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.
Elementary School Library Variables  Factor 1  Factor 2  Factor 3  Factor 4  Factor 5  Factor 6  Factor 7  Factor 8  Factor 9 

Library staff per 100 students    .844               
Library staff hours per 100 students    .802               
Library adult volunteer hours per 100 students        .522*           
Library student volunteer hours per 100 students                .775   
Library hours of operation per 100 students    .810               
Planning instructional units with teachers          .641         
Teaching cooperatively with teachers          .759         
Providing staff development to teachers            .414*       
Participating in cirriculum committee meetings      .728             
Assisting teachers to access and utilize information on state funded programs          .701         
Identifying materials for instructional units developed by teachers              .488*     
Providing information skills instruction to individuals or groups              .653     
Meeting with building and district staff              .622     
Meeting with out of district library staff                  .865 
Meeting with principal      .648             
Attending faculty meetings      .809             
Library computers per 100 students  .923                 
Library computers with Internet connections per 100 students  .936                 
Library computers with access to catalog per 100 students  .854                 
Library computers with access to library databases  .536*                 
Library computers with CD ROM drives per 100 students  .932                 
Library computers with networked access to CD ROM resources per 100 students  .712                 
Library computers connected toa modem per 100 students            .704       
Print volumes per student    .624               
Current print subscriptions to newspapers and magazines per 100 students    .682               
Library video materials per 100 students    .600               
Library software packages per 100 students            .653       
Volumes purchased in 199900 per 100 students        .831           
Library operational expenditures per student        .816           
* 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 199900 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
Elementary School Library Variables  Factor 1  Factor 2  Factor 3  Factor 4  Factor 5  Factor 6  Factor 7  Factor 8  Factor 9 

Library staff per 100 students    .871               
Library staff hours per 100 students    .890               
Library adult volunteer hours per 100 students              .438*     
Library student volunteer hours per 100 students            .680       
Library hours of operation per 100 students    .802               
Planning instructional units with teachers          .613         
Teaching cooperatively with teachers          .707         
Providing staff development to teachers        .342*           
Participating in curriculum committee meetings        .739           
Assisting teachers to access and utilize information on state funded programs          .715         
Identifying materials for instructional units developed by teachers                .717   
Providing information skills instruction to individuals or groups                  .709 
Meeting with building and district library staff                .582*   
Meeting with out of district library staff                  .659 
Meeting with principal        .640           
Attending faculty meetings        .825           
Library computers per 100 students  .925                 
Library computers with Internet connections per 100 students  .918                 
Library computers with access to catalog per 100 students  .851                 
Library computers with access to library databases  .635                 
Library computers with CD ROM driver per 100 students  .921                 
Library computers with networkds access to CD ROM resources per 100 students  .811                 
Library computers connected to a modem per 100 students              .494*     
Print volumes per student    .602               
Current print subscriptions to newspapers and magazines per 100 students    .775               
Library video materials per 100 students    .423               
Library software packages per 100 students            .780       
Volumes purchased in 199900 per 100 students      .859             
Library operational expenditures per student      .877             
Percent of student meeting minimum expectations on TAAS Reading        .103  .124    .747  .134   
* 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.
Variables  1  2  3  4  5  6  7  8  9  10  11  12  13  14 

