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• App. A

6. Association Among Library Variables: Factor Analysis

While bivariate correlation identifies the strength of association between two variables, factor analysis expands the relationship beyond just two variables. The objective of factor analysis is to examine the relationship among library variables and create groupings of variables (factors). Generally, a procedure known as a varimax rotation is performed as part of the factor analysis for the purpose of accentuating these factor loadings. This makes it easier to determine which variables should be grouped together. Each grouping consists of variables that are most strongly associated with each other. The groupings created by a factor analysis and the strength of association among variables in a grouping are presented in a matrix that shows the correlation (factor loading) of each variable with that factor. Only factor loadings beyond a cutoff of +/- .600 are considered in describing and interpreting the groupings. The groupings created by factor analysis are expected to make sense as a group. However, it is possible for variables to be highly correlated with one another without there being an obvious explanation for that association.

6.1 Elementary School Factor Analysis

Elementary school library variables were entered into a factor analysis in order to identify variables that correlated highly with one another, forming variable groupings (factors). Only groupings with an eigenvalue of at least 1 were retained. The factor analysis resulted in nine factors that explained 67 percent of the variance in the elementary school library data.

* The highest factor loadings for these variables were lower than the +/-.600 cutoff point for inclusion in the groupings.

The following nine factors were formed for elementary school library variables:

Factor 1: Library Technology

• Library computers per 100 students
• Library computers Internet connections per 100 students
• Library computers with access to catalog per 100 students
• Library computers with CD ROM drives per 100 students
• Library computers with networked access to CD ROM resources per 100 students

Factor 2: Program Development (Staffing, Hours of Operation, and Collection)

• Library staff per 100 students
• Library staff hours per 100 students
• Library hours of operation per 100 students
• Print volumes per student
• Current print subscriptions to newspapers and magazines per 100 students
• Library video materials per 100 students

Factor 3: Leadership

• Attending faculty meetings
• Meeting with principal
• Participating in curriculum committee meetings

Factor 4: Financial and Collection Resources

• Volumes purchased in 1999-00 per 100 students
• Library operational expenditures per student

Factor 5: Collaboration

• Planning instructional units with teachers
• Teaching cooperatively with teachers
• Assisting teachers to access and utilize information on state funded programs

Factor 6: Modems and Software

• Library modems per 100 students
• Library software packages per 100 students

Factor 7: Instruction and Meetings with Peers

• Providing information skills instruction to individuals and groups
• Meeting with building and district library staff

Factor 8: Student Volunteers

Library student volunteer hours per 100 students

Factor 9: Out of District Meetings with Peers

Meeting with out of district library staff

To determine the relationship between the elementary school library variables and the percent of students who passed TAAS reading, the "TAAS performance" variable was added to the factor analysis. The factor analysis resulted in nine factors that differed somewhat from the factor analysis that included only library variables, as shown in the following matrix. The results of the factor analysis showed that elementary school students’ TAAS performance was strongly associated with Factor 7. Factor 7 consists of two variables:

• Library adult volunteer hours per 100 students
• Library computers connected to a modem per 100 students

* The highest factor loadings for these variables were lower than the +/-.600 cutoff point for inclusion in the groupings.

The following graphs present the relationship between elementary school student TAAS performance and the two library variables associated with Factor 7: adult volunteer hours per 100 students, and library modems per 100 students. Each of the graphs illustrates a definite, but nonlinear relationship with TAAS. In each instance, as the library variable (used as an independent variable) increases in value, the variance in TAAS performance decreases and the percentage of students who meet minimum expectations on TAAS increases over what is seen at lower levels of the library variable (used as an independent variable). Greater consistency in TAAS performance is associated with higher values of the library (independent) variable.

Graph IV.1 - TAAS Reading and Adult Volunteer Hours Per 100 Students

Graph IV.2 - TAAS Reading and Library Modems Per 100 Students

In the next step, a factor analysis using both library and school variables was conducted. The purpose of this step was to create a set of factors that were uncorrelated with one another for use in a multiple regression procedure. Using a set of uncorrelated factors in a multiple regression analysis is important in order to avoid multicollinearity that can make the results of multiple regression highly unreliable. The factor analysis yielded 14 factors, as shown in the following table. The 14 factors have eighenvalues of 1 or higher.

