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# Analysis

The following analysis examines many of the variables in the previous sections. In general, the analysis centers on the question of whether there are substantial and statistically significant differences in the default rates of borrowers who are grouped according to the categories defined by these variables. The default rate is defined as the percentage of borrowers who entered repayment within a given federal fiscal year and who defaulted either within that year or the following year.

This report provides the default rates for each category of borrower defined by the variables. Statistical measures will ascertain the strength of relationship between an explanatory variable and the default behavior variable and will determine whether the relationship is statistically significant. For some numeric variables, the analysis will additionally determine whether the means for those variables are different for defaulters and non-defaulters (See Appendix A). As an example, the analysis will pool defaulters and non-defaulters into separate groups and calculate an average SAT equivalency score for each group.

Each section is organized in the following manner. A short overview of the findings will lead off a section. Then, a summary table will describe the results of the applicable statistical tests for the variables in that section. Following the summary table, a subsection describes the results for each individual variable. The results are provided in both a narrative and tabular form.

The summary table for each section indicates whether statistically significant relationships exist and provides tests for strength of association. The summary tables are sorted in descending order of a statistic called the Uncertainty Coefficient, which indicates strength of association between each variable and default. Strength of association will be at its highest when a variable defines a category (or group of categories) that has a relatively high default rate and also contains most of the defaulters. The Uncertainty Coefficient ranges in value between 0 and 1. The higher the value of the Uncertainty Coefficient, the stronger the relationship between the variables is. The summary table also lists values for Cramer’s V, Gamma and the Spearman Correlation Coefficient, the latter two of which measure strength of relationship for ordinal variables – variables whose values indicate some sort of natural ordering. Cramer’s V, like the Uncertainty Coefficient, varies between 0 and 1, with higher values indicating greater strength of association. For the Gamma and Spearman measures, values can range from -1 to +1 and higher absolute values of a statistic indicate a greater strength of relationship. If a Gamma or Spearman measure is statistically significant, it will have a gray highlight in the table. This study will regard a variable as statistically significant when the probability is 5 percent or less that there is no association between the variable and default.

The default rate table within each variable’s subsection is arranged for easy interpretation. Tables that display variables with a natural order to them – like Number of Semesters Enrolled Before Departure – will be sorted in order of increasing value of the variable. However, tables that describe variables with named categories – like Type of Admission – will be sorted in ascending order of the percentage of borrowers who default. The gray shaded areas in every table identify the categories that have default rates lower than the average default rate (4.7 percent, or 600 defaulters out of 12,776 total undergraduate borrowers). The white areas of a table indicate the groups who have default rates that are greater than the average.

This study utilizes an average default rate (of 4.7 percent) that is higher than Texas A&M’s official cohort default rate for fiscal year 2000, which is 2.3 percent. The rate is higher than

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