The role of the local school district is problematic in the on-going school restructuring that focuses on student learning. Centralization by state governments and decentralization to individual schools as proposed in systemic reform leaves districts' role unsettled (Elmore 1993). Research is needed to examine the impact of district policymaking on student learning. Such research entails linking standardized achievement measures at the student level to district-level policy information comparable across jurisdictions.

This study explored policy and methodological issues relevant to these concerns. We analyzed NAEP data in combination with the Common Core of Data (CCD) to examine the extent to which student achievement was related to districts' control over expenditure, adjusting for relevant key factors at both district and student levels.

Education reformers face a dilemma in trying to redefine the local school district role in relation to state government. On the one hand, the local district, as an independent political entity for local control of public schools, is supposed to buffer the schools against external political influences. On the other hand, as a legal creation of the state, the district is expected to work as an instrument of state government and to implement state policies and regulations with minimal change. The notion of simultaneous decentralization and centralization gives states and individual schools more policymaking authority, but leaves the local districts in an ambiguous position (Hannaway 1992; Clune 1993; Keedy 1994; Marsh 1997). As the authority and responsibility of the state governments continue to expand in public education, districts' role as a governmental unit seems to be diminishing (e.g., see Walberg & Walberg 1994; Elmore 1993).

State governments are playing an increasingly important role in fiscal control and prescriptive policymaking in a wide range of areas that were historically the domains of local district decisionmaking. States are contributing a large and growing share to local school revenue, specifying requirements on staffing and instruction (General Accounting Office 1998). State aid formulas have often incorporated specific mechanisms for district inefficiency control, linking spending to performance (Duncombe & Yinger 1998; Marsh 1997). Frequently, state governments threaten to and occasionally do take over local schools when persistent failure by local administration is confirmed (e.g., Iannaccone & Lutz 1994; Guskey 1993).

The districts' power is also threatened by decentralization in forms of site-based management and the school as a professional community (Marsh 1997; Elmore 1993; Clune 1993; Porter 1994; Newmann & Wahlage 1995). State education departments now often select individual schools as administrative units for deregulation and interact directly with them to encourage local initiatives (Fuhrman & Elmore 1995). Local schools are expanding their options in mobilizing community support, making innovations in instruction and curriculum, and making decisions on spending and staffing (Elmore 1993; Hannaway 1993). Research appears to support such restructuring as recent studies focus on school-level professional autonomy and its link to authentic instruction and achievement outcomes (e.g., Lee, Smith & Croninger 1995; Newmann & Wahlage 1995). One implication is that decentralization is reducing bureaucratic influence—including district influence—in local school decisionmaking.

The 16,000 local districts in the U.S. are, however, more than a historical heritage. National data reports describe local districts as solid administrative units with diverse conditions (e.g., Levine & Christenson 1998; Protheroe 1997). The question for reformers is how to adjust the system to the changing environment, since the underlying logic of American federalism requires multiple jurisdictions that compromise different interests and generate productive tension and dependence among jurisdictions (Elmore 1993). Available research suggests that it is possible for local districts to push reform further by building up strong local constituencies and developing policy initiatives (Fuhrman & Elmore 1990; Admundson 1993). This research, however, has been conducted largely with local or state information sources and has rarely used national data. To conduct research at national scale requires nationwide data on both student achievement and local fiscal conditions. Synthetic analysis of the National Assessment of Educational Progress (NAEP) and the Common Core of Data (CCD), explored in this study, seems an efficient approach to this goal.

Our basic assumption is that although state governments are constitutionally responsible for public education, local districts have an important role in improving instruction. An approach districts take in playing that role is to adjust fiscal policy to increase the proportion of expenditure for instruction above the state average.

Instructional expenditure as a district policy

School districts differ in instructional expenditure. A recent study used the Bureau of the Census Annual Survey of Local Government data from 1980 to 1994 to calculate multiple indicators of cross-district disparity in instructional expenditure (Hussar & Sonnenburg 1999). This study found that while disparity in instructional expenditures across districts seemed to decline in many states, disparity measures and the pattern of decline varied substantially. Furthermore, in a fairly large number of states, the disparity measures were inconsistent, and, in a small number of states, disparity increased over the same period of time. While these disparity measures may imply inequity they also reflect local fiscal policy differences because instructional expenditures, relative to current expenditures, are more subject to government control (Hussar & Sonnenburg 1999).

