8. Graphic Analysis: The Relationship Between TAAS Performance and Library and School Variables

Analyses based on correlation coefficients assume a linear relationship between and among variables. For example, the Pearson correlation coefficient is a measure of the tendency of two variables to have a linear relationship. However, many important relationships between variables are nonlinear. Consequently, many key features will not be detected by a correlation coefficient when the relationship is not linear.

This section examines the relationship between the library and school variables included in the factors identified through the multiple regression as important in explaining the variance in TAAS performance. The relationship between TAAS performance, used as the dependent variable and each of the library and school variables is shown graphically.

8.1 Elementary Schools

Ten library and school variables were associated in the multiple regression analysis with TAAS performance of elementary school students. These include:

  • Library computers connected to a modem per 100 students
  • Library software packages per 100 students
  • Number of volumes purchased in 1999-00 per 100 students
  • Library operational expenditures per 100 students
  • Percent of Limited English Proficiency (LEP) students
  • Percent of economically disadvantaged students
  • Percent of white students
  • Percent of Hispanic students
  • Percent of African American Students
  • Percent of Asian American students

The relationship shown in the following graphs is largely nonlinear. At the lower levels of each of the library variables there is greater variance in TAAS performance than in the high levels. As the library variables increase in value, the variation in TAAS performance decreases considerably and clusters around higher TAAS performance (i.e. schools with a larger percent of students meeting minimum expectations on TAAS).

Graph IV.5 - TAAS Reading and Library Volumes Purchased Per 100 Students

Bivariate scattergram with most data points grouped between 0 and 200 library volumes purchased per 100 students and TAAS reading between 60 and 100

Graph IV.6 - TAAS Reading and Library Operational Expenditures Per Student

Bivariate scattergram with most data points grouped between 0 and 50 library operational expenditures per student and TAAS readings between 60 and 100

Graph IV.7 - TAAS Reading and Library Modems Per 100 Students

Bivariate scattergram with most data points grouped between 0 and 2 library modems per 100 students and TAAS readings between 50 and 100

Graph IV.8 - TAAS Reading and Library Software Packages Per 100 Students

Bivariate scattergram with most data points between 0 and 20 library software packages per 100 students and TAAS readings between 50 and 100

In some of the following graphs that associate TAAS performance with student characteristics such as percentages of students with limited English proficiency (LEP), economically disadvantaged students, white students, Hispanic students, African American students, and Asian American students, a definite linear relationship is seen. The linear relationship is particularly clear between TAAS performance and the percent of economically disadvantaged students and white students. The percent of students meeting minimum expectations on TAAS tends to decrease as the percent of economically disadvantaged students increases. The variance in TAAS performance also shows an interesting increase. The relationship between the percent of Hispanic students and TAAS performance is more amorphous. The graphic relationship between the percent of Asian American students and TAAS performance is similar to the graphs depicting the library variables.

Graph IV.9 - TAAS Reading and School LEP Percent

Bivariate scattergram with cluster between 0 and 20 school LEP percent and TAAS reading between 50 and 100

Graph IV.10 - TAAS Reading and School Economically Disadvantaged Percent

Bivariate scattergram with scattered points trending downward for disadvantaged percent and TAAS reading between 50 and 100

Graph IV.11 - TAAS Reading and School White Percent

Bivariate scattergram with points scattered for school white percent and TAAS reading between 50 and 100

Graph IV.12 - TAAS Reading and School Hispanic Percent

Bivariate scattergram with data points scattered for school Hispanic percent and TAAS reading between 50 and 100

.Graph IV.13 - TAAS Reading and School African American Percent

Bivariate scattergram with data points grouped between 0 and 20 for school African American percent and 60 and 100 for TAAS reading

Graph IV.14 - TAAS Reading and School Asian Percent

Bivariate scattergram with most data points grouped between 0 and 10 school Asian percent and TAAS reading between 80 and 100

Although causal relationships between variables are not established solely on the basis of statistical analysis, several statistically significant relationships between TAAS performance and library activities were found. For example, the factor analysis performed using library variables and TAAS performance, showed that TAAS performance seemed to have a positive relationship with the number of library adult volunteer hours per 100 students and the number of library computers connected to a modem per 100 students. A graphic exploration of these variables and TAAS performance depicted a nonlinear relationship in which increases in each variable were associated with increases in the percent of students who meet minimum expectations on TAAS as well as a reduction in the variability of that variable. The multiple regression analysis identified the number of library volumes purchased per 100 students, the number of library operational expenditures per student, the number of library computers connected to a modem per 100 students, and the number of library software packages per 100 students as contributors to an explanation of the variance in TAAS performance. The graphical analysis confirmed the relationships between these variables and TAAS performance. Consequently, elementary schools and their libraries should consider the following actions as well as assess whether these actions appear to be causes of better TAAS performance at their institution:

