GIVE NOW  | 

Mr. Geary Don Crofford
Dean of Academics at Sequoyah Schools, Tahlequah, Oklahoma
Doctoral student at the University of Oklahoma

Dr. Jon E. Pedersen, Ph.D
Director of Science Education for the Center for Mathematics, Science and Computer Education at the University of Nebraska-Lincoln

Dr. Gregg Garn
Associate Dean of the Jeannine Rainbolt College of Education at the University of Oklahoma

Introduction

Numerous studies in the United States and abroad have confirmed that American high school students are lagging behind their international peers, particularly in the areas of science and mathematics. According to the National Science Board (2006), the fastest growing occupations are in fields that are dependent upon a knowledge base in science and mathematics. Furthermore, the National Science Board’s report indicated a widespread lack of student proficiency on national and international tests of mathematics and science as well as a decreased rate of U.S. students pursuing science and engineering degrees from universities nationwide as a cause for economic apprehension. These findings have alarmed the U.S. educational community as well as concerned stakeholders outside the educational sphere, including community leaders, business owners, and parents (Molfese et al., 2006). Accordingly, research that supports a relationship between teacher credentials and student and/or school achievement, in any form, is valuable to educators and policy makers.

Findings for a lack of student proficiency in science and mathematics present questions as to how and why many teachers are unable to sufficiently engage their students to achieve at acceptable levels. It is necessary to find ways to enable educators not only to enhance student proficiency but also to develop the relevance perceived by students in their learning. The enhancement of teacher education, including National Board Certification (NBC) and providing incentives for teachers to attain certification, may influence the academic achievement and proficiency of students. In 1987, after the Carnegie Forum on Education and the Economy’s Task Force on Teaching as a Profession released “A Nation Prepared: Teachers for the 21st Century,” the National Board for Professional Teaching Standards (NBPTS) was created. Immediately following its inception, NBPTS issued its first policy statement: “What Teachers Should Know and Be Able to Do.” This policy statement established the vision of the NBPTS for accomplished teaching. The NBPTS issued Five Core Propositions, which formed the framework for the knowledge, skills, dispositions, and beliefs that characterized National Board Certified Teachers (NBCTs). According to the NBPTS website,

The fundamental requirements for proficient teaching are relatively clear: a broad grounding in the liberal arts and sciences; knowledge of the subjects to be taught, of the skills to be developed, and of the curricular arrangements and materials that organize and embody that content; knowledge of general and subject-specific methods for teaching and for evaluating student learning; knowledge of students and human development; skills in effectively teaching students from racially, ethnically, and socioeconomically diverse backgrounds; and the skills, capacities and dispositions to employ such knowledge wisely in the interest of students.

National Board Certification is intended to complement (and not replace) state certification for teachers. Ideally, NBC contributes to producing and selecting the most effective teachers possible by enhancing positive aspects of all levels of certification. Data indicate that differences between effective and non-effective teachers have a remarkable influence on student achievement (Darling-Hammond, 2000). Similarly, research by Goldhaber (2006) indicates that National Board Certified Teachers (NBCTs) are significantly more effective teachers (Goldhaber, 2006). Teacher quality is inextricably linked with the degree of teachers’ preparation and experience in subject area matter and pedagogy. In other words, subject knowledge (the information) and pedagogy (the methods of instructional delivery) are both essential for student achievement.

Past research shows mixed results with regard to the positive impact of NBC in improving teacher practice, professional development, and other facets of school improvement that are presumed essential to elevating student achievement. However, the research on the effectiveness of initial teacher certification and professional development for in-service teachers has also yielded mixed findings. State certification and licensure, alternative certification, and NBC each represent differing levels of teacher preparation and professional development that have been and are being studied in terms of their impact on student and school achievement, with the relative effectiveness of each still in debate (Ballou & Podgursky, 2000; Darling-Hammond, Holtzman, Gatlin, & Heilig, 2005; Ferguson, 1991; Finn, 1999; Sanders, Ashton, & Wright, 2005).