Research is unsettled about the relationship between school expenditure and student achievement (for reviews and debates, see Conn 1995; Lockwood 1994; Hanushek 1994, 1996; Hedges & Greenwald 1996; Hough 1993). An emerging consensus, however, is that overall funding and per-pupil expenditure may be overly simplistic as a predictor of learning outcomes, since schooling is conditioned by complicated factors of administration, family, and community (e.g., Wainer 1993; Hough 1993). While recent research has provided some evidence supporting the view that increased funding relates to better performance (e.g., Payne & Biddle 1999; Wenglinsky 1997), whether overall revenue or average per-pupil expenditure substantially affects academic outcomes remains controversial (e.g., Hanushek 1996; Hedges & Greenwald 1996). Research needs to relate performance outcomes to variations in resource allocation in general and teaching resources devoted to specific program areas in particular (Brent, Roellke & Monk 1997; Monk & Hussain 2000). How the money is spent may be crucial to improving achievement (Childs & Shakeshaft 1986; Conn 1995). Research examining the impact of public school spending, particularly spending for disadvantaged schools, suggests that learning can be improved if investment targets improving teacher quality (e.g., Kazal-Thresher 1993; Ferguson 1991), core curriculum, and standardized achievement (e.g., Lockwood 1994).

Policy analyses in systemic reform highlight the importance of fiscal control as an incentive/sanction mechanism directly linking to academic performance (Lockwood 1994; Elmore 1994). Under this mechanism, schools and teachers are encouraged to develop pedagogical initiatives for reaching high-standard curricular goals and are held accountable for improving student performance. In this line of thinking, the amount of money spent directly on improving instruction/learning relative to the amount spent on administrative operations and support services should be a crucial determinant of achievement outcomes (Childs & Shakeshaft 1986; Elmore 1993). On the other hand, current expenditure per pupil (CEPP), which covers spending on broad and immediate local needs, to some extent indicates local initiatives and priorities in fiscal control. Encompassing obligatory capital outlay and district discretionary spending, CEPP may also be a valid predictor of student achievement.

In this study, we ask how districts change state prescribed patterns of expenditure and how such changes relate to academic achievement. The departure of a district's proportional spending on instruction from the state baseline proportion may imply local autonomy in fiscal policy, which has been advocated as a fundamental mechanism for maintaining local stake and accountability (Murphy 1994; Strang 1987). Conceptualizing fiscal control as an essential element of local autonomy, we attempted to pinpoint a key issue in redefining the district role. We hypothesized that, other conditions being equal, a higher district instructional spending rate relative to the state average is associated with higher district average math achievement. In addition, we also examined CEPP, a more generic indicator of local financial control, by assessing its relationship to student performance.

Factors related to district spending

Communities are often constrained from spending more on instruction by local conditions. For example, poor communities have to spend more on basic social services, and sparsely populated areas must pay more for transportation. A large state contribution to district revenue probably constrains local discretion. The larger the share of the state contribution, the more likely the recipient districts fund instruction at a level close to the state baseline. Local cost of living is another factor that needs to be considered when examining school resources as it obviously affects the spending for teacher hiring and instruction.

The power of districts varies depending on local socioeconomic conditions, enrollment size, and geographic locale. Local socioeconomic conditions as a determinant of local autonomy may alter the intended consequence of district policy. Wealthy districts with their well educated populations and organized political support may push reform farther and benefit more from focusing on instruction and learning (Elmore 1993). In contrast, poor districts with populations of low education and income but high mobility often cannot come up with powerful political support for reform. Increasing spending on instruction may compromise desperately needed social services and ultimately undermine student learning. The influence of district policy probably also varies across urban-rural areas. Traditionally, rural residents are demographically homogeneous within communities but diverse across communities (Nachtigal 1982), have strong ties to local schools, and are skeptical about external governance (DeYoung 1990). Within different sociodemographic contexts, districts' investment in instruction may result in quite different achievement outcomes.

Prior studies have explored school funding in connection to standard achievement by synthetic analyses of data from CCD and NAEP (Wenglinsky 1997, 1998) or international standardized tests (Payne & Biddle 1999). In particular, Wenglinsky (1997) aggregated achievement measures to the district level and used both school-level and district-level variables to predict achievement. Taking the district as the unit of analysis, single-level analyses of aggregated performance show that average performance is positively associated with school resources. While such aggregated studies deal with the broad issues linking school resources to performance, they were not meant to and did not address specific questions concerning district fiscal policy in relation to individual student achievement. Furthermore, there are methodological problems in converting NAPE's multi-level stratified sample design into a single-level district sample design. The district sample resulting from attaching aggregated NAEP performance data to CCD district records does not necessarily represent the national population of school districts.