Library staff per 100 students      .811                       
Library staff hours per 100 students      .808                       
Library adult volunteer hours per 100 students                .395*             
Library student volunteer hours per 100 students                        .644     
Library hours of operation per 100 students      .788                       
Planning instructional units with teachers              .631               
Teaching cooperatively with teachers              .738               
Providing staff development to teachers                    .321*         
Participating in curriculum committee meetings          .714                   
Assisting teachers to access and utilize information on state funded programs              .702               
Identifiying materials for instructional units developed by teachers                  .450*           
Providing information skills instruction to individuals or groups                      .477       
Meeting with building and district library staff          .373*                   
Meeting with out of district library staff                          .820   
Meeting with principal          .673                   
Attending faculty meetings          .791                   
Library computers per 100 students    .933                         
Library computers with Internet connections per 100 students    .936                         
Library computers with access to catalog per 100 students    .858                         
Library computers with access to library databases    .524*                         
Library computers with CD ROM drives per 100 students    .938                         
Library computers with networked access to CD ROM resources per 100 students    .661                         
Library computers connected to a modem per 100 students                    .669         
Print volumes per student      .638                       
Current print subscriptions to newspapers and magazines per 100 students      .666                       
Library video materials per 100 students      .565*                       
Library software packages per 100 students                    .650         
Volumes purchased in 199900 per 100 students                .814             
Library operational expenditures per student                .794             
School computers per 100 students  .928                           
School computers with Internet connections per 100 students  .943                           
School computers with access to catalog per 100 students  .839                           
School computers with access to library databases  .750                           
School computers with CD ROM drivers per 100 students  .913                           
School computers with networked access CD ROM resources per 100 students  .749                           
School computers connected to a modem per 100 students  .725                           
School finance instruction percent                            .686 
School dollars per students      .688                       
Average teacher base salary            .763                 
Average teacher experience            .691                 
Teacher turnover ratio            .590*                 
Percent teachers with advanced degrees            .531*                 
Studentteacher ratio      .675                       
Percent of LEP students        .846                     
Percent of economically disadvantaged students        .846                     
Percent of white students        .882                     
Percent of African American students                  .795           
Percent of Hispanic students        .894                     
Percent of Native American students              .347*               
Percent of Asian American students                      .766       
* 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
 Studentteacher 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 199900 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.
Middle/Junior High School Library Variables  Factor 1  Factor 2  Factor 3  Factor 4  Factor 5  Factor 6  Factor 7  Factor 8  Factor 9 

Library staff per 100 students    .930               
Libaray staff hours per 100 students    .943               
Library adult volunteer hours per 100 students                  .433* 
Library student volunteer hours per 100 students            .688       
Library hours of operation per 100 students    .725               
Planning instructional units with teachers      .613             
Teaching cooperatively with teachers                .479*   
Providing staff development to teachers      .674             
Participating in curriculum committee meetings              .625     
Assisting teachers to access and utilize information on state funded programs      .753             
Identifying materials for instructional units developed by teachers          .812         
Providing information skills instruction to individuals or groups          .831         
Meeting with building and district library staff            .831       
Meeting with out of district library staff      .659             
Meeting with principal      .623             
Attending faculty meetings        .426*           
Library computers per 100 students  .877                 
Library computers with Internet connections per 100 students  .922                 
Library computer with access to catalog per 100 students  .893                 
Library computers with access to library databates  .893                 
Library computers with CD ROM per 100 students  .897                 
Library computers with networked access to CD ROM resources per 100 students  .802                 
Library computers connected to a modem per 100 students              .606     
Print volumes per student    .600               
Current print subscriptions to newspapers and magazines per 100 students                .780   
Library video materials per 100 students      .355*             
Library software packages per 100 students                  .893 
Volumes purchased in 199900 per 100 students        .747           
Library operational expenditures per student        .775           
Percent of students who met minimum expectations on TAAS reading        .315  .187  .367  .308  .365  .299 
* 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 199900 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
Middle/Junior High School Library Variables  Factor 1  Factor 2  Factor 3  Factor 4  Factor 5  Factor 6  Factor 7  Factor 8  Factor 9 

Library staff per 100 students    .929               
Library staff hours per 100 students    .942               
Library adult volunteer hours per 100 students                .456*  .433* 
Library student volunteer hours per 100 students            .833       
Library hours of operation per 100 students    .753               
Planning instructional units with teachers      .492*             
Teaching cooperatively with teachers                .543*   
Providing staff development to teachers      .805             
Participating in curriculum committee meetings      .598*             
Assisting teachers to access and utilize information on state funded programs      .606             
Identifying materials for instructional units developed by teachers        .805           
Providing information skills instruction to individuals or groups        .808           
Meeting with building and district library staff              .688     
Meeting with out of district library staff      .610             
Meeting with principal      .658             
Attending faculty meetings              .666     
Library computers per 100 students  .867                 
Library computers with Internet connections per 100 students  .913                 
Library computers with access to catalog per 100 students  .898                 
Library computers with access to library databases  .898                 
Library computers with CD ROM drives per 100 students  .888                 
Library computers with networked access to CD ROM resources per 100 students  .804                 
Library computer connected to a modem per 100 students            .572*       
Print volumes per student    .615               
Current print subscriptions to newspapers and magazines per 100 students                .698   
Library video materials per 100 students    .338*               
Library software packages per 100 students                  .863 
Volumes purchased in 199900 per 100 students          .750         
Library operational expenditures per student          .718         
Percent of students who met minimum expectation on TAAS reading        .315  .187  .367  .299  .365  .299 
* 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.
Variables  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15 