From the above cited research, questions arise as to whether more effective teaching is the result of specialized education in how to teach, more general academic ability and knowledge of subject matter, or some combination of these components and others, including school locale, size, Title I status, SES, and parental levels of education and involvement. National Board Certification represents the synthesis of all of these teacher education variables coupled with invaluable classroom experience and reflection. In this paper, we focus on the impact of NBCTs on student academic achievement. Therefore, the scope and purpose of this study is to determine if NBCTs produce measurable and significant increases in high school student achievement in their schools. This study is unique in that it incorporated secondary, school-level data in a particular state, and that it attempted to find relationships between the presence of NBCTs, student academic achievement, and distinctions of locale, size, and Title I status. We hope to build on existing research as well as point out new factors and combinations of factors affecting student achievement that may lead to further research.

In her comprehensive review of state policy, Darling-Hammond (2000) argued, “Quantitative analyses indicate that measures of teacher preparation and certification are the strongest correlates of student achievement in reading and mathematics, both before and after controlling for student poverty and language status” (pp. 1-2). Studies in a variety of states have examined NBC specifically, and many have found that NBCTs contribute to a significantly measurable difference in student and school achievement. For example, Vandevoort, Beardsley, and Berliner (2004) discovered that student proficiency was higher in 75% of the NBCTs’ classrooms when compared with students in non-NBCT classrooms. According to Goldhaber and Anthony (2004), the NBPTS is successfully identifying more effective teachers among applicants, and that NBPTS-certified teachers were more effective than were their non-certified counterparts at increasing student achievement, especially among minority students. The statistical significance and relevance of this NBPTS effect, however, tends to differ significantly by grade level and student type. Smith, Gordon, Colby, and Wang (2005) indicated that the relationship between student learning outcomes and teacher certification status was highly statistically significant on 6 of the 7 student outcomes measured, with the results in favor of NBCTs over non-NBCTS.

Although quantitative approaches have dominated the research on NBCTs and student academic achievement, qualitative research also provides insight into this issue. A case study of three high school teachers suggested that NBC affected teachers’ pedagogical content knowledge (PCK) positively through their reflection on teaching practices, implementation of new and/or innovative teaching strategies, inquiry-oriented instruction, assessments of students’ learning, and understanding of students (Park & Oliver, 2007). In spite of the limitations imposed by analyzing only three cases, such research may give us some idea as to how NBC enhances teacher effectiveness. Other researchers have investigated several aspects of teacher certification and found links to student achievement; studies have also found that when student demographic variables are controlled, schools with a larger proportion of NBCTs demonstrate moderately higher test scores (Bundy, 2006; Cavalluzzo, 2004; Clotfelter, Ladd, & Vigdon, 2007). In addition, research has found that a larger proportion of NBCTs in a given school coincides with a small increase in teacher empowerment, but these gains are unrelated to the improvement in student test scores. It is possible and probable that increased proportions of NBCTs on school campuses produce increases in student achievement across academic subjects, regardless of other factors such as student population diversity, locales, and size of schools. Despite mixed results and a variety of methodologies employed in prior studies, NBC appears to show a positive impact on academic achievement (McColskey & Stronge, 2005; Sanders et al., 2005). Our research question is whether the presence of NBCTs in high schools is related to campus-wide performance on standardized state examinations, independently of other factors, or in conjunction with other factors.

Methodology

The purpose of this study was to investigate whether the number of NBCTs to which students in a given high school are exposed correlated to the school’s outcomes on standardized state examinations. Data sets used in the analysis consisted of End-of-Instruction tests (EOIs) in Biology, Mathematics, and Reading, which were obtained from the state’s Department of Education through an Open Records Request for the test data of all high schools (including those with grades 9-12 and 10-12) in the state. Data on the total number of faculty with NBC for each high school in the state was also obtained through the state’s Department of Education.

