Haves, Halves, and Have-Nots: School Libraries and Student Achievement in California Page: 105
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Prior to multiple regression, factor analysis was used to combine variables within each of
three areas: school library media program elements such as staffing, budget, and services
available; school variables such as average teacher salary, percent of teachers fully credentialed,
and percentage of English language learners; and community variables such as parent education
level and percent of students eligible for free and reduced lunch. In a hierarchical solution,
predictor variables are entered in a series of groups, allowing the researcher to determine if each
new group of variables adds predictive value. The hierarchical model is frequently used to
control for one set of variables while determining the effect of another set of variables on the
dependent variable (Pedhazur, 1982). In this study, school and community variables were
entered in the first step, followed by library variables. Each regression was examined to make
sure assumptions about linearity, normality and multicollinearity were met. Linearity was tested
by examining plots of standardized residuals against standardized estimates of the dependent
variable to see if the pattern was random. In addition, each regression was checked to see that the
standard deviation of the residuals exceeded the standard deviation of the dependent variable
(Hutcheson & Sofroniou, 1999). Normality was tested by inspecting histograms of the residuals
and values of skewness and kurtosis (Hutcheson & Sofroniou, 1999). Multicollinearity was
tested through inspection of tolerance and variance inflation factor (VIF) values (Leech, 2005).
When statistically significant correlations were found between specific library services
and student achievement in either partial correlations or multiple regression, bivariate
correlations were also used to determine the relationship between that particular service and the
level of both certificated and total library staffing .n For the purposes of this study, statistical
significance was set at p <.05. Data was gathered and analyzed using the Statistical Package for
the Social Sciences (SPSS 14.0).
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Achterman, Douglas L. Haves, Halves, and Have-Nots: School Libraries and Student Achievement in California, dissertation, December 2008; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc9800/m1/119/: accessed October 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .