Effects of School Funding on Student Academic Achievement

Education Policy Analysis
Maya Boyle
 

Mike Robinson
 
 
Introduction
Background
For the past 50 years, SAT scores for high schools across the nation have been steadily falling. Because the SAT is a fairly consistent method of testing the academic aptitude of high-school age children, this trend is concerning. As it stands, by the standards of the College Board, high school academics are preparing students less and less adequately for the rigours of secondary education. This paper seeks to address what policy initiatives can be taken by states to raise these scores.

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Research
I hypothesised at the beginning of the study that per capita expenditures on primary and secondary education would have a significant effect on SAT scores. By using multiple data sets: population data from the US Census Bureau, education expenditure results from the Department of Education, a partial data set from STATA, and participation levels by the College Board, I amassed a collection of variables that I considered to be most valuable to determining the relationship between state education policy and SAT scores

Mean scores of college-bound seniors

The SAT

Stacks of college test prep books
Basic Conclusions
By analysing what I determined to be the most significant factors affecting SAT performance, I concluded that the factor which could most effectively boost SAT scores came on the heels of SAT participation. SAT scores were strongly correlated with participation levels. A greater percentage of high school students taking the exam in each state resulted in a weaker performance. A disproportionately high number of high-scoring participants take the SAT whether or not initiatives are undertaken by state governments or schools to boost participation. Those students typically score higher. The increase in participation of students taking the SAT will come from a portion of the population who otherwise would transition straight to career paths out of high school. Education initiatives typically give these students an opportunity to take the test, and these students typically score lower.
Ultimately, from a policy perspective, the best way to boost scores is to ready the portion of students who are being given the opportunity to take the SAT through funding and other education initiatives. It is useless for them to take the exam if all it does is prove that they are not ready for college.
Literature Review
Zajonic, Robert B., Bargh, John A. “Birth order, family size, and decline of SAT scores.” American Psychologist 79.1 (1989): 179-197. http://www.apa.org. Web. 4 Dec. 2012.
The survey of SAT scores and birth order demonstrated that a negligible fraction of the decline in SAT scores can be explained by changes in family dynamics. In general, SAT scores showed little variation with birth order and family size, which was far less than that which was found in other data sets.
Murray, Charles, and Richard J. Herrnstein. “What’s Really behind the SAT-Score Decline?.” Public Interest 106 (1992): 32-56.
This survey of SAT scores and population distinguished between the separate populations of high school students who took the SAT and those who did not. Suggested that the greatest effect on the SAT-score decline was the regression of academic capabilities of high-school age teenagers. This possibly came from the ‘dumbing-down’ of textbooks
Wharton, Yvonne L. “List of Hypotheses Advanced to Explain the SAT Score Decline.” (1976).
The hypotheses analysed in this study suggested that changes in schools, society, population, and an increase in problems with the tests themselves are the greatest contributors to the decrease in SAT Scores. A list of variables: “The first major category (changes in the schools) is further broken down into hypotheses related to curriculum, institutional policies, teachers, and students. The second major category (changes in society) lists hypotheses related to family, religion, civil rights, crisis of values, national priorities, economic, labor movement in education, and technological changes. (Abstract)”
Model
Objective
In this report, I will attempt to determine which two variables would most significantly positively effect mean SAT scores in college-bound high-school adolescents. An exhaustive list of the variables I used were: Mean Composite SAT scores, Mean Verbal, Mean Math, Geographical Region (dummy variable), Population, Per pupil expenditures (primary and secondary education), Government education spending, Median household income, Percent of High School graduates taking SAT.
Models
The primary models I used to determine which two variables that could be affected by state education policy were:
Regressing SAT scores against government spending and income
Regressing SAT scores against state population and percentage of high school students who took the SAT
Regressing SAT scores against per pupil expenditures on primary and secondary education and percentage of high school students who took the SAT
Finally, I developed a model with each of the variables that ultimately seemed most relevant:
Regressing mean SAT scores, controlling for population, per pupil expenditures, median household income, and the percent of students taking the SAT.
Hypothesis
Before I ran the regressions, I hypothesised that the main factors affecting SAT performance would be median household and per pupil expenditures for primary and secondary education. I anticipated that states with a higher portion of domestic wealth would score better because there would be more local money going into infrastructure, and assumed that states with higher levels of spending on primary and secondary education would be higher because they reflect a greater education initiative.
Methodology/Data
Testing the Hypothesis
For each regression, I focused most specifically on the coefficient, t-statistic, and r-squared result.
Regression 1

I hypothesised that an increase in government spending will increase states’ SAT scores, controlling for median household income

Null hypothesis was not proven

What does this mean?
R-squared: accounted for about 1/4 of the variance
Coefficients were both negative

Government spending raises, SAT scores decrease
As median income increased, SAT scores decreased

T-statistics

Both are statistically significant

y=-6.62*107×1+-4.458199×2+1107.044

Regression 2

I hypothesised that larger states receive more funding, and thus would have higher scores. Additionally, more people would lead to greater variance in scores

Null hypothesis was not proven
What does this mean?
R-squared: accounted for about 82% of variance
Coefficients: Negative relationship between both population and participation
T-statistics: Participation is highly significant, population minimally.

y=-1.24*106×1-2.8×2+1021

Regression 3

I hypothesised that primary/secondary education funding would significantly play a role on SAT scores. Additionally, a larger pool of participants accounts for a wider breadth of performance

Null hypothesis was not proven
What does this mean?
R-squared accounted for about 82% of variance
Coefficients: Weak, positive relationship with funding, yet a stronger negative relationship with student participation
T-statistics: Participation is highly significant

y=.0043277×1-1.984192×2+999.483

Regression 4

I hypothesised that funding for primary and secondary education and the percentage of high school students who take the exam will be most important
Hypothesis proven true
What does this mean?

