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Running head: EXCEL PROJECT
Public School Expense and Academic Performance
Carly Schwarmann
Seattle Pacific University
EDU 6976 Interpreting & Applying Educational Research II
Fall Quarter, 2008
1
Data was gathered from the article “Getting What You Pay For: The Debate Over Equity in Public School Expenditures” to examine 9 variables across all 50 states. They looked at equity in public school expenditures. Many people believe that the system of financing local schools is unfair, however, media suggest, that school spending and academic performance are not statistically related.
Data was taken from 1997 Digest of Education Statistics, an annual publication of the U.S. Department of Education. Data from tables were downloaded from the National Center for Education Statistics (NCES) website: http://nces01.ed.gov/pubs/digest97/index.html.
Variable Descriptions:Name Name of state Expenditure Current expenditure per pupil in average daily attendance in public
elementary and secondary schools, 1994-95 (in thousands of dollars)Ratio Average pupil/teacher ratio in public elementary and secondary schools, Fall 1994Salary Estimated average annual salary of teachers in public
elementary and secondary schools, 1994-95 (in thousands of dollars)Eligible Percentage of all eligible students taking the SAT, 1994-95Verbal Average verbal SAT score, 1994-95Math Average math SAT score, 1994-95 Total Average total score on the SAT, 1994-95 Region 1= West; 2=Midwest; 3= South; 4=Northeast
I will show and analyze the data represented in graphs and tables, including histograms, box plots, ANOVA, and scatterplots. The figures will show how variables are related and which pairs are statistically significant. We begin by looking at histograms showing the frequency for all the variables across the United States.
Histograms
<=11
(11,
12]
(12,
13]
(13,
14]
(14,
15]
(15,
16]
(16,
17]
(17,
18]
(18,
19]
(19,
20]
(20,
21]
(21,
22]
(22,
23]
(23,
24]
(24,
25]
(25,
26]
>26
0
2
4
6
8
10
12Ratio
2
The Ratio shows a positive skew. I am surprised to see such low averages for teacher student ratio. I have 33 students in each of my classes. The fact that elementary data is included must bring the mean down, because elementary classes generally have much lower class sizes than high school. I wonder if the para-eduactors and specialist teachers were included in the count.
<=2 (2, 3] (3, 4] (4, 5] (5, 6] (6, 7] (7, 8] (8, 9] (9, 10] >100
2
4
68
10
12
1416
18Expenditure
In Thousands of Dollars.
Expenditure shows a positive skew. It is close to a normal curve which makes sense because the mode should fall in the middle of the means. Only one state spends $3,000 per pupil and only a few states spend over $8,000 per pupil. It probably has a lot to do with the cost of living in each state.
<=24
(24, 26]
(26, 28]
(28, 30]
(30, 32]
(32, 34]
(34, 36]
(36, 38]
(38, 40]
(40, 42]
(42, 44]
(44, 46]
(46, 48]
(48, 50]
(50, 52]
>520
2
4
6
8
10
12Salary
In thousands of dollars.Salary shows a positive skew, which makes sense because there is high turn-over for new teachers so there are more younger teachers receiving lower salaries. Taking the mean salary skews the results because there are fewer people who stay in teaching for a long period of time and earn higher salaries.
3
<=3 (3, 8]
(8, 13]
(13, 18]
(18, 23]
(23, 28]
(28, 33]
(33, 38]
(38, 43]
(43, 48]
(48, 53]
(53, 58]
(58, 63]
(63, 68]
(68, 73]
(73, 78]
(78, 83]
>830
2
4
6
8
10
12
14Eligible
The graph shows the percentage of eligible students taking the SAT has a positive skew. There are a large number of eligible students that don’t take the SAT. I would infer that those states are areas that are more focused on agriculture, and manual labor and put less emphasis on higher education.