In a second study, Wenglinsky used a hierarchical linear model (HLM) technique to analyze merged 1992 NAEP and CCD data on 12^th grade mathematics (Wenglinsky 1998). Again, this analysis did not focus on district fiscal control. It addressed the broad concern of school resources in connection to social distribution of academic achievement. Further, the study did not distinguish district and school spending measures in the analysis. It did not deal with the methodological difficulty stemming from the data merge, namely, the possible unreliability of the estimates resulting from the merged data. (Note 1) Our study was designed to continue this line of research by synthesizing national data on student achievement and district spending, using sampling adjustment procedures and the technique of two-level hierarchical linear modeling.

Research questions

The first question in our study was whether or not student achievement varies across districts. The answer to this question sets the basis for addressing the substantive concern of district-level effect and for statistical testing of two-level models. The second question was how student achievement relates to district instructional spending—and CEPP. As the central issue in this analysis, we asked how district mean achievement related to district fiscal policy, adjusting for other variables at the district level and sociodemographics at the student level. District fiscal policy was indicated by two variables, CEPP and District Discretionary Rate of instructional spending. The latter was simply the difference of the district instructional spending rate from the state instructional spending rate. Compatible to the concept underlying such disparity measures as the coefficient of variation and the Gini coefficient (see Hussar & Sonnenberg 1999), DDR should make it straightforward to interpret the HLM estimates of the district fiscal policy effect.

The third question was: to what extent did DDR and CEPP, together with other district factors, account for the achievement outcome variance after adjusting for relevant district-level factors (e.g., enrollment size, state contributed share to district revenue, minority rate, poverty rate, geographic locale). In addition, we examined the possible interaction effects of DDR with three district conditions: the proportion of district revenue that came from the state, the average socioeconomic status (SES), and urban-rural locale. This would allow us to ask whether DDR had different effects on achievement under different conditions.

A final question about the achievement gaps: did higher district instructional spending help reduce math achievement gaps associated with race and SES? In other words, did increased instruction spending above the state average not only work to promote academic excellence, but also equity?

For this study, we combined data from NAEP 1990, 1992, and 1996 National Comparison Grade 8 Files and the Common Core of Data (CCD) in school years 1989—90, 1991—92, and 1995—96. As the most comprehensive and reliable national data source on academic achievement, the NAEP math tests in these three years shared a framework supported by the National Council of Teachers of Mathematics (Reese, Miller, Mazzeo & Dossey 1997).

CCD, covering the universe of U.S. public school districts, provides district-level itemized revenue/expenditures on an annual basis (National Center for Education Statistics 1995). It also contains a state file that gives spending data at the state level, which can be used to compute DDR. CCD offers information for examining district fiscal policies, including core expenditures per pupil, current expenditures per pupil, total expenditures per pupil, percent of total instruction expenditures, and percent of total salary expenditures, as well as related state spending measures. Additionally information on local sociodemographic conditions is available, including extensive 1990 Census data that were incorporated into district records. A linkage file is available for linking NAEP national and state assessments files with CCD data for the years between 1990 and 1998 (Westat 1998).

File Merge

First, we extracted data from the 1990, 1992, and 1996 NAEP National Comparison of math in 8th grade and CCD district files for school years 1989—90, 1991—92, and 1995—96. Using district identification code in both the NAEP and CCD files, we merged the two datasets for these years. With assistance from Westat and ETS, the three years' data were matched reasonably well. Most districts contained adequate numbers of students for two-level analysis (see Table 1).

¹ For the 1990 data one district (LEAID 3701530) had two cases and was excluded from the analysis.
² For the 1992 data two districts (with LEAIDs 5304920 and 1713970) had fewer than three cases and were excluded from the HLM analysis.

The resulting files contain NAEP 8th grader records, with affiliated district variables attached. Additionally, district-level cross-product terms were constructed to represent the interaction effects of DDR and the child poverty rate, DDR and urban locale, and DDR and the percentage of district revenue from the state (see Tables 2.1—2.3 for unweighted descriptive statistics at the two levels).

Sample Modification and Overall Weight

The resulting student subsamples within districts might not have been reliable in presenting the student populations of the given districts, because schools, not districts, were a sampling stage in the original NAEP design. Therefore, we reweighted and poststratified the data to improve its statistical reliability. The purpose was to shift the sampling stage from the school to the district in order to examine differences across groups of students who were hypothetically influenced by local districts' instructional.

