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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