* Highest factor loading but lower than the .600 used as a cutoff.

Please note that this value is negative.

Extraction Method: Principal Components Analysis.

Rotation Method: Verimax and Kaiser Normalization

The factor analysis including both library and school variables resulted in 14 factors with eigenvalues of 1 or higher. These 14 factors are:

Factor 1: School Technology

• School computers per 100 students
• School computers with Internet connections per 100 students
• School computers with access to catalog per 100 students
• School computers with access to library databases
• School computers with CD ROM drives per 100 students
• School computers with networked access to CD ROM resources per 100 students
• School computers connected to a modem per 100 students

Factor 2: Library Technology

• Library computers per 100 students
• Library computers with Internet connections per 100 students
• Library computers with access to catalog per 100 students
• Library computers with CD ROM drives per 100 students
• Library computers with networked access to CD ROM resources per 100 students

Factor 3: Library and School Staffing, Print and Financial Resources

• Library staff per 100 students
• Library staff hours per 100 students
• Library hours of operation per 100 students
• Volumes per students
• Current subscriptions to newspapers and magazines per 100 students
• School dollars per student
• Student-teacher ratio

Factor 4: Student Ethnic and Economic Composition

• Percent of LEP students
• Percent of economically disadvantaged students
• Percent of white students
• Percent of Hispanic students

Factor 5: Leadership

• Participating in curriculum committee meetings
• Meeting with principal
• Attending faculty meetings

Factor 6: Teacher Pay and Experience

• Average teacher base salary
• Average teacher experience

Factor 7: Collaboration

• Planning instructional units with teachers
• Teaching cooperatively with teachers
• Assisting teachers to access and utilize information on state funded programs

Factor 8: Library Financial Resources

• Volumes purchased in 1999-00 per 100 students
• Library operational expenditures per student

Factor 9: African American Students

Percent of African American students

Factor 10: Library Technology Resources

• Library computers connected to a modem per 100 students
• Library software packages per 100 students

Factor 11: Asian American Students

Percent of Asian American students

Factor 12: Student Volunteers

Library student volunteer hours per 100 students

Factor 13: Meeting with Out of District Librarians

Meetings with out of district librarians

Factor 14: School Instructional Finance

Percent of school funds allocated to instruction

6.2 Middle/Junior High School Factor Analysis

The objective of the middle/junior high school factor analysis was to identify library variables correlated highly with one another, and form variable groupings (factors). Only groupings with an eigenvalue of at least 1 were retained. The factor analysis performed on middle/junior high school variables resulted in nine factors that explained 74 percent of the variance in the library data. The factor analysis produces a matrix that shows the correlation (factor loading) of each variable with that factor. The nine factors and the loadings associated with each are also listed.

* The highest factor loadings for these variables were lower than the +/-.600 cutoff point for inclusion in the groupings.

The following nine factors were formed for middle/junior high school library variables:

Factor 1: Library Technology

• Library computers per 100 students
• Library computers with Internet connections per 100 students
• Library computers with access to catalog per 100 students
• Library computers with access to library databases
• Library computers with CD ROM drives per 100 students
• Library computers with networked access to CD ROM resources per 100 students

Factor 2: Program Development (Staffing, Hours of Operation, and Print)

• Library staff per 100 students
• Library staff hours per 100 students
• Library hours of operation per 100 students
• Print volumes per student

Factor 3: Collaboration and Training

• Planning instructional units with teachers
• Providing staff development to teachers
• Assisting teachers to access and utilize information on state funded programs
• Meeting with out of district library staff
• Meeting with principal

Factor 4: Financial and Collection Resources

• Volumes purchased in 1999-00 per 100 students
• Library operational expenditures per student

Factor 5: Teaching

• Providing information skills instruction to individuals and groups
• Identifying materials for instructional units developed by teachers

Factor 6: Student Volunteers and Peer Meetings

• Library student volunteer hours per 100 students
• Meeting with building and district library staff

Factor 7: Involvement with Faculty

• Attending faculty meetings
• Library computers connected to a modem per 100 students

Factor 8: Subscription

Current subscriptions to newspapers and magazines per 100 students

Factor 9: Software Resources

Library software packages per 100 students

To determine the relationship between the nine middle/junior high school library factors and students’ TAAS performance, the "TAAS performance" variable was added to the factor analysis. This resulted in nine factors that had slightly different groupings. The results of the factor analysis showed that middle/junior high school students’ TAAS performance was primarily associated with Factor 6 and Factor 8.