<=400
(400, 410]
(410, 420]
(420, 430]
(430, 440]
(440, 450]
(450, 460]
(460, 470]
(470, 480]
(480, 490]
(490, 500]
(500, 510]
(510, 520]
>5200
1
2
3
4
5
6
7
8
9Verbal SAT
The distribution is bimodal. Some states scores may be affected by the population, such as students who are bilingual. Again, some states place more emphasis on education.
4
<=430
(430,
440]
(440,
450]
(450,
460]
(460,
470]
(470,
480]
(480,
490]
(490,
500]
(500,
510]
(510,
520]
(520,
530]
(530,
540]
(540,
550]
(550,
560]
(560,
570]
(570,
580]
(580,
590]
(590,
600]
>600
0
1
2
3
4
5
6
7
8Math SAT
The distribution is bimodal. Many of the states with higher math scores have big businesses and corporations, so students and are more likely to be exposed to math.
<=830
(830, 850]
(850, 870]
(870, 890]
(890, 910]
(910, 930]
(930, 950]
(950, 970]
(970, 990]
(990, 1010]
(1010,
1030]
(1030,
1050]
(1050,
1070]
(1070,
1090]
(1090,
1110]
>1110
0
2
4
6
8
10
12Total SAT
The distribution is bimodal, which makes sense because both math and verbal scores were bimodal.
5
<=0 (0, 1] (1, 2] (2, 3] (3, 4] (4, 5] >50
2
4
6
8
10
12
14
16Region
Region is the only categorical variable. The frequency of the region ranges from 11 to 14, with the highest frequency in region 4.
Box Plots
SalaryLower
WhiskerLower Hinge Median
Upper Hinge
Upper Whisker
25.994 30.9775 33.2875 38.54575 47.951
The lowest average salary is $25,994, the median is $33,287 and the highest is $50,050.
Expenditure
Lower Whisker
Lower Hinge Median
Upper Hinge
Upper Whisker
3.66 4.88175 5.77 6.434 9.77
6
20 25 30 35 40 45 50
2 3 4 5 6 7 8 9 10 11
The lowest expenditure per student is $3,660, the median is $5,770, and the highest $9,770.
RatioLower
Whisker
Lower Hinge Median
Upper Hinge
Upper Whiske
r13.80 15.225 16.60 17.575 24.30
The lowest teacher to pupil ratio is 14 students per teacher the median is 17 and the maximum is 24.
Eligible
Lower Whisker
Lower Hinge Median
Upper Hinge
Upper Whisker
4.0 9 28.0 63 81.0
The lowest percentage of eligible students that take the SAT is 4%. The median is 28% and the highest is 81%. This is a surprisingly wide distribution.
SAT Verbal
Lower Whiske
rLower Hinge Median
Upper Hinge
Upper Whiske
r401.00 427.25 448.00 490.25 516.00
7
12 14 16 18 20 22 24
0 10 20 30 40 50 60 70 80 90 100
400 420 440 460 480 500 520
The lowest average verbal SAT score was 401, the median was 448 and the highest was 516. In 1994 the verbal SAT removed the antonym questions and increased the focus on passage reading.
SAT MathLower
Whisker
Lower Hinge Median
Upper Hinge
Upper Whiske
r443.00 474.75 497.50 539.5 592.00
The lowest average math SAT score was 443, the median was 497, and the highest was 592. These scores are higher than the averages of the verbal SAT. Either students are better at math than reading and writing, or the math test is easier than the verbal. In 1994 they added the use of calculators and non multiple choice questions.
SAT Total
Lower Whisker
Lower Hinge Median
Upper Hinge
Upper Whisker
844.00 897.25 945.50 1032 1,107.00
The lowest average SAT score was 844, the median was 945 and the highest average score was 1,107. The changes in the SAT format in 1994 probably had a lot to do with the scores that year.
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400 420 440 460 480 500 520 540 560 580 600
800 850 900 950 1000 1050 1100 1150 1200
AnovaThe regions differ in size. All null hypotheses were rejected. All have very low p-values and Tukeys were used to analyze the significance of differences.
