.

Conduct a discriminant analysis of these data. Use the same methods and choices found in the textbook’s sample study. Include tests for homogeneity of group variances.

Save the SPSS file as R7034_M7_A1_LastName_FirstInitial.sav.

Prepare a two- to three-page (plus Appendix for tables) response, which presents a summary report of the following information:

• State a research question that could be studied using the specified variables for a discriminant analysis.
• Report the results of prescreens for the missing data, multivariate outliers (Mahalanobis distance), univariate normality, and linearity (bivariate scatter plots). Indicate if any transformations or other decisions are required.
• In your Appendix, report group descriptive statistics, analysis of variance (ANOVA) summary tables, summary of steps, eigenvalues, Wilks’ lambda table, standardized discriminant function coefficients, cannonical correlation or structure matrix, classification of results, and discriminant function means.
• Summarize the results of the discriminant analysis, including an interpretation of discriminant functions. Compare the outcomes in terms of the research question.

Create your response in Microsoft Word. Name your file R7034_M7_A1_LastName_FirstInitial.doc. Submit your response to the Discussion Area by the due date assigned.

All written assignments and responses should follow APA rules for attributing sources.

Assignment 1 Grading CriteriaMaximum PointsCorrectly created a nominal variable for number of hospitalizations and assigned cases to each group.4Identified and justified choice of continuous variables to use as predictor variables for the DA.4Accurately interpreted the results of prescreens for the missing data, multivariate outliers, univariate normality, and linearity.8Conducted discriminant analysis and reported the results correctly for group descriptive statistics, ANOVA summary tables, summary of steps, eigenvalues, Wilks’ lambda table, standardized discriminant function coefficients, correlation coefficients or structure matrix, classification of results, and discriminant function means.36Presented an informative narrative summary of the analysis.24Participated actively in the Discussion Area by asking for or providing clarification of a response, addressing gaps, offering suggestions, and asking for help, as needed.8Wrote in a clear, concise, and organized manner; demonstrated ethical scholarship in accurate representation and attribution of sources, displayed accurate spelling, grammar, and punctuation.4Total:88

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