In 2005, Senate Bill (SB) 982, known as the Achieving Classroom Excellence (ACE) Act, changed the curriculum, testing, and graduation requirements for students in all public schools in the state. Students entering 9th grade in the 2008-2009 school year must demonstrate mastery of state academic content standards. Mastery is defined as a satisfactory or advanced score on four of seven criterion-referenced EOI exams in core content areas:

Secondary ACE Testing Requirements:

(See OS §70-1210.523)

All secondary students enrolled in a “core” course are required to take an EOI exam as a part of the course. Students have three retesting opportunities each year to take and pass any exam on which they do not score satisfactory or above. The State Board of Education and the Department of Education developed and field-tested EOI exams in Algebra II, Geometry, and English III in the 2006-2007 school year. These examinations were fully implemented in 2007-2008, and a student’s highest performance levels (that are satisfactory and above) will become a part of his/her permanent transcript in 2008-2009 (OS §70-1210.508). The ACE District Remediation Plan is also in place in an attempt to provide intervention activities for students who fail to gain a satisfactory score. ACE provides remediation for any ninth-grade student on any EOI test. The EOI secondary-level tests are aligned to the state-mandated curriculum, the Priority Academic Student Skills (PASS), which has been adopted by the State Board of Education and is the foundation for curriculum development in all public schools. In order to assure the content validity of the state EOI assessments, commercial content developers, who analyzed a pool of items that existed previously to determine the status and viability of each item, studied the PASS objectives. State content area specialists and teachers worked with the commercial developers to develop a pool of items that measured PASS in each content area. The Content and Bias/Sensitivity Review committees carefully reviewed and discussed these items to ensure content validity and the quality and appropriateness of the items. These committees were comprised of state teachers and State Departments of Education staff.

Criteria for Aligning the Test with the PASS Standards and Objectives

1. Categorical Concurrence
   The test is constructed so that there are at least six items measuring each PASS standard with the content category consistent with the related standard. The number of items, six, is based on estimating the number of items that could produce a reasonably reliable estimate of a student’s mastery of the content measured.
2. Depth-of-Knowledge Consistency
   The test is constructed so that at least 50% of the test items measuring a PASS objective are at or above the depth of knowledge of the related PASS objective.
3. Range-of-Knowledge Correspondence
   The test is constructed so that at least 50% of the objectives for a PASS standard have at least four corresponding assessment items.
4. Balance-of-Representation
   The test is constructed according to the Alignment Blueprint which reflects the degree of representation given on the test to each PASS standard and objective in terms of the percent of total test items measuring each standard and the number of test items measuring each objective.
5. Source-of-Challenge
   Each test item is constructed in such a way that the major cognitive demand comes directly from the targeted PASS skill or concept being assessed, not from specialized knowledge or cultural background that the test-taker may bring to the testing situation. (State EOI Technical Report 2001-02)

All data used in this study relied strictly on secondary data sets from the 2006-2007 school year. The study excluded private schools and the 72 smallest schools in the state, primarily because of concerns about effect size, as few of these schools had any NBCTs on campus. The dependent variables included EOI scores in biology, math, and reading, and the independent variables included Title I or non-Title I, School Locale and School Size, and the number of NBCTs in each school. Excluding the number of NBCTs, the independent variables were categorical or nominal. The 30 largest schools from each of the six size classifications were included in the sample for convenience, for a total sample of N = 175 schools. The results of the study are constrained from three limitations: (a) we used school-level data, not student-level data, (b) we assumed PASS and EOIs are aligned, (c) and convenience sampling. Results were disaggregated by Locale (urban, suburban, town, and rural high school settings), Size, and Title I status. Pearson’s correlation, basic regression, and ANOVA techniques were used to examine this large data set to see if any relationship existed between the independent and dependent variables. A significance value of .05 was established a priori.

Results

The results show that the number of NBCTs on a high school campus correlates positively and significantly with student achievement (in terms of EOI test scores) when the data were analyzed in aggregate for math, reading, and biology EOI mean scores (see Table 1). About 3% of teachers were NBCTs throughout all high schools in the state, and the mean scores for math and reading were higher than were those for biology on the EOIs.