Eligibility
ANOVA Table 5%
Source SS df MS F Fcritical
p-value
Between 17914.1 3 5971.4 15.988 2.8068 0.0000 RejectWithin 17181.1 46 373.5Total 35095.1 49
Estimates of Group MeansGroup Confidence Interval
Region 1 30.3846 ± 10.789 95%Region 2 12.5833 ± 11.23 95%Region 3 29.8182 ± 11.729 95%Region 4 63.4286 ± 10.397 95%
Tukey test for pairwise comparison of group means
Regio
n 1
r 4Region
2 Region
2
n - r 46Region
3 Region
3
q0 3.76Region
4 Sig Sig Region
4T 21.9098
Region 1= West; 2=Midwest; 3= South; 4=Northeast
Region 2 (Midwest) has very low eligibility. Region 4 (Northeast) has very high eligibility. Region 1 (West) and 3 (South) have very similar means of eligibility. The differences between region 1 and 4 and region 2 and 4 are significant. I would like to know more information about how eligibility for the SAT is determined. It could mean that students can’t afford it or they have physical or mental handicap that prevents them from taking the SAT. I assume that the students who are eligible to take it, but don’t, do so by choice.
Total SAT Scores
ANOVA Table 5%
Source SS df MS F Fcritical
p-value
Betwee 12984 3 43283 13.783 2.8068 0.0000 Rejec
9
n 9 t
Within14445
9 46 3140.4
Total27430
8 49
Estimates of Group MeansGroup Confidence Interval
Region 1
963.846 ± 31.285 95%
Region 2
1048.08 ± 32.563 95%
Region 3
952.273 ± 34.011 95%
Region 4
908.143 ± 30.147 95%
Tukey test for pairwise comparison of group means
Regio
n 1
r 4Regio
n 2 SigRegio
n 2
n - r 46Regio
n 3 SigRegio
n 3
q0 3.76Regio
n 4 Sig Regio
n 4
T63.530
8
Region 4 has the lowest mean SAT score and Region 2 has the highest. It could be that students choose to take the ACT instead of the SAT. However, we can conclude from this that overall the students in the Midwest outperform the rest of the regions in the United States. There is a significant difference between region 1 and 2, 2 and 3, and 2 and 4.
Salary
ANOVA Table 5%
Source SS df MS F Fcritical
p-value
Between551.67
8 3 183.89 7.1811 2.8068 0.0005 Reject
Within1177.9
5 46 25.608
Total1729.6
3 49
Estimates of Group MeansGroup Confidence Interval
Region 1
34.7125 ± 2.8251 95%
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Region 2 33.381 ± 2.9405 95%
Region 3
30.4786 ± 3.0712 95%
Region 4
39.5961 ± 2.7223 95%
Tukey test for pairwise comparison of group means
Region
1
r 4Region
2 Region
2
n - r 46Region
3 Region
3
q0 3.76Region
4 Sig Region
4
T5.7368
9
Region 4 has the highest mean salary and region 3 has the lowest. The northeast has a lot of wealthy areas, especially in New York. The south has a lot of poor areas such Mississippi and Louisiana. There is a significant difference between region 2 and 4.
ExpenditureANOVA Table 5%
Source SS df MS F Fcritical
p-value
Between
38.3015 3 12.767 11.143 2.8068 0.0000
Reject
Within52.703
4 46 1.1457
Total91.004
8 49
Estimates of Group MeansGroup Confidence Interval
Region 1
5.54308 ± 0.5976 95%
Region 2
5.74158 ± 0.622 95%
Region 3 4.847 ± 0.6496 95%
Region 4
7.21336 ± 0.5758 95%
Tukey test for pairwise comparison of group means
Regio
n 1 r 4 Regio Regio
11
n 2 n 2
n - r 46Regio
n 3 Regio
n 3
q0 3.76Regio
n 4 Sig Sig Regio
n 4
T1.2134
8
The means of region 1 and 2 are similar. The mean expenditure for region 3 is the lowest and region 4 is the highest. This is not surprising considering the population and opportunities available in the northeast versus the south. There is a much higher cost of living in the northeast. There is a significant difference between region 1 and 4 and 2 and 4.