The modification of the NAEP school-student sample into a district-student sample entailed reweighting the original sample and establishing the formal statistical status of the district-student sample. Within a sampled PSU, the NAEP school sample via "post-allocation" induced a district sample that included districts with which the sample schools were affiliated. With modification the representativeness of the school sample to PSUs would lead to the representativeness of the district sample to PSUs. The procedure is highlighted below; see Appendix I for details.

Student sample weighting

We assigned weights to each sample district within a PSU according to the district's post-inclusion probability, which was defined as the inclusion probability of the union of sample schools in the district. The calculation of this probability is described in Appendix I. The post-inclusion probabilities were used as a reference scale for assigning the district weights. The weight assigned to a sample district was proportionate to the reciprocal of its post-inclusion probability.

The students within a district were weighted by the reciprocal of the student sampling rate within the district. To calculate the weight we used the student population size of the sample district at a given grade. The CCD school file provided student enrollment size for each grade of the school, which was aggregated to the district level. We made a ratio adjustment (Deville & Sarndal 1992; Deville, Sarndal & Sautory 1993; Little 1993) of the student weights within the districts via poststratification according to important geographic/demographic features. We used this procedure to improve the representativeness of the student samples within districts to the district student populations.

The PSU weights remained intact. The obtained student weights were further adjusted at the national level in the same way as the poststratification conducted for the 1992 NAEP (see Wallace & Rust 1994, section 5.1.4). The resulting student sample preserved the goal of the original NAEP sampling design; namely, the targeted number of students at the given grades for the assessment were selected at a uniform probability nationwide (Wallace and Rust 1994, chapter 2).

District sample weighting

Multilevel linear modeling requires the use of level-2 unit (district) weights in analysis to assure that the level-2 sample represents the specified population (Bryk & Raudenbush 1992). We weighted the district sample to make it represent the national district population using the national district population information from CCD. To improve the representativeness of the district sample calibration (ratio adjustment), poststratification was carried out along race and Census region. These demographic and geographic characteristics were selected after a comparison of the sample and population distributions of those characteristics (Deville, Sarndal & Sautory 1993; Little 1993) (see Appendix II for the modified sampling distribution of race and Census region).

Analytical Approach

Before data analysis, we edited the data, examined missing data patterns, and constructed indicators to represent concepts to be analyzed (see Tables 2.1—2.3 for descriptive statistics of the variables at the student- and district levels).

Expenditure measures

District instructional spending measures and other fiscal variables were made comparable across locations by adjusting for local cost of living and inflation. We used the Teacher Cost Index (TCI) for states and districts available from NCES for the adjustment (National Center for Education Statistics 1995; also see Fowler & Monk 2001). TCI, an index of costs for hiring teachers, was developed through a regression analysis that estimated the effects of multiple factors, including the cost of living and quality of life for each state and district. The TCI score for states were centered by the national average of 100 (National Center for Education Statistics 1995).

We multiplied each state's total capital outlay per pupil by the TCI score for the given state and each district's by the district's TCI. Instructional expenditure rates at both district and state were calculated by dividing instructional expenditure per pupil with the adjusted total capital outlay per pupil. The resulting district rate was centered around the given state rate to generate the DDR in instructional expenditure. This TCI adjustment did not change the values of DDRs within a state, but it adjusted the difference in DDR for districts in different states.

Rescaling data

We recoded student race/ethnicity into a binary variable (White/Asian vs. minorities) and parent's education into two binary variables (with some postsecondary education vs. without). All per-pupil total expenditure measures were rescaled in thousands of dollars, total expenditure in millions of dollars, and total enrollment in thousands of students. In HLM modeling, each of the district-level variables was further centered around the grand mean, whereas each student variable was centered around the district mean.

Missing data

We examined nonresponse patterns to assure there were no systematic missing data to bias statistics. Approximately 12 percent of the 1992 NAEP student records and 3 percent of the 1996 records had missing data on one or more district variables due to unmatched records. There were no such missing data for 1990. We flagged the cases that had no district fiscal data in each file with a single missing indicator. One indicator was sufficient because missing data occurred quite consistently for most of the district fiscal measures. We then imputed data with grand mean on each missing variable and examined the missingness in a series of single-level regular regression analyses that included all the predictor variables of math achievement (for rationale see Cohen & Huang 2000; Little & Rubin 1986). We found that the missing data were largely random as the regression coefficient for the missing flag was not statistically significant in the three years. Thus, in the HLM analysis, we simply used the mean-imputed values for the missing data without using the missing flag.

