Default Rate Default rate was used both as an outcome variable and as an explanatory variable in the analyses. It was used as an outcome variable to determine if there are school characteristics that predict what the default rate of the school will be. It was also used as an explanatory variable to determine if the default rate of schools is related to school performance as measured by graduation, withdrawal, and TRP. Obviously, default could not have a direct, causal relationship with these outcomes because it occurs after them. Default rate could, however, be an indirect measure of the qualifications of the students recruited by the school or the quality of the instruction these students are provided. Default rate, for example, in each of the five years for which we have data has had a high one-to-one correlation with the percentage of students classified as ATB (r = .42 in the 1994 data). This coefficient indicates a strong tendency for default rates at schools to increase as the percentage of students classified as ATB at those schools increases. The multiple regression analysis tests whether this relationship remains when variables measuring many other school characteristics are entered into the equation. The default rates are calculated by the U.S. Department of Education. For schools with 30 or more former students in default for the fiscal years that ended two years prior to the time of calculation. The Department does not calculate rates for schools with less than 30 students in default, because rates based on small numbers can vary widely. It is very unlikely, however, that the schools for which the Department did not calculate rates have no defaults. Consequently, we have substituted the mean calculated for schools with reported default rates for those schools for which default rates were not reported. Schools that actually reported zero default rates were used in the calculation of the mean that was used for schools that did not report rates. Measures of School Characteristics The annual report filed with the Accrediting Commission includes questions about prior education of students, sources of student aid, staffing, facilities, complaints or legal actions, and other aspects of the school's operation. Many of these questions were converted into measures that could be entered into a multiple regression equation. These measures were of two types, categorical and continuous variables. Categorical Variables A categorical variable indicates whether a characteristic is present or not. Values of 1 and O are assigned arbitrarily to indicate the presence or absence of a characteristic. The variables used in this analysis were coded so that the 1 value was always assigned to the "Yes" answer. There are certain "Yes" answers, however, that were considered likely to be associated with less positive outcomes. The following variables usually have negative relationships with positive outcomes (graduation and TRP) and positive relationships with negative outcomes (withdrawal and default): Some other characteristics usually have positive relationships with positive outcomes and negative relationships with negative outcomes. These variables include: linkage programs with public or private funding sources for funding occupational training, — articulation agreements with other institutions, having separate facilities, being the main rather than branch campus of a school. When reviewing the results presented in this report, it is important to keep in mind that a negative sign on a regression coefficient does not always indicate a relationship that schools should try to avoid. Both the nature of the characteristic and the nature of the outcome must be considered. If the outcome is undesirable, withdrawal or default, and the school characteristic is desirable, e.g., dual accreditation, a significant negative coefficient indicates a condition a school should try to achieve. The negative coefficient indicates that schools that have the characteristic tend to have lower rates of the undesirable outcome. In the reverse condition when the outcome is positive, graduation or TRP, and the school characteristic is undesirable, e.g., complaints under review, a negative coefficient once again indicates a desirable condition. In this case, the negative coefficient indicates that schools that do not have the undesirable characteristic have higher rates of the desirable outcome. Continuous Variables Continuous variables can have a wide range of values. Most of the continuous variables used in this analysis are percentages or rates calculated by dividing a characteristic of interest by a base number that enables comparisons to be made across schools. For example, the actual number of students at a school who are classified as Ability to Benefit (ATB) has little meaning in itself. When the number of ATB is converted to a percentage of all enrolled students, comparisons can be made across schools. report: These are the continuous variables that were used for the analyses presented in this Percentage of full-time enrollment receiving the following kinds of financial aid Stafford loans Supplemental loans to students Pell grants Percentage of full-time enrollment- With General Educational Development (GED) certificates Percentage of part-time enrollment With other postsecondary education With high school diploma With General Educational Development (GED) certificates Average length of programs in weeks, weighted by number of students in each program3. Number of full-time equivalent instructional staff Student/faulty ratio, calculated by dividing student full-time equivalent enrollment by the number of full-time equivalent instructors. Staff turnover rate, calculated by dividing number of instructors that departed during the year