Library staff per 100 students    .778                           
Library staff hours per 100 students    .818                           
Library adult volunteer hours per 100 students                        .658       
Library student volunteer hours per 100 students                  .781             
Library hours of operation per 100 students    .765                           
Planning instructional units with teachers                      .664         
Teaching cooperatively with teachers                      .668         
Providing staff development to teachers          .573*                     
Participating in curriculum committee meetings                            .626   
Assisting teachers to access and utilize information on state funded programs          .757                     
Indentifying materials for instructional units developed by teachers              .799                 
Providing information skills instruction to individuals or groups              .821                 
Meeting with building and district library staff                  .552*             
Meeting with out of district library staff          .778                     
Meeting with principal          .661                     
Attending faculty meetings                              .767 
Library computers per 100 students  .899                             
Library computers with Internet connections per 100 students  .936                             
Library computers with access to catalog per 100 students  .861                             
Library computers with access to library databases  .862                             
Library computers with CD ROM drives per 100 students  .914                             
Library computers with networked access to CD ROM resources per 100 students  .778                             
Library computers connected to a modem per 100 students                  .447*             
Print volumes per student    .682                           
Current print subscriptions to newspapers and magazines per 100 students                            .489*   
Library video materials per 100 students    .308*                           
Library software packages per 100 students                        .620       
Volumes purchased in 199900 per 100 students    .638                           
Library operational expenditures per students    .675                           
School computers per 100 students      .868                         
School computers with Internet connections per 100 students      .685                         
School computers with access to catalog per 100 students      .957                         
School computers with access to library databases      .954                         
School computers with CD ROM drives per 100 students      .607                         
School computers with networked access to CD ROM resources per 100 students            .751                   
School computers connected to a modem per 100 students            .823                   
School finance instruction percent                        .502*       
School dollars per student    .821                           
Average teacher base salary                    .765           
Average teacher experience                    .696           
Teacher turnover ratio                            .727   
Percent teachers with advanced degrees                    .539*           
Studentteacher ratio    .775                           
Percent of LEP students        .806                       
Percent of economically disadvantaged students        .916                       
Percent of white students        .897                       
Percent of African American students                          .779     
Percent of Hispanic students        .938                       
Percent of Native American students                .794               
Percent of Asian American students                              .504* 
* 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 199900 per 100 students
 Library operational expenditures per student
 School dollars per student
 Studentteacher 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.
High School Library Variables  Factor 1  Factor 2  Factor 3  Factor 4  Factor 5  Factor 6  Factor 7  Factor 8 

Library staff per 100 students    .924             
Library staff hours per 100 students    .924             
Library adult volunteer hours per 100 students        .798         
Library student volunteer hours per 100 students                .602 
Library hours of operation per 100 students    .803             
Planning instructional units with teachers            .729     
Teaching cooperatively with teachers          .624       
Providing staff development to teachers            .780     
Participating in curriculum committee meetings            .467*     
Assisting teachers to access and utilize information on state funded programs              .695   
Identifying materials for instructional units developed by teachers          .601       
Providing information skills instruction to individuals or groups          .787       
Meeting with building and district library staff      .619           
Meeting with out of district library staff      .894           
Meeting with principal      .877           
Attending faculty meetings      .944           
Library computers per 100 students  .911               
Library computers with Internet connections per 100 students  .747               
Library computers with access to catalog per 100 students  .836               
Library computers with access to library databases  .819               
Library computers with CD ROM drives per 100 students  .893               
Library computers with networked access to CD ROM resources per 100 students  .826               
Library computers connected to a modem per 100 students  .684               
Print volumes per student    .688             
Current print subscriptions to newspapers and magazines per 100 students    .731             
Library video materials per 100 students              .474*   
Library software packages per 100 students              .459*   
Volumes purchased in 199900 per 100 students        .774         
Library operational expenditures per student        .762         
* The highest factor loadings for these variables were lower than the +/.600 cutoff point for inclusion in the groupings.
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 199900 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
High School Library Variables  Factor 1  Factor 2  Factor 3  Factor 4  Factor 5  Factor 6  Factor 7  Factor 8 

