Bachelor's Degree Seekers: Analysis of Variation
Range of Variation
Institution versus Program
For bachelor’s degree-seeking students who enrolled in 2008-09, variation in cumulative net VAE across programmatic cohorts in a single institution was larger than variation in cumulative net VAE across institutional cohorts.
This finding is visible in the exhibit below, in which the range of the green dots (which represent cumulative net VAE of programmatic cohorts within a single institutional cohort) is larger than the range of the yellow hashmarks (which represent cumulative net VAE of institutional cohorts).
Exhibit B9. Cumulative Net VAE for Bachelor’s Degree-seeking Students in Institutional Cohorts and in Programmatic Cohorts within Institutional Cohorts, Entry Year 2008-09
Exhibit Note: In the exhibit above, yellow hashmarks represent institutional cohorts of bachelor’s degree-seeking students who enrolled in 2008-09, and columns of green dots represent programmatic cohorts within the associated institutional cohort. Cumulative net VAE values in this exhibit are averages, stated in 2023 dollars, for cohorts of entering students that include a mix of eventual completers and non-completers.
Institution versus Demographic Group
For bachelor’s degree-seeking students who enrolled in 2008-09:
Variation in cumulative net VAE across demographic cohorts organized by students’ household income level, within a single institutional cohort, was smaller than variation in cumulative net VAE across institutional cohorts.
Similarly, variation in cumulative net VAE across demographic cohorts organized by students’ high school math achievement, within a single institutional cohort, was smaller than variation in cumulative net VAE across institutional cohorts.
These two findings are visible in the exhibit below, in which the range of the red dots (which represent cumulative net VAE for demographic cohorts organized by students’ income level, within a single institutional cohort) and the range of the green dots (which represent cumulative net VAE for demographic cohorts organized by students’ high school math achievement, within a single institutional cohort) are smaller than the range of the yellow hashmarks (which represent cumulative net VAE of institutional cohorts).
Exhibit B10. Cumulative Net VAE for Bachelor’s Degree-seeking Students in Institutional Cohorts and in Demographic Cohorts within Institutional Cohorts, Entry Year 2008-09
Exhibit Note: In the exhibit above, yellow hashmarks represent institutional cohorts of bachelor’s degree-seeking students who enrolled in 2008-09, and columns of red and green dots represent various demographic cohorts within the associated institutional cohort. Cumulative net VAE values in this exhibit are averages, stated in 2023 dollars, for cohorts of entering students that include a mix of eventual completers and non-completers.
ANOVA
Introduction
Mathematica’s technical report includes a comprehensive analysis of the variation that we observe in cumulative net VAE outcomes across institutional, program, and demographic cohorts of bachelor’s degree-seeking students who enrolled in 2008-09. This analysis is referred to in Mathematica’s report as an ANOVA. ANOVA is short for “analysis of variation.”
The ANOVA quantifies how much of the variation in bachelor’s degree-seeking students’ cumulative net VAE can be explained, on the one hand, by their choice of institution (holding constant their choice of program, their level of high school math achievement, or their income level) versus, on the other hand, by their choice of program, their level of high school math achievement, or their income level (holding constant their choice of institution).
ANOVA Findings
The ANOVA for bachelor’s degree-seeking students who enrolled in 2008-09 is summarized in the findings and exhibit below.
- Institution Choice versus Program Choice. Bachelor’s degree-seeking students’ choice of program, holding constant their choice of institution, explained more of the variation in their cumulative net VAE (35%) than did their choice of institution, holding constant their choice of program (20%).
- Institution Choice versus High School Math Achievement. Bachelor’s degree-seeking students’ level of high school math achievement, holding constant their choice of institution, explained less of the variation in their cumulative net VAE (13%) than did their choice of institution, holding constant their level of high school math achievement (51%).
Institution Choice versus Income Level. Bachelor’s degree-seeking students’ household income level, holding constant their choice of institution, explained substantially less of the variation in their cumulative net VAE (4%) than did their choice of institution, holding constant their income level (85%).
This finding implies that cumulative net VAE for bachelor’s degree-seeking students — regardless of their household income level — is closely related to the attributes of the institutions in which they enroll.
Exhibit B11. Variation in Cumulative Net VAE Explained by Students’ Institution Choice Versus Students’ Choice of Program, High School Math Achievement Level, or Income Level for Bachelor’s Degree-seeking Students, Entry Year 2008-09
Exhibit Note: In the exhibit above, percentages in blue represent the percent of variation in cumulative net VAE explained by students’ choice of institutions, holding constant their choice of program, high school math achievement level, or income level. Percentages in red represent the percent of variation in cumulative net VAE explained by students’ choice of program, high school math achievement level, or income level, holding constant their choice of institution. Percentages in gray represent the unexplained percent of variation in cumulative net VAE.