by total number of instructors employed during the year. Calculated separately for full- and part-time staff. Ratio of number of full-time staff to part-time staff employed during the year Total full-time enrollment. Total part-time enrollment. The enrollment variables were used as continuous variables in the one-to-one correlational analyses. For the multiple regression analyses, however, it was necessary to convert enrollment into a categorical variable. Enrollment was used as the denominator in the calculation of many of the rates used in the analysis. This leads to a technical problem in regression analysis called multicollinearity. When independent variables have substantial intercorrleation, multiple regression can yield misleading results. To deal with this problem and still yield estimates of the effects of enrollment on the outcomes, total full-time enrollment was converted to a set of variables with the following categories: The percentage of students with prior postsecondary education is reported, but because of the technical requirements of multiple regression, not used as independent variable. 3 Another measure of program length was also calculated: weighted average program clock hours. Preliminary analyses found that 90 schools did not provide clock hours data so this variable was not used. Schools with total enrollment of 300 or less These categories are interpreted in a way similar to the interpretation of the single categorical variables discussed above. The regression coefficient for a single categorical variable reflects the effects of the presence of that variable and is interpreted with reference to the absence of that variable. With a set of variables, such as that created for total enrollment, the regression coefficients are interpreted with reference to the one category in the set that is not entered into the equation. In the regressions presented in chapter 3, the category not entered was enrollments of 901 or more. Schools in the categories with lower enrollments are thus interpreted in comparison to schools in the largest enrollment category. Two other variables were also created to facilitate the analysis. A comparison of the ATB and default rate variables in the 1990 data found some schools with very high percentages of ATB students had very low default rates and vice-versa. The simple correlation of percent ATB and default rates reflects only the linear (straight-line) component of this relationship. To test if the curved (quadratic) components in the relationships between ATB and the outcome variables were significant, the variable ATB2 was created by squaring the ATB variable. The second variable was created to determine if there is an interaction between the percentage of students at a school that received Pell grants and the percentage of ATB students at that school. Separately these variables reflect the presence in a school of students from low income families (Pell) and those who have not done well in school in the past (ATB). There is considerable evidence in educational research that low family income and poor school performance tend to go together. The interaction variable was created by multiplying the percent of students receiving Pell at a school by the percent of ATB students at that school. The variable resulting from this multiplication tests if these two variables have a joint effect on the outcome variables independent of their separate effects. Since these are unusual variables, a note on their presentation in the tables in Chapter 2 is necessary. The multiplication use to create these two variables yielded very large values. Regression coefficients are interpreted as the rate of change in dependent variables for a unit change in the independent variables. With such large values in the independent variables, the rates of change in the dependent variables are quite small, albeit, sometimes statistically significant. To present the regression coefficients in the tables without the required zeros after the decimal point, they are multiplied by 100. There are some variables which have been developed or added to the annual report form in recent years for which we do not five years of data: In preliminary analyses of the 1990 data the largest enrollment category was divided into 901 to 1200 and 1200 or more. These analyses indicated that these two categories did not differ significantly and only 3 percent of the schools were in the 901 to 1200 category. Consequently, the two largest categories were combined for subsequent analyses. Unemployment rate of the area where the school is located Percentage of students who received English as a Second Language (ESL) training Ratio of part-time to full-time students School operating under a Show Cause Order or on Reporting Average years on staff of Director of Education, Director of Placement/Placement Average tenure of instructors Because these variables were not examined all five years, we have less confidence in the results they yielded. The regression results for these variables are not presented in this report. The general direction of the findings are reported if there were statistically significant relationships with school outcomes. In the next chapter we present the summary statistics for all of the variables defined above. The chapter also includes an analysis of school outcomes by size of the full-time enrollments and by the average length of the programs offered by the schools. Chapter 3 presents the main results from the multiple regression analyses of the annual total data for the past five years. Chapter 4 compares the results obtained from the annual total data to those obtained from the cohort data. Chapter 5 summarizes the major findings of the report and discusses the implications of these findings. |