R-squared: accounted for about 88% of variance
Coefficients: Expense, Participation, and Region 1 were negatively correlated; all the rest had positive effects
T-statistics: Only participation was under -1.96; Regions 2 and 4 were over 1.96. These were the most significant. The t-statistic of population was at -1.94, which I considered significant for the intents and purposes of this data.

y=-1.36*106×1 + .0000282×2 – .0066046×3 + 1.796×4 -2.0516×5 – 2.329155×6 + 45.028×7 + 23.8149×8 + 989.8613

Analysis
Regression 1
Government spending as a whole ultimately does not aid SAT performance. Regardless of whether or not it builds infrastructure, it seems as if funds set aside specifically for primary and secondary education are the most necessary to boost SAT scores. Additionally, I determined that- at least when it comes to SAT scores in high schoolchildren, Wealth does not denote academic success.
As was determined from the methodology of regression 1, the statistical relevance of income and insignificance of government spending led me to reason that income played a greater role in determining SAT scores than government spending.
Further, I questioned if the results for regression 1 had anything to do with causality, because the states that score more poorly on SATs will receive more money from the government to ameliorate educational infrastructure.
Regression 2
Participation was negatively correlated with SAT scores, and significantly so. I reasoned that a base participation rate includes a skewed population of students who intend to go to college regardless of domestic initiatives to send high school students to college before allowing them into the workforce. Therefore, if more students choose to take the SAT, those students will be those who had not necessarily planned their high school education to ready them for the SAT. There scores thus will be lower.
Regression 3
While the results of my first regression clearly suggested that government spending as a whole has little to no effect on SAT scores, I aimed to determine that per pupil expenditures on education for primary and secondary schooling had a strong positive correlation with students’ SAT readiness. This was not the case. Government education expenditures was loosely correlated with SAT scores, but not significantly so. This result could possibly have come from different years of availability for each variable. Many of the variables were derived from an old STATA data set that suited my intents, but I added other variables to develop a more individual project. Government spending was one of these variables, and the data may have been more recent than others.
Further, as was the case with regression 2, the levels of participation played a strong and significant factor in determining the rate at which students would score on the SAT. The t-statistic was highly significant, so I trust that this correlation is true. I expect the population shift that I described in my previous analysis will still stand.
Regression 4
Ultimately, I determined that as much as I had hoped that income and per-pupil education expenditures would have strong effects on the scoring of high schoolers on the SAT, because such effects are easily fixable through initiatives. I was wrong. Expense and income both were determined to be insignificant, with expense ultimately having a negative correlation with SAT scores. This cannot show the whole picture, however. Wealthier states traditionally have stronger educational infrastructures and students who perform better on the SAT. I can only assume that wealthier states are those which have educational initiatives to give more students the chance to take the SATs in the first place, and thus have a pool of lower-scoring students. Conversely, students in states with low median incomes had to have a significant personal initiative to take the Test in the first place. Therefore, the relationship between income and infrastructure is that which renders the relationship negative.
Tables
Table 1: Table of Means

Variable

Observation

Mean

Std. Dev.

State

0

 
 

Region

50

 
 

Population

50

4962040

5459782

Area

50

70759.14

85796.76

Csat

51

944.098

66.93497

Expense

51

5235.961

1401.155

Income

51

33.95657

6.423134

Participation

51

39.33333

32.1538

 
 
 
 
Table 2: Description of Data
Variable | Obs Mean Std. Dev. Min Max
————-+——————————————————–
state | 0
region | 50 2.54 1.128662 1 4
pop | 50 4962040 5459782 454000 2.98e+07
area | 50 70759.14 85796.76 1045 570374
csat | 51 944.098 66.93497 832 1093
————-+——————————————————–
vsat | 51 447.8431 31.87562 395 515
msat | 51 496.2549 35.58418 435 578
percent | 51 35.76471 26.19281 4 81
expense | 51 5235.961 1401.155 2960 9259
income | 51 33.95657 6.423134 23.465 48.618
————-+——————————————————–
high | 51 76.26078 5.588741 64.3 86.6
college | 51 20.02157 4.16578 12.3 33.3
spending | 51 1.75e+07 2.03e+07 270000 1.03e+08
participat~n | 51 39.33333 32.1538 3 93
 
 
 
 
Table 3: Regression 1

R2=.2607

Coefficient

t

Spending

-6.62*107

-1.58

Income

-4.458199

3.37

Table 4: Regression 2

R2=.8149

Coefficient

t

Population

-1.24*106

-1.59

Participation

-2.8

-13.56

 
Table 5: Regression 3

R2=.8158

Coefficient

t

Expense

0.0043277

1.19

Participation

-1.984192

-12.49

Table 6: Regression 4

R2=.8772

Coefficient

t

Population

-1.36*106

-1.94

Area

0.0000282

0.53

Expense

-0.0066046

-1.26

Income

1.796

1.85

Participation

-2.0516

-10.15

Region 1

-2.329155

-0.21

Region 2

45.028

2.96

Region 4

23.8149

2.03

 
 
 
 
 
 
 
 
 
 
 
Table 7: College Board Participation Rates
Table 8: College Board Participation Rates (cont.)
Basically this isn’t really done. 80
Mount Holyoke CollegeSAT Scores: An Econometrics Perspective

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