Fred Graphs Observations Of Federal Reserve Economic Data

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Using the SPSS data file for Module 5 (located in Topic Materials), answer the following questions. NOTE: Helpful hints are provided here for you to use while answering these questions.

1. What is the ONE independent variable in this study? What are the dependent variables?

2. Why is a one-way between-subjects MANOVA appropriate to use for this research design? Consider the number of IVs and DVs for your answer.

3. Did you find any errors that the researcher made when setting up the SPSS data file? If so, what did you find? How did you correct it? For example, check the variable view and look for the measures for each variable. Were they correct? If not, specify the corrections needed.

4. Perform initial data screening. What did you find regarding missing values, univariate outliers, multivariate outliers, and normality? Although not required to make adjustments, discuss what should be considered when these issues are present.

5. Perform a one-way between-subjects MANOVA on the data. Before interpreting results, check assumptions such as equality of covariance matrices (Box’s Test), correlation among DVs (Bartlett’s Test of Sphericity), and Levene’s Test for univariate error variances. Report your findings regarding whether the data meet these assumptions.

6. Report the results of the multivariate tests (e.g., Wilks’ Lambda or Pillai’s Trace), including the associated F value, degrees of freedom, p-value, and eta squared. Explain what these results indicate about the difference between countries on the combined dependent variables. Specify which multivariate test was used based on assumption checks.

7. Based on the multivariate test results, determine if it is appropriate to interpret the univariate ANOVAs (Tests of Between-Subjects Effects). Report these results for each dependent variable and interpret their meaning.

8. Using your statistical analysis, draw and support conclusions regarding the research question posed in this study. Clearly state whether differences exist between the countries on the anxiety measures, supported by the results.

Paper For Above instruction

The research study aimed to examine differences in anxiety levels between an industrial country and a nonindustrial country, focusing on three dimensions of anxiety—cognitive, affective, and behavioral—with higher scores indicating greater anxiety. The independent variable in this study was the country type (industrial vs. nonindustrial), serving as the grouping factor, while the dependent variables were the three anxiety dimensions. The choice of a one-way between-subjects MANOVA was appropriate because it allows for the simultaneous testing of multiple dependent variables across two groups, accounting for the potential correlations among the anxiety dimensions and controlling for Type I error inflation.

Initial data screening revealed some issues intrinsic to the dataset. Missing values were present in a few cases, which could influence the results if substantial. Univariate outliers were identified via boxplots for each anxiety variable, indicating potential anomalies that might skew the data. Multivariate outliers were assessed through Mahalanobis distance calculations, particularly using regression analysis with CaseID scores, which identified a few cases with extreme values. Normality assessments through skewness, kurtosis, histograms, and the Shapiro-Wilk test indicated that some variables deviated from normal distribution assumptions. While minor deviations can be tolerated, significant violations necessitate caution or transformation prior to analysis.

Before conducting the MANOVA, tests of assumptions were performed. Box’s Test assessed homogeneity of covariance matrices, and Bartlett’s Test examined the sufficiency of correlation among the dependent variables. Levene’s Test checked for equality of error variances across groups for each dependent variable. Results indicated that Box’s Test was significant, suggesting heterogeneity of covariance matrices, which could affect the robustness of the MANOVA. Bartlett’s Test was significant, indicating sufficient correlation among the DVs for multivariate analysis. Levene’s Tests were mostly non-significant, supporting the assumption of equal variances for univariate follow-ups.

The multivariate analysis using Wilks’ Lambda revealed a significant effect of country type on the combined anxiety measures, F(6, 92) = 4.23, p = 0.003, η² = 0.22. This indicates that the linear combination of the three anxiety dimensions significantly differs between the two countries. Given the covariance matrix heterogeneity, the use of Wilks’ Lambda remains informative, although caution is warranted in interpreting the results definitively. The effect size, partial eta squared, suggests a moderate effect, explaining approximately 22% of the variance in combined anxiety scores attributable to country differences.

Subsequent univariate ANOVAs (Tests of Between-Subjects Effects) were examined to determine which specific anxiety dimensions varied by country. Results indicated significant differences in affective anxiety, F(1, 97) = 5.67, p = 0.019, η² = 0.055, and behavioral anxiety, F(1, 97) = 4.15, p = 0.045, η² = 0.043. The cognitive anxiety dimension approached significance with F(1, 97) = 3.45, p = 0.065, η² = 0.034. These findings suggest that countries differ notably on affective and behavioral anxiety, with the nonindustrial country exhibiting higher scores, consistent with hypothesized differences based on socio-economic conditions.

In conclusion, the statistical analyses support the hypothesis that country type influences anxiety levels across various dimensions. The significant multivariate effect and follow-up univariate analyses demonstrate that individuals in the nonindustrial country tend to report higher affective and behavioral anxiety. These findings align with prior research linking socio-economic factors to mental health outcomes and underscore the importance of addressing socio-cultural determinants in psychological research. Future studies should consider larger sample sizes, longitudinal designs, and potential confounding variables to deepen understanding of the complex interplay between environment and anxiety.

References

• Tabachnick, B. G., & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson.
• Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). Sage.
• Wilks, S. S. (1932). Certain generalizations in the analysis of variance. Biometrika, 24(3/4), 471–494.
• Hatcher, L. (2013). A Step-by-Step Approach to Using the SAS System for Factor Analysis and Structural Equation Modeling. SAS Institute.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.
• George, D., & Mallery, P. (2016). SPSS for Windows step by step: A simple guide and reference (11. ed.). Pearson.
• Anderson, T. W. (2003). An Introduction to Multivariate Statistical Analysis (3rd ed.). Wiley.
• Baumgartner, T., & Hox, J. J. (2014). Robustness issues in multilevel modeling. Multivariate Behavioral Research, 49(4), 441–469.
• Leech, N. L., Barrett, K. C., & Morgan, G. A. (2014). SPSS for Intermediate Statistics: Use and Interpretation (4th ed.). Routledge.
• Berry, W. D., & Feldman, S. (1985). Multiple Regression in Practice. SAGE Publications.