Table 1
Pearson Correlation for All Schools

Note. *Significant at the .05 level

Taking NBCT as the independent variable, and Biology, Math, and Reading as the dependent variables, we can perform basic regression and ANOVA analysis for statistical significance, the results of which are summarized in Tables 2-4.

Table 2
NBCT vs. Biology

Note. (a) Dependent Variable: Biology; (b) R Square = .073; (c) F = 12.114

From the F and t-tests above, we can conclude at the 5% significance level and at a p-level .001 that NBCTs are a statistically significant predictor of Biology test scores. This means that students in schools with a greater proportion of NBCTs tended to score higher on EOI tests in Biology.

Table 3
NBCT vs. Math

Note. (a) Dependent Variable: Math; (b) R Square = .036; (c) F = 7.533.

From the F and t-tests above, we can conclude at the 5% significance level and at a p-level .007 that NBCTs are a statistically significant predictor of Math test scores. This means that students in schools with a greater proportion of NBCTs tended to score higher on EOI tests in Math.

Table 4
NBCT vs. Reading

Note. (a) Dependent Variable: Reading; (b) R Square = .049; (c) F = 8.913

From the F and t-tests above, we can conclude at the 5% significance level and at a p-level .003 that NBCTs are a statistically significant predictor of Reading test scores. This means that students in schools with a greater proportion of NBCTs tended to score higher on EOI tests in Reading.

However, it is not sufficient to state that a relationship exists between NBCTs and test scores; it is also necessary to show that there are no underlying factors driving the relationship. In our study, several factors like Locale, School Size, or Title 1 status might be correlated with both NBCTs and test scores. In that case, such factors may drive the relationship between NTCBs and test scores, and any appearance of a correlation might have been due to the underlying cause. In order to address the concern, the following ANOVA tests conclusively showed that no such general relationship exists between NBCT and Locale or Title 1 status. Although there exists a relationship between NBCT and school size, a relationship does not exist between test scores and school size (however, a relationship does exist between title 1 status, and locale and test scores). Because the two cases in which scores and outside force were correlated were exactly the two cases in which outside force and NBCT were not correlated (and vice versa), we can safely state that no such outside force is driving the relationship between NBCT and student test scores.

Table 5
NBCT vs. Locale

The analysis of the data revealed some marginal differences in means, particularly among the town/rural section as compared to city/suburb. The F-test results are F(3, 171) = 1.948, p = .124. Our p-level is .124 versus our alpha-level of .05; therefore, the test is not statistically significant enough to reject the null that Locale does not affect the NBCT.

Table 6
NBCT vs. Size

In this comparison, the results revealed that there are significant differences between the NBCT rates and size, and we should expect to see that fact reflected in our F-test: F(5, 169) = 4.348, p = .001. Our p-level is .001 versus our alpha-level of .05; therefore, the test is statistically significant enough to reject the null that Size does not affect the NBCT.

Table 7
NBCT vs. Title

As a group, Title I schools exhibited no significant positive correlation, but non-Title I schools exhibited a significant positive correlation with student academic achievement as measured by the test scores. For Title I schools, 2.2% of the teachers were NBCT compared to 2.8% in Non-Title I schools. Non-Title I schools generally had higher mean test scores, but only a slightly higher frequency of NBCTs. There are more than twice as many non-Title I schools in our sample of high schools throughout the state. Further analysis showed that NBCT is not only correlated, but can also be identified as a statistically significant causal factor in student test scores. The difference in means here is rather small when compared to standard error: F(1, 173) = 1.244, p = .266. Our p-level is .266 versus our alpha-level of .05; therefore, the test is not statistically significant enough to reject the null that Title 1 status does not affect the influence of NBCTs. The ANOVA tests concerning student scores and outside factors (locale, size, title 1 status) are located in the appendix.
Further statistical analyses were undertaken to investigate the influence of Title I status versus non-Title I status in the particular academic subjects of Math, Reading, and Biology.

