12 Association of Research Libraries Research Library Issues 290 2017 standard deviation of the control group) in the treatment and control groups before and after matching. We detected no large imbalances above .25 after matching in each analysis, meeting the threshold suggested by Rosenbaum and Rubin.32 Before matching procedures were implemented, the covariates within the treatment and control groups differed significantly. These results also suggest that the propensity score matching decreased bias by making the observed and treatment groups more similar with regard to their covariates. Finally, we used ordinary least squares regression to examine the relationships between library users and non-library users’ development of learning outcomes. We included the propensity scores as controls to remove the component of their correlation that is due to the assignment process.33 We tested assumptions of multicollinearity, homoscedasticity, linearity, and independent/ normal errors. We found that multicollinearity assumptions were not violated and, in testing homoscedasticity, we found random scatter and variability in scatterplots of standardized residuals against the standardized predicted values. In producing histograms of standardized residuals and normal probability plots comparing the distribution of standardized residuals to a normal distribution, we found evidence for normality. Examinations of matrix scatterplots suggested the relationships between the predictor and outcome variables were relatively linear and the residual errors were independent across models. Overall, the results of these tests suggested that the assumptions were not violated for ordinary least squares regressions in this study.34 Results The first model assessed whether first-year students who used a library resource at least once were significantly more likely to report development of critical thinking and analytical skills. The results of the first regression suggest that first-year students who used any library resource at least once had significantly higher
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