Factor 6 consists of:

Library student volunteer hours per 100 students

Factor 8 includes:

Current subscriptions to newspapers and magazines per 100 students

* The highest factor loadings for these variables were lower than the +/-.600 cutoff point for inclusion in the groupings.

However, the relationship between these two variables and TAAS performance is weak. This is reflected in the low factor loadings for the TAAS variable. Indeed, none of these variables has a correlation with TAAS that is significantly different from zero.

In the next step, a factor analysis using both library and school variables was conducted. The purpose of this step was to create a set of factors that are uncorrelated with one another for use in a multiple regression procedure. The factor analysis yielded 15 factors, as shown in the following table. The 15 factors have eighenvalues of 1 or higher.

* Highest factor loading but lower than the .600 used as a cutoff.

Please note that these values are negative.

Extraction Method: Principal Components Analysis.

Rotation Method: Verimax and Kaiser Normalization

The factor analysis including both library and school variables resulted in 15 factors with eigenvalues of 1 or higher. These 15 factors are:

Factor 1: School Technology A

• School computers per 100 students
• School computers with Internet connections per 100 students
• School computers with access to catalog per 100 students
• School computers with access to library databases
• School computers with CD ROM drives per 100 students
• School computers with networked access to CD ROM resources per 100 students

Factor 2: Library and School Staffing, Print and Financial Resources

• Library staff per 100 students
• Library staff hours per 100 students
• Library hours of operation per 100 students
• Volumes per students
• Volumes purchased in 1999-00 per 100 students
• Library operational expenditures per student
• School dollars per student
• Student-teacher ratio

Factor 3: Library Technology

• Library computers per 100 students
• Library computers with Internet connections per 100 students
• Library computers with access to catalog per 100 students
• Library computers with access to library databases
• Library computers with CD ROM drives per 100 students

Factor 4: Student Ethnic and Economic Composition

• Percent of LEP students
• Percent of economically disadvantaged students
• Percent of white students
• Percent of Hispanic students

Factor 5: Leadership

• Meeting with out of district library staff
• Meeting with principal
• Assisting teachers to access and utilize information on state funded programs

Factor 6: School Technology B

• School computers with networked access to CD ROM resources per 100 students
• School computers connected to a modem per 100 students

Factor 7: Planning with and Training Teachers

• Identifying materials for instructional units developed by teachers
• Providing information skills instruction to individuals or groups

Factor 8: Native American Students

Percent of Native American students

Factor 9: Student Volunteers

Library student volunteer hours per 100 students

Factor 10: Collaboration

• Planning instructional units with teachers
• Teaching cooperatively with teachers

Factor 11: Teacher Pay and Experience

• Average teacher base salary
• Average teacher experience

Factor 12: Adults Volunteers and Software

• Library adult volunteer hours per 100 students
• Library software packages per 100 students

Factor 13: African American Students

Percent of African American students

Factor 14: Participation in Curriculum Meetings and Teacher Turnover

• Participating in curriculum committee meetings
• Teacher turnover ratio

Factor 15: Faculty Meetings

Attending faculty meetings

6.3 High School Factor Analysis

A factor analysis was used to identify high school library variables that correlated highly with one another and formed variable groupings (factors). Only groupings with an eigenvalue of at least 1 were retained. This resulted in eight factors that explained 75 percent of the variance in the high school library data. The eight factors and the loadings associated with each are listed below.

* The highest factor loadings for these variables were lower than the +/-.600 cutoff point for inclusion in the groupings.

return

The following eight factors were formed for high school library variables:

Factor 1: Library Technology

• Library computers per 100 students
• Library computers with Internet connections per 100 students
• Library computers with access to catalog per 100 students
• Library computers with access to library databases
• Library computers with CD ROM drives per 100 students
• Library computers with networked access to CD ROM resources per 100 students
• Library computers connected to a modem per 100 students

Factor 2: Program Development (Staffing and Hours of Operation)

• Library staff per 100 students
• Library staff hours per 100 students
• Library hours of operation per 100 students