Table 8
Title I and Non-Title I Schools

*Significant at the .05 level

As can be seen in Table 8, when the data for the comparison of Title I and non-Title I schools is disaggregated by subject, the results confirm those presented in Table 7. Across the board, in all subjects, student academic achievement in Math, Reading, and Biology were all significantly correlated to NBCTs in non-Title I schools.

Table 9
Statistics for Locale

*Significant at the .05 level

When the data was analyzed by Locale, only suburban schools (in Reading and Biology) and rural schools (in biology) showed a positive and significant correlation between the number of NBCTs and EOI scores. No clear pattern emerged in this particular data analysis and categorization, with the exception of a decrease in the number of NBCTs as the locale changed from city schools to rural schools. The relative number of schools in each category may also have influenced the results, with rural schools having the lowest number of NBCTs. For these classifications, the total percentages of NBCTs were: city 3.5%; suburb 3.7%; town 2.3%; and, rural 2.2%.

Table 10
Statistics for School Size

*Significant at the .05 level

When the schools were grouped by size, only the smallest and largest classifications showed more than one significant and positive correlation. In fact, the other groups showed some negative correlations. In this state, school size classifications are determined by the Secondary School Activities Association (SSAA) based on enrollment numbers provided by the schools. 6A populations ranged from 4,395-1,259 average daily attendance, 5A from 1,240-667, 4A from 661-490, 3A from 489-378, 2A from 377-244, and 1A from 243-104. The two smallest classifications were not included because of limitations presented by the effect size, the presence of a large number of private schools, and because virtually none had any NBCTs. For these classifications, the total percent of NBCT’s are: 1A, 1.0%; 2A, 1.5%; 3A, 2.6%; 4A, 2.5%; 5A, 3.5%; and, 6A, 4.2%.

Discussion
The results of the statistical analyses of this study revealed several notable findings, which are expanded upon in this section. A more detailed comparison of the EOI mean scores indicated that the biology EOIs were the lowest overall, and non-Title I high schools showed higher EOI scores than Title I schools (see appendix). No significant differences of EOI means emerged from the breakdown of the data by other factors, with the exception that suburban high schools showed higher mean EOI scores than other categories of locale. The locale of schools yielded no clear pattern as to the relationship between NBCTs and EOIs, yet when grouped by size, the smallest (1A) and largest schools (4A, 5A, and 6A) showed a positive effect.

However, medium size schools showed a negative correlation between the number of NBCTs and EOIs. It is possible that this negative correlation (and positive correlation for 1A Schools) was caused by the effect size of the smaller faculties and student populations within the small schools, increased emphasis on NBCT certification, and other factors, such as socioeconomics and parental education and involvement in the larger schools. Analyzing data by locale yielded few correlations between EOIs and NBCTs, except for the suburban category. Again, this may be due to superior socioeconomic status associated with suburban schools as well as increased resources in suburban schools in general. In addition, because of the rural nature of the state, many more schools were classified as rural relative to schools classified as suburban.

The disparity between the Title I and non-Title I schools is intriguing and requires further investigation (see appendix). It is possible that non-Title I schools demonstrated a stronger apparent relationship between NBCTs and student achievement as measured by EOI scores because of socioeconomic and parental education levels, as well as other factors that were not addressed in this analysis. It is significant to note that although the percentage of the NBCTs for these two categories were similar (2.8% for non-Title I versus 2.2% for Title I schools), the EOI score means were consistently higher for the non-Title I schools. In addition, many of the non-Title I high schools have feeder middle schools with Title I designation and middle schools were not included in this analysis.

