Lab 10. A factorial MANOVA example.
This lab will use data from the 2019 Survey of Household Economics and Decision Making:
Since 2013, the Federal Reserve Board has conducted the Survey of Household Economics and Decisionmaking (SHED), which measures the economic well-being of U.S. households and identifies potential risks to their finances. The survey includes modules on a range of topics of current relevance to financial well-being including credit access and behaviors, savings, retirement, economic fragility, and education and student loans.
We will define, run, interpret and discuss a 2 x 3 factorial MANOVA on these data.
A. Read the provided .CSV file into R. This dataset is a SUBSET of the variables provided by the SHED 2019 survey, but it includes all observations.
B. Substantial cleaning of the data will be necessary, as follows.
The dependent variables you will analyze are built from provided variables B2, B3, B6, B7_a, and B7_b. For variable definitions and the range of variable values, see the provided extract from the codebook for the SHED 2019 publicly released data, file “SHED survey 2019 CODEBOOK EXTRACTS” . Create new versions of these variables, coded with numeric codes 1-4 or 1-5, as appropriate. If the respondent ”Refused” the item, define it as missing data.
The two independent variables (factors) we will use are Sex and Edu (education). Sex is a factor defined from survey variable ppgender. It has values Male and Female (only). Edu is a factor defined from survey variable ppeducat. It will have values HS (ppeducat=”Less than high school”,”High school”), SC (ppeducat=”Some College”), or BD (ppeducat=”Bachelor’s degree or higher”).
C. Check MANOVA assumptions, assuming that we will run a 2x3 MANOVA with predictors Sex and Edu, including the interaction. First, assess multivariate normality, both graphically and via an appropriate statistic, and report your conclusions. Eliminate any outliers if you find them. Second, assess homogeneity of the variance-covariance matrices. Does this seem to be satisfied (justify/discuss your answer)? Third, can you assess independence of residuals?
D. Regardless of your results from part C, run the MANOVA (omitting any observations with missing values) and discuss your findings. If there is any disparity in the results based on using different multivariate statistics, let the results for Pillai’s trace criterion guide your conclusions. Use something resembling APA format in your one-paragraph report. Add a second paragraph clarifying whether this is a balanced or unbalanced design, and mentioning what are the implications for estimation and interpretation.
E. Do you see any need to conduct tests of simple effects or simple main effects? Discuss.