SPSS/Excel Project 1
Running Head: SPSS/EXCEL PROJECT
Getting What You Pay For: The Debate Over Equity in Public
School Expenditures
Alicia Keegan
Seattle Pacific University
EDU 6976 Interpreting and Applying Educational Research II
November 20, 2009
SPSS/Excel Project 2
Getting What You Pay For: The Debate Over Equity in Public School Expenditures
This study is about controversy over equity in expenditures of public schools across the
nation. Some people think that the financing system, as it stands, is unfair. However, the media
suggests that school spending and academic performance are unrelated. The following data has
been analyzed to determine whether or not financing makes a significant impact on student
performance in the 50 states plus Washington D.C.
Below are several frequency tables and box plots of variables connected with the states
in four separate regions. Information deduced from each frequency table and box plot is
summarized below all of the tables.
Enrollment 05 Histogram
<=70000 (70000, 1070000]
(1070000, 2070000]
(2070000, 3070000]
(3070000, 4070000]
(4070000, 5070000]
(5070000, 6070000]
(6070000, 7070000]
>70700000
5
10
15
20
25
30
35
40
Frequency
X Axis-Number of Students Enrolled in 2005Y Axis-Number of States
SPSS/Excel Project 3
Enrollment 06 Histogram
<=70000 (70000, 1570000]
(1570000, 3070000]
(3070000, 4570000]
(4570000, 6070000]
(6070000, 7570000]
>75700000
5
10
15
20
25
30
35
40
45
Frequency
X Axis-Number of Students Enrolled in 2006Y Axis-Number of States
Expenditure Histogram
<=5000 (5000, 8500] (8500, 12000]
(12000, 15500]
(15500, 19000]
(19000, 22500]
>225000
5
10
15
20
25
30
Frequency
X Axis-Current Expenditure Per Pupil 2005-06Y Axis-Number of States
SPSS/Excel Project 4
Math Histogram
<=450 (450, 500] (500, 550] (550, 600] (600, 650] >6500
5
10
15
20
25
30
Frequency
X Axis-Math SAT ScoresY Axis-Number of States
Money Histogram
<=500000
(500000,
7000000]
(7000000,
13500000]
(13500000,
20000000]
(20000000,
26500000]
(26500000,
33000000]
(33000000,
39500000]
(39500000,
46000000]
(46000000,
52500000]
(52500000,
59000000]
(59000000,
65500000]
>65500000
0
5
10
15
20
25
30
Frequency
X Axis-Total Revenues for the Year 2005-06 (in thousands)Y Axis-Number of States
SPSS/Excel Project 5
Reading Histogram
<=450 (450, 500] (500, 550] (550, 600] (600, 650] >6500
2
4
6
8
10
12
14
16
18
20
Frequency
X Axis-Reading SAT ScoresY Axis-Number of States
Salary Histogram
<=35000 (35000, 40000]
(40000, 45000]
(45000, 50000]
(50000, 55000]
(55000, 60000]
(60000, 65000]
>650000
5
10
15
20
25
Frequency
X Axis-Average Annual Salary of Teachers 2005-06Y Axis-Number of States
SPSS/Excel Project 6
Writing Histogram
<=450 (450, 500] (500, 550] (550, 600] (600, 650] >6500
2
4
6
8
10
12
14
16
18
20
Frequency
X Axis-Writing SAT ScoresY Axis-Number of States
Ratio 1 Histogram
<=10
(10, 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, 27]
(27, 28]
>280
2
4
6
8
10
12
Frequency
X Axis-Average Pupil/Teacher Ratio Fall 2005Y Axis-Number of States
SPSS/Excel Project 7
Ratio 2 Histogram
<=10
(10, 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, 27]
(27, 28]
>280
2
4
6
8
10
12
14
Frequency
X Axis-Average Pupil/Teacher Ratio Fall 2006Y Axis-Number of States
Eligible Histogram
<=0 (0, 10] (10, 20]
(20, 30]
(30, 40]
(40, 50]
(50, 60]
(60, 70]
(70, 80]
(80, 90]
(90, 100]
>1000
2
4
6
8
10
12
14
16
18
20
Frequency
X Axis-Percent of Graduates Taking the SAT 2006-07Y Axis-Number of States
SPSS/Excel Project 8
Students Histogram
<=20000
(20000, 195000]
(195000, 370000]
(370000, 545000]
(545000, 720000]
(720000, 895000]
(895000, 1070000]
(1070000,
1245000]
(1245000,
1420000]
(1420000,
1595000]
