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PEDAR: Research Methodology  The Road Lsss Traveled? Students Who Enroll in Multiple Institutions
Beginning Postsecondary Students Longitudinal Study
The 2001 Baccalaureate and Beyond Longitudinal Study
Accuracy of Estimates
Item Response Rates
Data Analaysis System
Statistical Procedures
Differences Between Means
Linear Trends
Multivariate Commonality Analysis
Missing Data and Adjusting for Complex Sampling Design
Interpreting the Results
Executive Summary
Full Report (PDF)
Executive Summary (PDF)
 Statistical Procedures: Linear Trends

While many descriptive comparisons in this report were tested using Student’s t statistic, some comparisons among categories of an ordered variable with three or more levels involved a test for a linear trend across all categories (in particular for persistence risk index and income), rather than a series of tests between pairs of categories. In this report, when differences among percentages were examined relative to a variable with ordered categories, Analysis of Variance (ANOVA) was used to test for a linear relationship between the two variables. To do this, ANOVA models included orthogonal linear contrasts corresponding to successive levels of the independent variable. The squares of the Taylorized standard errors (that is, standard errors that were calculated by the Taylor series method), the variance between the means, and the unweighted sample sizes were used to partition total sum of squares into within- and between-group sums of squares. These were used to create mean squares for the within- and between-group variance components and their corresponding F statistics, which were then compared with published values of F for a significance level of .05.9 Significant values of both the overall F and the F associated with the linear contrast term were required as evidence of a linear relationship between the two variables. Means and Taylorized standard errors were calculated by the DAS. Unweighted sample sizes are not available from the DAS and were provided by NCES.

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