Despite the variation seen when schools were placed in specific groups for comparison, the overall positive impact of a higher proportion of NBCTs in a given faculty on students’ EOIs is unmistakable in the results of the analysis. Further causal analysis is necessary to investigate the potential impact on student EOIs from other critical factors, such as SES, which must be addressed separately. However, our results show a general positive relationship between number of NBCTs and student performance in the measures that we chose to incorporate in our analysis. Specifically, the proportion of NBCTs predicts test scores for all three of our investigated subjects: biology, reading, and mathematics. Furthermore, the significance levels are very low, which implies a strong rejection of the null and supports no doubt that NBCT is a significant factor for high school student test scores. The presence of NBCT does not change the results of the data anlayses when different locales are taken into account. However, the presence of NBCT changes with differences in school size. In other words, school size is a potential reason for differing student scores. Last, NBCT does not change over Title I status, which means that whether or not a school is Title I has no bearing on whether or not it is NBCT.

What does this mean? Our goal is to prove that NBCT is the cause of test score differences, as opposed to locale, size, and Title I status. As long as NBCT is not related to a variable, that variable cannot cause the test score difference. Therefore, we can automatically rule out locale and Title I status as “driving” the correlation between NBCT and scores. Furthermore, the only variable with which NBCT is related (school size), is not related to test scores. In other words, school size has no effect on student test scores, so obviously the differences we observed in NBCT with regard to test scores is not caused by school size. In short, our conclusion is that the presence of NBCTs is a predictor of test scores, and that none of the three primary factors forwarded by the study (locale, size, or Title I status) are potential problems. In other words, our first conclusion, that NBCTs predict test scores, is very strong.

The key question we attempted to address, “Does the number of NBCTs correlate to a higher EOI score for students,” seems to have been answered in the broadest sense by the data analysis. However, disaggregation of the data raises key questions pertaining to the influence of NBCTs on students, particularly those that attend school in rural and urban settings. From our perspective, these results sound a call for more effort and incentives to be put forth by policy makers, school boards, and administrators toward encouraging secondary teachers to become NBC. The overall positive impact of having more NBCTs in school faculties has been documented by studies in various states through quantitative and qualitative methodologies. The data from the present study and analysis demonstrated a similar finding in high schools. Despite mixed results when the data were disaggregated, there is no indication (all other factors being equal or controlled for) that the presence of more NBCTs in a school has any type of negative impact on student achievement.

Consequently, NBC could be viewed as an adjunct to other approaches and environments that enhance student achievement such as increased parental involvement. In fact, the NBPTS Research Pocket Card (2008) acknowledged,

More than 150 studies have examined National Board Certification. The vast majority found NBCTs make a significantly measurable impact on teacher performance, student learning, engagement and achievement. While some of the results are mixed, most are positive about National Board Certification accomplishments and its potential for improving education nationwide. (p. 1)

Although the process of NBC is an expensive, demanding, and time-consuming process for the teachers who undertake it, it appears that the benefits for our school systems, and thus for our students and communities, outweigh the costs. Given that our results suggest that the percentage of NBCTs has a campus-wide effect on student achievement, future studies should investigate this pattern further. Because of the many unanswered questions raised by this study, we cannot posit the conclusion that NBCTs influence all students at all locales in the same manner. The findings of the study clearly show that having NBCTs on a campus do not always yield positive correlations to achievement (EOIs), and future studies should investigate why this is the case. For example, researchers should consider such possible mitigating factors as campus and department leadership roles of NBCTs and the number of NBCTs to which students are exposed at the elementary and middle level. More research is needed to examine the influence of NBCTs on those schools with children at the highest risk. Schools in socioeconomically depressed areas (in this state, rural and urban schools make up the majority of these schools) underperformed even when compared to higher SES schools with the presence of NBCTs. In addition, this research only looked at overall NBCT frequency on each campus. In the future, a more specific study should break down the analysis in terms of actual subjects taught by NBCTs. The state EOI means were substantially lower for biology than they were for reading and math. Is this a factor of the number of NBCTs, and if so, will increasing the number of NBCTs improve science achievement?