  • Increase the library budget to the recommended level
  • Increase the number of volumes purchased annually
  • Increase the number of software packages for use in the school library by students
  • Explore the feasibility of expanding the use of adult volunteers

8.2 Middle/Junior High School

Six library and school variables were associated in the multiple regression analysis with TAAS performance of middle/junior high school students. These include:

  • Identifying materials for instructional units developed by teachers
  • Providing information skills instruction to individuals or groups
  • Percent of LEP students
  • Percent of economically disadvantaged students
  • Percent of white students
  • Percent of Hispanic students

The graphic presentation of the two library variables and TAAS performance does not reveal the presence of a clear relationship. The linear relationships between these two library variables and TAAS performance are weak and not significantly different from zero.

Graph IV.15 - TAAS Reading and Library Teacher Materials

Bivariate scattergram with most data points loosely grouped between 0 and 7.5 library teacher materials and 70 and 100 TAAS reading

Graph IV.16 - TAAS Reading and Library Information Skills

Bivariate scattergram with most data points grouped between 0 and 5 library information skills and TAAS reading between 70 and 100

However, a significant relationship between these two library variables and TAAS performance is discerned when the relationship is reversed; that is, when TAAS performance is treated as an independent variable and each of the library variables is treated as the dependent variable, as shown in the two graphs that follow. In each case, the analysis was performed using only the 17 schools with the highest and the 17 lowest percent of students who met minimum expectations on TAAS. In both instances, a significant difference in the variance of the library variable was detected between the low and the high groups. This analysis indicates that in schools with a low percent of students meeting minimum expectations on TAAS:

  • Librarians are more likely to spend little time identifying materials for instructional units developed by teachers
  • Librarians are more likely to spend little time providing information skills instructions to individuals or groups

While in schools where a high percent of the students meet minimum expectation on TAAS, there is more variation in the amount of time librarians are likely to spend on these activities.

Table IV.28 Identifying Materials for Instructional Units Planned by Teachers
Percent of Students Meeting Minimum Expectations on TAAS Number of Schools Mean Variance Std Dev. Standard Error
High 17 5.089 29.667 5.447 1.321
Low 17 2.368 10.304 3.210 0.779
Group Variance Ratio Num. DF Den DF F-Value P-Value
Both 2.879 16 16 2.879 .0416
Table IV.29 Providing Information Skills Instruction
Percent of Students Meeting Minimum Expectations on TAAS Number of Schools Mean Variance Std Dev. Standard Error
High 17 4.631 49.527 7.038 1.707
Low 17 3.536 15.816 3.977 0.965
Group Variance Ratio Num. DF Den DF F-Value P-Value
Both 3.131 16 16 3.131 .0284

Graph IV.17 - Library Teacher Materials and TAAS Reading

Bivariate scattergram with most data points grouped between 0 and 7.5 library teacher materials and TAAS reading between 70 and 100

Graph IV.18 - Library Information Skills and TAAS Reading

Bivariate scattergram with most data points grouped between 80 and 90 TAAS reading and library information skills between 0 and 5

The relationship between student characteristics and TAAS performance, shown in the following graphs, is stronger and more clearly linear. This relationship is especially notable with regard to the percent of students who are economically disadvantaged. Additionally, as the percent of such students increases the variance in the percent of students meeting minimum expectations on TAAS increases.

Graph IV.19 - TAAS Reading and School Economically Disadvantaged Percent

Bivariate scattergram showing a trend from 100 TAAS and 0 disadvantaged percent to 80 TAAS and 100% disadvantaged

Graph IV.20 - TAAS Reading and School LEP Percent

Scattergram showing trend from 0% school LEP and 100 TAAS reading to 50% LEP and about 80 TAAS reading

Graph IV.21 - TAAS Reading and School White Percent

Scattergram showing trend from 0% white and about 80 TAAS reading to 100% and about 95 TAAS reading

Graph IV.22 - TAAS Reading and School Hispanic Percent

Scattergram showing trend from 0% and about 95 TAAS reading to 100% and about 85 TAAS reading

The graphic analysis demonstrated that at the middle/junior high school level:

  • While most of the variance in TAAS performance is due to racial/ethnic variables, economic variables, and the percentage of students with limited English proficiency, the amount of variance accounted for by these variables is less than what was seen at the high school level.
  • A factor that was most strongly associated with two library variables accounted for 3.9 percent of the variance in TAAS performance.
  • Aside from student characteristics comprised of racial/ethnic, economic, and limited English proficiency background, library variables appear to impact TAAS performance more than any of the other school variables.

