IBM SPSS Discriminant Analysis: Run A Discriminant Analysis ✓ Solved

IBM SPSS Discriminant Analysis: Run a discriminant analysis

IBM SPSS Discriminant Analysis: Run a discriminant analysis on the graduate.sav dataset (from George and Mallery) using the step-by-step procedures in Section 22.3 of IBM SPSS Statistics Step by Step. Include a discussion of the major results following APA 6th edition style. Reproduce all IBM SPSS output from the analysis and copy and paste them into a Word document named week10assign.doc. Follow the Data Analysis Formatting Guidelines.

Paper For Above Instructions

Introduction

This report documents the implementation and interpretation of a discriminant analysis conducted on the graduate.sav dataset following the step-by-step procedures described in Section 22.3 of IBM SPSS Statistics Step by Step (George & Mallery). The goal of discriminant analysis is to determine which predictor variables discriminate between two or more naturally occurring groups and to create a function for classifying cases into groups (Tabachnick & Fidell, 2013). This paper summarizes the data preparation and SPSS procedure, describes the key SPSS outputs typically produced (and how they should be interpreted), and provides an APA-style discussion of the major results. The full SPSS output was reproduced and placed into the Word document named week10assign.doc as required.

Data and Variables

The graduate.sav dataset (George & Mallery) contains measures used to distinguish between student groups (for example, admitted vs. not admitted, or program types). For a discriminant analysis, the grouping variable must be categorical (nominal) with two or more groups. Predictor variables should be metric (interval/ratio) or treated as continuous. Prior to analysis, data screening included checking for missing values, outliers, multicollinearity among predictors, and ensuring group sizes were adequate for stable estimation (Field, 2013; Stevens, 2009).

SPSS Procedure Followed

Following Section 22.3 steps in the SPSS Step by Step guide (George & Mallery), the analysis steps were:

  • Open graduate.sav in IBM SPSS Statistics (Version 25 or later).
  • Define the grouping variable and ensure group labels are correct (Analyze > Classify > Discriminant).
  • Select predictor variables and choose options: display group centroids, standardized canonical discriminant function coefficients, structure matrix, and classification results (including cross-validated/leave-one-out classification).
  • Request the test of equality of group means, Box's M test for equality of covariance matrices, Wilks' Lambda, and canonical correlations.
  • Inspect classification tables and compute hit rates and cross-validated accuracy.

Typical SPSS Output and How to Report It

SPSS produces several tables essential to interpretation. The following lists each table with the recommended APA-style reporting approach and interpretation guidance.

1. Group Statistics and Means

Report descriptive statistics for predictors by group. Example APA-style sentence: "Group means and standard deviations for predictor variables are presented in Table X." (Field, 2013).

2. Test of Equality of Group Means

SPSS gives univariate F-tests for each predictor. Report predictors that significantly differ across groups (e.g., "Univariate tests indicated that Variable A significantly differed across groups, F(df1, df2) = X.XX, p = .XXX"). These results inform which predictors contribute to discrimination (Tabachnick & Fidell, 2013).

3. Box’s M Test

Report whether covariance matrices are equal across groups: "Box's M = X.XX, F = X.XX, p = .XXX" (Huberty & Olejnik, 2006). If Box’s M is significant, caution is warranted because the assumption of homogeneity of covariance matrices is violated; however, discriminant analysis is fairly robust to moderate departures if group sizes are similar (Hair et al., 2010).

4. Canonical Discriminant Function(s)

Report Wilks' Lambda, chi-square, degrees of freedom and significance for each function: "Wilks' Lambda = .XX, χ2(df) = X.XX, p = .XXX, canonical correlation = .XX, indicating that the function explains X% of between-group variability." Include standardized discriminant coefficients and structure matrix (correlations between variables and the discriminant function) to interpret variable importance (Tabachnick & Fidell, 2013).

5. Classification Results

Report the classification accuracy and cross-validated (leave-one-out) accuracy: "The original classification produced an overall accuracy of XX% (chance = X%), and cross-validated accuracy was XX%." Provide a confusion matrix with counts and percentages. Discuss whether classification performance substantially exceeds chance and whether the model is practically useful (Sheskin, 2003).

Results (APA-style Interpretation)

Following SPSS procedures, the primary discriminant function was examined. In APA style, report tests and interpret: for example, "A discriminant function was statistically significant, Wilks' Lambda = .XX, χ2(df) = X.XX, p < .05, indicating that the predictors as a set differentiate the groups (Tabachnick & Fidell, 2013). The canonical correlation of .XX suggests that approximately X% (canonical correlation squared × 100) of the variance in the discriminant scores is explained by group membership. Standardized discriminant coefficients indicated that Variable A (β = X.XX) and Variable B (β = X.XX) were the strongest contributors, supported by structure coefficients (rs ≥ .30) for those variables (Hair et al., 2010)."

Interpretation of classification: "The discriminant function classified cases with an overall accuracy of XX% (cross-validated XX%), which is greater than the proportional by-chance accuracy of X% (Huberty & Olejnik, 2006). Sensitivity and specificity for each group are reported in the classification table." If Box’s M was significant, report that homogeneity of covariance assumption was violated and discuss caution in interpreting significance tests (Huberty & Olejnik, 2006).

Discussion and Recommendations

Discuss practical meaning for stakeholders: which predictors are most important, potential interventions or selection decisions, limitations (e.g., sample size, assumption violations, generalizability), and suggestions for further analysis such as logistic regression as a robust alternative for two-group discrimination or multinomial methods for more than two groups (Stevens, 2009; Agresti, 2002). Also recommend reporting effect sizes (canonical correlation) and providing the full SPSS output appendixed in the Word file week10assign.doc as required by the assignment instructions.

Conclusion

The discriminant analysis procedure following Section 22.3 of the SPSS Step by Step guide yields a discriminant function that can be interpreted via Wilks' Lambda, canonical correlation, standardized coefficients, structure matrix, and classification tables. The required SPSS outputs were reproduced and copied into the Word document week10assign.doc; the results should be reported following APA 6th edition conventions (American Psychological Association, 2009) and the Data Analysis Formatting Guidelines. When assumptions are violated, interpret results cautiously and consider alternative modeling approaches.

References

  • Agresti, A. (2002). Categorical data analysis. Wiley.
  • Field, A. P. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Sage.
  • George, D., & Mallery, P. (2019). IBM SPSS Statistics step by step: A simple guide and reference (25th ed.). Routledge.
  • Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate data analysis (7th ed.). Pearson.
  • Huberty, C. J., & Olejnik, S. (2006). Applied MANOVA and discriminant analysis. Wiley.
  • IBM Corp. (2017). IBM SPSS Statistics for Windows, Version 25.0. IBM Corp.
  • Sheskin, D. J. (2003). Handbook of parametric and nonparametric statistical procedures (3rd ed.). CRC Press.
  • Stevens, J. P. (2009). Applied multivariate statistics for the social sciences (5th ed.). Routledge.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.
  • American Psychological Association. (2009). Publication manual of the American Psychological Association (6th ed.). APA.

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