Teacher to student ratio
ANOVA Table 5%
Source SS df MS F Fcritical
p-value
Between
107.355 3 35.785 11.405 2.8068 0.0000
Reject
Within144.32
7 46 3.1375
Total251.68
2 49
Estimates of Group MeansGroup Confidence Interval
Region 1
19.0615 ± 0.9889 95%
Region 2 16.2 ± 1.0293 95%
Region 3
17.0818 ± 1.075 95%
Region 4 15.2 ± 0.9529 95%
Tukey test for pairwise comparison of group means
Regio
n 1
r 4Regio
n 2 SigRegio
n 2
n - r 46Regio
n 3 Regio
n 3
q0 3.76Regio
n 4 Sig Regio
n 4
T2.0081
1
12
There is a significant difference in ratio between Region 1 the west and 2 the Midwest and 1 (west) and 4 the northeast. Region 4 has the lowest mean ratio and region 1 has the highest. I believe this is because there is a large number of students in the northeast that attend private schools, which can mean lower class sizes for public education. I also think it has to do with population density. There are not as many big cities in the Midwest, therefore the lower numbers in the population create smaller class sizes.
Comparing Variables of 50 states
ANOVA Table 5%
Source SS df MS F Fcritical p-value
Between 3.6E+07 4 9E+06 6996.52.408
5 0.0000 Reject
Within 311475 245 1271.3
Total 3.6E+07 249
Estimates of Group Means
Group Confidence Interval
expenditure 5.90526 ± 9.9321 95%
ratio 16.858 ± 9.9321 95%
salary 34.8289 ± 9.9321 95%
eligible 35.24 ± 9.9321 95%
total 965.92 ± 9.9321 95%
Tukey test for pairwise comparison of group means
expenditur
e total
r 5 ratio ratio
n - r 245 salary Sig salary
q0 3.86 eligible Sig eligible
T 19.4639 total Sig Sig
13
When comparing all 50 states using an ANOVA there are significant differences and we would reject the null hypothesis with an alpha level of .05. The Tukey results tell us there is a significant difference among expenditure and salary eligibility, and total SAT scores. There is also a significant difference between ratio and total SAT score.
There may not be homogeneity of variance because the regions vary with regard to teacher salary, teacher student ratio, expenditures, eligibility, and total SAT scores. Different areas in United States are diverse in terms of each of the variables. The amount they value education can affect eligibility. The resources they have available for teaching and learning can affect eligibility and expenditures. Cost of living can affect salary and expenditures. Population size can affect ratio.
Scatter plots
With 48 degrees of freedom using the critical value for r table for an alpha of .05 you need .279 and for alpha .01 you need .361. If the calculated r is greater or equal to the table value the null hypothesis is rejected. The regression line and its equation are shown on the graph where y is a function of x.
800.00 900.00 1,000.00 1,100.00 1,200.000.00
2.00
4.00
6.00
8.00
10.00
12.00
f(x) = − 0.0069312275908571 x + 12.6002713545607R² = 0.144808410884018
SAT Score and expenditure
expenditureLinear (expenditure)
SAT Score
expe
nditu
re
SAT scores and expenditures show a negative correlation. As more money is spent on each student, their SAT score actually goes down. There are several outliers. It could be due to the student attitude toward the test. Pearson r equals .380. Reject Null hypothesis at .05 and .01. These results are surprising. I would like to see an analysis of expenditures to better understand the breakdown of what the expenses go toward. How much of the money is spent on classes that are related to SAT content and SAT prep? Given this information, I would suggest expenditures be reallocated to go toward proven effective methods for SAT preparation.