Two-level hierarchical modeling

After reweighting the samples, we conducted univariate and bivariate analyses to examine data quality. Single-level multiple regression analyses were run with conceptually important variables to explore the general pattern of relationships between district variables and math achievement. We also examined the data to make sure that no obvious anomalies existed.

The central research question was whether student achievement was related to district discretionary rates in instructional spending (DDR). To address this question with data for each specified year, the two-level modeling took the math composite plausible values as the independent variables and DDRs as the predictor variables controlling for district- and student-level variables. See appendix III for a formal discussion of the HLM procedure. We used software package HLM Windows 5.03, which has a component to run the repeated procedure with multiple plausible values and to average the estimated coefficients (see Bryk, Raudenbush & Congdon 1996).

We conducted the two-level analysis in four steps. First, we examine the extent to which achievement varied across districts and the proportion of variability attributed to student effects and to district effects. With a one-way random effects ANOVA model, we separated the total variance of math achievement into between- and within-district components. By assessing the intraclass correlation and reliability of district means, we determined that district-level variance was substantial and statistically significant for further modeling.

Second, we estimated the relationships of a district's average math score to DDR and CEPP, adjusting for the effects of total enrollment size, minority student rate, poverty rate, state contribution to the district revenue, and geographic locale. With a random-interception model, we examined the extent to which district average achievement related to DDR and CEPP, controlling for the district-level variables specified above.

Next, we explored the interaction effects between DDR and district factors that might have potential combined effect on achievement. We asked of the DDR effect on achievement differentiated by some district characteristics. For example, DDR was probably more influential to achievement in disadvantaged districts; or, DDR might affect achievement in districts that relied more on local revenue than on state contributions. We specifically estimated the effect of the cross-product terms of DDR and poverty, DDR and rural-urban locale, and DDR and the state share in district's revenue.

Finally, we tested three important student-level variables—sex, SES, and minority status—in a random coefficient regression model. We assess the extent to which these three individual effects varied between districts. Given that these gaps did vary across districts, we then tested full models that included these student variables. The full model accounted for both district average achievement and district achievement gaps. We first determine whether DDR related to district average math score, adjusting for both district- and student-level variables. Then, we asked whether achievement gaps due to sociodemographic backgrounds related to DDR (or, whether DDR helped reduce math achievement gaps).

Including student variables in the model was also methodologically important. Students were not randomly associated with districts; the district-level estimates might be biased if we did not control for student background effects. Second, sex, SES, and minority status at student level were established background factors that strongly related to achievement. Controlling for these variables could reduce unexplained level-1 error and thus improve the precision of the estimates of district spending rates as well as the power of hypothesis tests (Bryk & Raudenbush 1992).

Problems and limitations

It is typically more difficult to model slopes than means with HLM techniques. Prior analyses of the NAEP data have reported unreliable estimation with slope equations (for example, Arnold 1995). While concentrated in intercept models, we did test slope models with limited number of variables at the two levels. The resulting slope estimates were considerably less reliable than those of intercept models.

Data across the three years appeared reasonably compatible in univariate statistics. At the student level, sex (with male coded 1 female coded 2) and minority (with the Asian and White coded zero, all the other groups coded 1) distributions were quite steady with data of the three years. Parents' educational levels seemed slightly rising. The rate of sample students whose parents had at least some college education was 52 percent in 1990, 54 percent in 1992, and 58 percent in 1996. The NAEP math achievement on average was higher in 1996 than in the other two years (approximately 268 in 1996, 259 in 1992, and 256 in 1990) with compatible standard deviations and ranges (see Tables 2-1 to 2-3).

At the district level, the descriptive statistics were reasonably compatible across years as well. The average state instructional spending rate (ASIER) barely differed over the years, ranging from 59.61 to 60.99 percent. DDR averaged very close to zero because by definition the scores were centered by the state average. This measure's standard deviation was similar across years though the range shifted slightly. CEPP on average rose from $4,310 in 1990 to $5,360 in 1996. The average proportion of district revenue that came from the state (C_STREVP) also seemed acceptable, with estimates ranging from 42.40 percent in 1992 to 48.43 percent in 1990. These sample estimates from the NAEP-CCD combined data were quite consistent with the released national statistics (e.g., National Center for Education Statistics 1996). Likewise, district level demographic statistics (total enrollment, Black student rate, poverty rate, and at-risk student rate) appeared reasonable for the three years. Tables 2.1—2.3 also present descriptive statistics for the interaction terms between DDR and district demographic variables.