Library staff per 100 students    .922             
Library staff hours per 100 students    .922             
Library adult volunteer hours per 100 students        .798         
Library student volunteer hours per 100 students                .581* 
Library hours of operation per 100 students    .802             
Planning instructionals units with teachers            .676     
Teaching cooperatively with teachers          .640       
Providing staff development to teachers            .772     
Participating in curriculum committee meetings        .455*         
Assisting teachers to access and utilize information on state funded programs              .610   
Identifying materials for instructional units developed by teachers          .599*       
Providing information skills instruction to individuals or groups          .771       
Meeting with building and district library staff      .619           
Meeting with out of district library staff      .896           
Meeting with principal      .886           
Attending faculty meetings      .943           
Library computers per 100 students  .911               
Library computers with Internet connections per 100 students  .742               
Library computers with access to catalog per 100 students  .835               
Library computers with access to library databases  .818               
Library computers with CD ROM drives per 100 students  .894               
Library computers with networked access to CD ROM resources per 100 students  .684               
Library computers connected to a modem per 100 students  .684               
Print volumes per student    .683             
Current print subscriptions to newspapers and magazines per 100 students    .734             
Library video materials per 100 students              .457*   
Library software packages per 100 students              .455*   
Volumes purchased in 199900 per 100 students        .769         
Library operational expenditures per student        .761         
Percent of students who met minimum expectations on TAAS reading    .222    .191    .461  .412   
* 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.
Variables  1  2  3  4  5  6  7  8  9  10  11  12 

Library staff per 100 students    .910                     
Library staff hours per 100 students    .928                     
Library adult volunteer hours per 100 students  .643                       
Library student volunteer hours per 100 students                        .588* 
Library hours of operation per 100 students    .830                     
Planning instructional units with teachers              .751           
Teaching cooperatively with teachers                    .673     
Providing staff development to teachers              .783           
Participating in curriculum committee meetings  .519*                       
Assisting teachers to access and utilize information on state funded programs                  .569*       
Identifying materials for instructional units developed by teachers                .620         
Providing information skills instruction to individuals or groups                .764         
Meeting with building and district library staff          .577*               
Meeting with out of district library staff          .888               
Meeting with principal          .903               
Attending faculty meetings          .930               
Library computers per 100 students      .888                   
Library computers with Internet connections per 100 students      .735                   
Library computers with access to catalop per 100 students      .854                   
Library computers with access to library databases      .834                   
Library computers with CD ROM drives per 100 students      .872                   
Library computers with networked access to CD ROM resources per 100 students      .814                   
Library computers connected to a modem per 100 students      .596*                   
Print volumes per students    .740                     
Current print subscriptions to newspapers and magazines per 100 students    .742                     
Library video materials per 100 students                  .478*       
Library software packages per 100 students                      .549   
Volumes purchased in 199900 per 100 students  .736                       
Library operational expenditures per student  .789                       
School computers per 100 students  .908                       
School computers with Internet connections per 100 students  .956                       
School computers with access to catalog per 100 students  .935                       
School computers with access to library databases  .938                       
School computers with CD ROM drives per 100 students  .951                       
School computers with networked access to CD ROM resources per 100 students  .909                       
School computers connected to a modem per 100 students  .878                       
School finance instruction percent                      .730   
School dollars per student    .822                     
Average teacher base salary                    .574*     
Average teacher experience            .624             
Teacher turnover ratio            .725             
Percent teachers with advanced degrees            .648             
Studentteacher ratio    .761                     
Percent of LEP students        .796                 
Percent of economically disadvantaged students        .855                 
Percent of white students        .863                 
Percent of African American students                  .609       
Percent of Hispanic students        .909                 
Percent of Native American students                    .449*     
Percent of Asian American students                  .364*       
* 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 199900 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
 Studentteacher 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