14
800.00 900.00 1,000.00 1,100.00 1,200.000.00
5.00
10.00
15.00
20.00
25.00
30.00
f(x) = 0.00246122164716642 x + 14.480656786569R² = 0.0066021837617769
Teacher Student ratio and SAT Score
T:S ratioLinear (T:S ratio)
SAT Score
Teac
her S
tude
nt R
atio
Teacher to student ratio and SAT scores have a weak positive correlation. When teachers are assigned to teach larger groups of students, the student SAT improves slightly. There are two outliers that show extra large classes. Pearson r equals .081. Accept null hypothesis at .05 and .01. The results could just be due to chance, so there is not enough evidence that class size affects SAT scores. I suspect the difference might have more to do with teacher experience and ability than class size. I would like to see more tests done with extreme high and low class sizes to look for differences. I would also like to know how many years students were in classes of these sizes. It could be that they had large class sizes in some classes and not others. Plus, class sizes can change from year to year.
20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.000.00
2.00
4.00
6.00
8.00
10.00
12.00
f(x) = 0.199514942822549 x − 1.04362998237114R² = 0.756554672828788
Salary and Expenditure
salaryLinear (salary)
Salary
Expe
nditu
re
Salary and Expenditure have a strong correlation. Pearson r equals .870. The null hypothesis must be rejected. It makes sense that schools that can afford to pay their teachers higher salaries
15
also have more money to spend on students. This is good for students in rich schools, but obviously has negative effects on impoverished areas.
25.00 30.00 35.00 40.00 45.00 50.00 55.000.00
5.00
10.00
15.00
20.00
25.00
30.00
f(x) = − 0.000437184075761682 x + 16.8732266492R² = 1.31350224075177E-06
Teacher to Student Ratio and Salary
T:S ratioLinear (T:S ratio)
Salary
Teac
her S
tude
nt R
atio
Teacher to Student Ratio and Salary have nearly a zero correlation. There are two outliers. As salary increases teacher to student ratio remains about the same. Class size has remained relatively constant over the years; however this can often create challenges for teachers with large class sizes. In theory as class size increases, teaches should be compensated for the extra work. It can be difficult to meet the needs of all students in large class sizes and creates extra work for teachers. Pearson r is very low at .001. Accept the null hypothesis.
ConclusionFrom the data presented here we can conclude that as schools spend more, student SAT scores do not improve. There were some results that were surprising to me. As teacher to student ratio increases, so do SAT scores. The school where I work is AAAA and overcrowded. Around 90% of students are college-bound. We have class sizes so big they would be off the charts. I suppose bigger schools offer more opportunities for success on tests like the SAT, such as advanced placement courses. Some of the most crowed classes are with the most popular teachers, so student success may have more to do with motivation and teacher skill.
Another ponderous statistic is that as more money is spent on the student, the more their SAT scores drop. There is no logical explanation for this except that the school expenditures are not helping growth in math and reading and writing. I wonder if it is helping in other areas. This would be an important point to look into to ensure that money is being used wisely and in a way that helps students.
I would suggest a more in depth study by region, since each area has unique factors that contribute to the variables. Another idea is to compare big cites and small towns separately. I recommend looking into reasons why students do not take the SAT. I would look at other data besides SAT scores, such as GPA, ACT score, and the number of AP classes the student takes. I
16
would look further into teacher ability and experience and focus only on high school to get a clearer picture of that specific age group.
A new study is called for because this data is out of date. The SAT is scored differently now. Cost of living has gone up with inflation along with teacher salary and student expenditure. It would be interesting to compare the data in this study to current data from the past year. I wonder if we would come up with the same results.
References
Sprinthall, R. C., (2007). Basic Statistical Analysis (8th ed.). Boston, MA: Pearson Ed. Inc.
17