Further qualitative case studies may be carried out that determine how NBC has affected individual teachers’ teaching philosophies and practices as well as their students’ achievement and attitudes toward their education. Such connections are especially urgent in light of the federal No Child Left Behind Act of 2001 (NCLB), which requires all states to establish state academic standards, tests, and accountability measures that meet federal requirements for monitoring the adequate yearly progress of schools. Furthermore, additional effort in exploring the differences found in schools’ Title I status, size, and locale in this study should be initiated as well. This may include analyzing a potential relationship between frequency of NBCTs and the state’s Academic Performance Index (API). The API was created to measure the performance and progress of a school or district based on several factors that are believed to contribute to overall educational success. The possible scores range from 0 to 1,500. The factors used in the calculation of an API score include the state’s School Testing Program (as measured by student success on state achievement tests), school completion (including attendance, dropout, and graduation rates), and academic excellence (including ACT scores and participation, Advanced Placement [AP] credit, and college remediation rates in reading and mathematics). An analysis involving APIs may give a more complete picture of the overall affect that NBCTs have on high school campuses. Similarly-focused research should include elementary and middle schools.

There is still much to determine with regard to the best ways to prepare our teachers at the beginning and throughout their careers in the classroom. Our study, among others, attempts to elucidate the effectiveness of the methods currently available to prepare teachers and describe their relative efficacies. This research is critical for our students because they deserve to be exposed to the best teachers possible, increasing their chances of current and future academic and personal success. Our study was limited to one state, one level of teacher education, and one set of student outcomes. However, in conjunction with other current and future studies, we can go beyond a narrow snapshot of the efficacy of teacher certification to a more complete and comprehensive canvas of how to most effectively prepare our teachers and successfully educate our students.

Appendix

Set 1

In the first series of tests, the null hypothesis is that there is no distinction across Title I status in the scores of the students. In other words, we would expect that a student in title 1 schools would receive the same math score as a student in non-title 1 schools.

Test 1
ANOVA, testing for differences between Title 1/Non-Title 1 schools in Math Score:

From the analysis above, the non-title 1 students perform better at mathematics than the title 1 students, and at a statistically significant level. Our p-value of .020 is lower than our alpha-level of .05, allowing us to reject the null hypothesis that no differences exist between the two samples.

Test 2
ANOVA, testing for differences between Title 1/Non-title 1 schools in Reading Score:

From the analysis above, the non-title 1 students perform better at reading than the title 1 students, and at a statistically significant level. Our p-value of .000 is lower than our alpha-level of .05, allowing us to reject the null hypothesis that no differences exist between the two samples.

Test 3
ANOVA, testing for differences between Title 1/Non-title 1 schools in Biology Score:

From the analysis above, the non-title 1 students perform better at Biology than the title 1 students, and at a statistically significant level. Our p-value of .003 is lower than our alpha-level of .05, allowing us to reject the null hypothesis that no differences exist between the two samples.

Set 2

Biology/Math/Reading vs Locale

The null hypothesis is that the locale should have no influence on student scores in Biology/Math/Reading. We will perform a cross sample ANOVA as well as Hukey-post hoc to compare across the different samples.

MEANS

*The mean difference is significant at the 0.05 level.

In general, the suburbs score the highest. Many, if not most, of the cross comparisons are significant, and the overall null that locale does not matter is thoroughly rejected at a p-value of .000 vs our alpha level of .05.

Set 3

Biology/Math/Reading vs. Size

The null hypothesis is that the size should have no influence on student scores in Biology/Math/Reading. We will perform a cross sample ANOVA as well as Hukey-post hoc to compare across the different samples.

Means

*The mean difference is significant at the 0.05 level.

These results are a bit mixed. In general, there are few differences across schools. The big difference exists in 6A and 5A being significantly different at the .05 significance level in their individual cross-comparison. The overall null, that size does not matter, is rejected in Math (.023 P level) and Reading (.024 P level) but not in Biology (.094 P level) when comparing to the standard alpha level of .05

Consequently, while we can state that size has an effect on scores, the effect is ambiguous, and the only pinpoint effect that was statistically significant was 6A vs 5A in Math and Reading.

Acknowledgements

Special thanks to John Hathcoat of the University of Oklahoma-Tulsa for his assistance and feedback, and Scott Goldman of the Oklahoma State Department of Education for providing data sets.

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