Although the analysis by itself does not prove a causal relationship, some significant relationships between TAAS performance and library activities were found. Consequently, middle/junior high school libraries should increase to appropriate levels:

  • Number of hours spent identifying materials for instructional units developed by teachers, and
  • Number of hours spent providing information skills to individuals and groups.

8.3 High School

Fourteen library and school variables were associated with the variance in TAAS performance at the high school level. These variables include:

  • Library staff per 100 hours
  • Library staff hours per 100 students
  • Library hours of operation per 100 students
  • Planning instructional units with teachers
  • Providing staff development to teachers
  • Volumes per students
  • Current subscriptions to magazines and newspapers per 100 students
  • School dollars per student
  • Student-teacher ratio
  • Percent of LEP students
  • Percent of economically disadvantaged students
  • Percent of white students
  • Percent of Hispanic students
  • Percent of African American students

The relationship between each of these variables and TAAS performance is depicted graphically. As shown graphically:

  • The relationship between these library variables and TAAS performance is nonlinear.
  • The percent of students meeting minimum expectations on TAAS tends to be higher as these library variables increase in value, and
  • The percent of students meeting minimum expectations on TAAS shows much less variation as the value of the library variables increase.
  • This relationship pattern demonstrates that greater consistency in TAAS performance is associated with higher values in these library variables.

Graph IV.23 - TAAS Reading and Library Staff Per 100 Students

Bivariate scattergram with most data points grouped between 0 and 0.5 library staff per 100 students and between 80 and 100 TAAS reading

Graph IV.24 - TAAS Reading and Library Staff Hours Per 100 Students

Bivariate scattergram with most data points between 0 and 20 library staff hours per 100 students and 75 and 100 TAAS reading

Graph IV.25 - TAAS Reading and Library Instructional Unit Planning

Bivariate scattergram with scattered data points but a group between 0 and 2 library instructional unit planning and 85 and 100 TAAS reading

Graph IV.26 - TAAS Reading and Library Teacher Training

Bivariate scattergram with scattered data points but with a large group at 0 library teacher training between 75 and 100 TAAS reading

Graph IV.27 - TAAS Reading and Library Print Volumes Per Student

Bivariate scattergram with a large group between about 5 and 20 library print volumes per student and TAAS reading between 90 and 100

Graph IV.28 - TAAS Reading and Library Newspaper and Magazine Subscriptions Per 100 Students

Bivariate scattergram with scattered data points and a group between 0 and 10 subscriptions per student and 75 to 100 TAAS reading

Graph IV.29 - TAAS Reading and School Finance Total Per Student

Bivariate scattergram with most data points grouped between 4000 and 6000 school finance total per student and 85 to 100 TAAS reading

Graph IV.30 - TAAS Reading and School Students Per Teacher

Bivariate scattergram with scattered data points

Graph IV.31 - TAAS Reading and School LEP Percent

Bivariate scattergram with most data points grouped between 0 and 10 school LEP percent and TAAS reading between 85 and 100

Graph IV.32 - TAAS Reading and School Economically Disadvantaged Percent

Bivariate scattergram with most scattered data points and trending downwards from high TAAS reading and low percentage of economically disadvantaged

Graph IV.33 - TAAS Reading and School White Percent

Bivariate scattergram with scattered data points

Graph IV.34 - TAAS Reading and School Hispanic Percent

Bivariate scattergram with scattered data points but a cluster between 0 and 20 and TAAS reading 90 to 100

Graph IV.35 - TAAS Reading and School African American Percent

Bivariate scattergram with scattered data points but with a cluster between 0 and 10 percent and TAAS reading between 80 and 100

Even though statistical analysis can only imply but not prove causality, the relationship between library variables and TAAS performance at the high school level strongly suggests that high school libraries should increase to appropriate levels:

  • The number of library staff
  • The number of library staff hours
  • The number of hours of library operations
  • The number of hours librarians spend planning instructional units with teachers
  • The number of hours librarians spend providing staff development to teachers
  • The size of the library's print volume collection
  • The number of current subscriptions to newspapers and magazines

Continue on to Chapter 4, Section 9

 

Page last modified: March 2, 2011