A possible anomaly was with the geographic locale. While the rate of urban districts ranged 26 to 30 percent for the years—again reasonable estimates—the rate of rural districts shifted somewhat excessively from 15 percent in 1996 to 37 percent in 1990. This problem could be indicative of the unreliability of the merged NAEP and CCD data.

Bivariate Statistics

A number of patterns revealed in the bivariate correlation analysis must be noted. First, fiscal measures at district level were correlated, often in large magnitude. The total expenditure and current expenditure, for example, had a correlation coefficient around 0.98 in all three years (the full matrix of the correlation coefficients is available upon request to the first author). Per pupil spending items (for example, CEPP, per pupil total expenditure, and per pupil instruction expenditure) were correlated to each other. These measures were substantially correlated with the total expenditure measures, albeit to a moderate extent. Expenditure measures were also closely related to enrollment size. Table 3 shows the estimates of bivariate correlation among the selected district-level variables.

Note that even in this selected group, there were pairs of variables that were well correlated. Proportion of district revenue from the state was strongly associated with CEPP (0.68 in 1996, 0.70 in 1992, and 0.66 in 1990). Poverty rate and at-risk student rate were also strongly related (0.62, 0.75, and 0.40, respectively, for the three years). We excluded at-risk student rate from the equation because it presumably overlapped with poverty rate to indicate the disadvantaged condition of a district, yet its range was smaller than the poverty rate. For similar reasons, we dropped rural locale and retained urban locale to make the model parsimonious. (Note 2)

The high multicollinearity required model specification with high selectivity of independent variables at the district level such that the included variables were not highly correlated to each other and adequately represented our conceptual model. After testing OLS regression analyses with SAS and an initial run of two-level models with HLM, we decided to specify in the final model the following independent variables at the district level:

• District discretionary rate in instructional spending,
• State average instructional spending rate,
• CEPP (in thousands of dollars),
• Proportion of revenue from the state,
• Total enrollment (in thousands of students),
• Black student enrollment rate,
• Child poverty rate, and
• Urban locale (in contrast with suburban).

* p < 0.05

HLM Modeling Results

Unconditional models were tested with each year's data. Without any independent variables, the models separately estimated the variance of the student math achievement at individual and district levels. Table 4 presents the estimates of the unconditional models. For each year, a substantial proportion of variance occurred at the district level, meaning that districts differed in their average math achievement. For 1996, 26 percent of the variance was at the district level, as indicated by the intraclass correlation coefficient. A chi-square statistic of 2401 with 159 degrees of freedom was highly significant for the district variance estimate. The reliability of school means (0.71) was also acceptable for further HLM analysis, as these sampled school means on average represented the true school means reasonably well. (Note 3) The two-level variance distribution pattern was similar in the 1992 and 1990 data. These statistics strongly suggested that HLM modeling with random effect at the both levels was necessary for analyzing student achievement in relation to district fiscal variables.

District average math achievement in relation to DDR

Using district variables to explain district average math achievement, we tested a series of means-as-outcomes models. At each level, the model specified a random effect. Fixed effects, however, were only specified at the district level, including state average instructional spending rate, DDR, total enrollment in thousands of students, Black student enrollment rate, CEPP in $1000, child poverty rate, at-risk student rate, urban and rural locale (both coded in contrast to suburban), and percent of revenue from the state. The resulting estimates are presented in Table 5.1.

Entering district-level independent variables in the model helped account for approximately a half of the district-level variance (49 percent in 1996, 62 percent in 1992, and 53 percent in 1990). Controlling for other variables, several district variables were found related to district average math achievement in one or more years. District total enrollment was related to low average math achievement in 1992, but not in 1990 and 1996. The minority enrollment rate was strongly related to low average achievement in all three years, with high statistical significance. The child poverty rate was related to low achievement mean, with a significant estimate for each year. These findings were compatible with prior research in school organization and achievement.

The effect of DDR was not substantiated with data for the three years. Net of the effects of other district variables, DDR was not statistically significantly related to district mean math achievement in any year. The estimate in the three years was essentially zero since it was trivial in size and not statistically significant. CEPP, on the other hand, was related to high average achievement, although the estimate for 1992 was not statistically significant (see Table 5).

With the NAEP-CCD combined data for the three years, we failed to find evidence to support our central hypothesis that high district instructional spending relative to the state average would increase district average performance level, holding other things constant.