Factor 3: Leadership

• Meeting with building and district library staff
• Meeting with out of district library staff
• Meeting with principal
• Attending faculty meetings

Factor 4: Resources

• Volumes purchased in 1999-00 per 100 students
• Library operational expenditures per student
• Library adult volunteer hours per 100 students

Factor 5: Teaching

• Teaching cooperatively with teachers
• Providing information skills instruction to individuals and groups
• Identifying materials for instructional units developed by teachers

Factor 6: Collaboration

• Providing staff development to teachers
• Planning instructional units with teachers

Factor 7: Assisting Teachers

Assisting teachers to access and utilize information on state funded programs

Factor 8: Student Volunteers

Library student volunteer hours per 100 students

To determine the relationship between the eight high school library factors and high school students’ TAAS performance, the "TAAS performance" variable was added to the factor analysis. The results of the factor analysis showed that high school students’ TAAS performance had the strongest association with Factor 6 which represents collaboration between librarians and teachers and consists of two library variables:

• Providing staff development to teachers
• Planning instructional units with teachers

* The highest factor loadings for these variables were lower than the +/-.600 cutoff point for inclusion in the groupings.

The relationship between these two library variables in Factor 6 and TAAS performance is not linear, as shown in the following graphs. However, important nonlinear relationships often exist between variables. As can be seen from the following graphs, the variation in TAAS performance tends to decrease as the independent library variable increases in value. In particular, TAAS performance tends to increase and become more consistent as library staff spend more time planning instructional units with teachers and providing training to teachers.

• Planning instructional units with teachers, and
• Providing staff development to teachers or other school staff.

Graph IV.3 - TAAS Reading and Library Instructional Unit Planning

Graph IV.4 - TAAS Reading and Library Teacher Training

In the next step, a factor analysis using both library and school variables was conducted. The purpose of this step was to create a set of factors that are uncorrelated with one another for use in a multiple regression procedure. The factor analysis yielded 12 factors, as shown in the following table. The 12 factors have eighenvalues of 1 or higher.

* Highest factor loading but lower than the .600 used as a cutoff.

Extraction Method: Principal Components Analysis.

Rotation Method: Verimax and Kaiser Normalization

The factor analysis including both library and school variables resulted in 12 factors with eigenvalues of 1 or higher. However, only 11 of the 12 factors had loadings greater than .600. These 11 factors are:

Factor 1: School Technology

• Volumes purchased in 1999-00 per 100 students
• Library operational expenditures per student
• School computers per 100 students
• School computers with Internet connections per 100 students
• School computers with access to catalog per 100 students
• School computers with access to library databases
• School computers with CD ROM drives per 100 students
• School computers with networked access to CD ROM resources per 100 students
• School computers connected to a modem per 100 students
• Library adult volunteer hours per 100 students

Factor 2: Library and School Staffing and Print Resources

• Library staff per 100 students
• Library staff hours per 100 students
• Library hours of operation per 100 students
• Volumes per students
• Current subscriptions to magazines and newspapers per 100 students
• School dollars per student
• Student-teacher ratio

Factor 3: Library Technology

• Library computers per 100 students
• Library computers with Internet connections per 100 students
• Library computers with access to catalog per 100 students
• Library computers with access to library databases
• Library computers with CD ROM drives per 100 students
• Library computers with networked access to CD ROM resources per 100 students
• Library computers connected to a modem per 100 students

Factor 4: Student Ethnic and Economic Composition

• Percent of LEP students
• Percent of economically disadvantaged students
• Percent of white students
• Percent of Hispanic students

Factor 5: Leadership

• Meeting with building and district library staff
• Meeting with out of district library staff
• Meeting with principal
• Attending faculty meetings

Factor 6: Teacher Characteristics

• Average teacher experience
• Teacher turnover ratio
• Percent teachers with advanced degrees

Factor 7: Planning with and Training Teachers

• Planning instructional units with teachers
• Providing staff development to teachers

Factor 8: Assisting and Instructing

• Identifying materials for instructional units developed by teachers
• Providing information skills instruction to individuals or groups

Factor 9: African American students

Percent of African American students

Factor 10: Collaboration

Teaching cooperatively with teachers

Factor 11: Instruction Dollars

Percent of school dollars devoted to instruction

Continue on to Chapter 4, Section 7