NCES 2012-046August 2012

## Chapter 8: Multivariate Analyses of Immediate Postsecondary Enrollment and Degree Attainment

#### Interpreting Logistic Model Results

For the most part, results from the logistic regression analyses are presented in the form of odds ratios that compare the odds9 of an event occurring in one group to the odds of it occurring in another group, after controlling for the effect of all of the other independent variables in the model. Odds ratios are calculated for each of the categorical independent variables used in the regression models and represent the likelihood of students in one category of an independent variable (referred to as the identity group) completing an event relative to a reference group. If the event is equally likely to occur for both groups, then the odds ratio value equals one. If a category has an odds ratio that is less than one, then students in the identity group have lower odds of immediate postsecondary enrollment than students in the reference group. For example, the odds ratio of 0.65 for males (table ELS-2) is the ratio of the odds of males immediately enrolling in postsecondary education after high school to the odds of females immediately enrolling, after accounting for the effect of all of the other independent variables in the model. The odds ratio of 0.65 indicates that the odds of a male immediately enrolling in postsecondary education after high school graduation are 35 percent lower ((odds ratio – 1) × 100) than the odds for a female (i.e., males are less likely than females to immediately enroll in postsecondary education). In this example, females are the reference category for the independent variable. If a group category has an odds ratio greater than one, then students in the identity category are more likely to exhibit a certain outcome than students in the reference category. For example, the odds ratio of 1.63 for students who first enrolled in a 4-year postsecondary institution (table BPS-2) indicates that a student who first enrolled in a 4-year institution has 63 percent higher odds of attaining a degree within 6 years than a student who first enrolled in a less-than-4-year institution. For continuous independent variables such as standardized test scores or number of postsecondary institution transfers, results are also interpreted in the form of odds ratios based on one unit of change in the independent variable. For example, in table ELS-2, the odds ratio of 1.88 for 9th-grade GPA indicates that a one-point increase in a student's 9th-grade GPA value (e.g., from a 2.0 to a 3.0) is associated with an 88 percent increase in the odds of the student immediately enrolling in postsecondary education. Asterisks (*) are used in tables to denote findings that are statistically significant at the .05 level. Detailed information about interpretation of the logistic regression coefficients is provided in the technical appendix of this report.

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9 Odds represent a ratio between p, the probability that an event will occur, and 1-p, the probability that the event will not occur (computed p/(1-p)).