(1595000,
1770000]
(1770000,
1945000]
(1945000,
2120000]
(2120000,
2295000]
(2295000,
2470000]
(2470000,
2645000]
(2645000,
2820000]
(2820000,
2995000]
(2995000,
3170000]
>3170000
0
2
4
6
8
10
12
14
16
18
20
Frequency
X Axis-Number of Students Eligible for Free/Reduced Lunch 2006-07Y Axis-Number of States
SES Histogram
<=0 (0, 10] (10, 20]
(20, 30]
(30, 40]
(40, 50]
(50, 60]
(60, 70]
(70, 80]
(80, 90]
(90, 100]
>1000
5
10
15
20
25
Frequency
X Axis-Percent of Students Eligible for Free/Reduced Lunch 2006-07Y Axis-Number of States
SPSS/Excel Project 9
IDEA Histogram
<=0 (0, 2] (2, 4] (4, 6] (6, 8] (8, 10]
(10, 12]
(12, 14]
(14, 16]
(16, 18]
(18, 20]
(20, 22]
(22, 24]
(24, 26]
(26, 28]
(28, 30]
>300
5
10
15
20
25
Frequency
X Axis-Percent of Students with Disabilities 2006-07Y Axis-Number of States
Enrollment 05-06 Box Plot
-3000000 -2000000 -1000000 0 1000000 2000000 3000000 4000000 5000000 6000000 7000000
Top-Enrollment 2005Bottom-Enrollment 2006
Expenditure Box Plot
0 5000 10000 15000 20000 25000
SPSS/Excel Project 10
Math Box Plot
300 350 400 450 500 550 600 650 700 750 800
Money Box Plot
-30000000 -20000000 -10000000 0 10000000 20000000 30000000 40000000 50000000 60000000 70000000
Reading Box Plot
200 300 400 500 600 700 800 900
Salary Box Plot
0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000
Writing Box Plot
200 300 400 500 600 700 800 900
SPSS/Excel Project 11
Ratio 1 Box Plot
0 5 10 15 20 25 30
Ratio 2 Box Plot
0 5 10 15 20 25 30
Eligible Box Plot
-200 -150 -100 -50 0 50 100 150 200 250 300
Students Box Plot
-1000000 -500000 0 500000 1000000 1500000 2000000 2500000 3000000 3500000
SES Box Plot
-40 -20 0 20 40 60 80 100 120
IDEA Box Plot
0 5 10 15 20 25 30
SPSS/Excel Project 12
The distributions of the variables follow a basic normal curve. However, most of the
states (including DC) will fall in the middle. For most variables, there is a distinct average or
mean. There are outliers for enrollment, money, students, and expenditures. The highest
enrollment, that stands out as an outlier, is from region 1. The other enrollment outliers of over
2,500,000 students are from regions 3 and 4. Outliers for money are in all regions with the
largest outlier belonging to region 1. This means that the state of California, in region 1, has the
largest revenue for 2005-2006. There are also outliers for ratio 1 and ratio 2 which means that
there are some states that have a higher teacher to student ratio than the average. Those states
happen to be in region 1. The SAT scores for reading, writing, and math are all very similar with
the mean being just over 500 in all categories. The range of the scores is very similar too. There
are no outliers, so no particular state or region stands out as incredibly exceptional in SAT scores
according to the box plots. For finances, the total expenditure per pupil is higher in region 4 than
the other regions. This expenditure does not seem to make an impact on the SAT scores that are
very similar for each region and subject. There is an average frequency of 13 states per region.
The largest region, region 3, has 17 states and the smallest region, region 4 has 9 states.
The regions differ in terms of expenditure per pupil.
SPSS/Excel Project 13
ANOVA Table 1.1 5%
Source SS df MS F Fcritical
p-value
Between
1.2E+08 3
4E+07
9.7512
2.8024
0.0000
Reject
Within1.9E+0
8 474E+0
6
Total3.1E+0
8 50
Estimates of Group Means Table 1.2
Group Confidence Interval
A9244.9
2 ±1130.5 95%
B9905.4
2 ±1176.7 95%
C9720.8
8 ±988.61 95%
D13601.
4 ±1358.7 95%
Tukey test for pairwise comparison of group means Table 1.3 A
r 4 B B n - r 47 C C q0 4.04 D Sig Sig D
T2728.5
8
The F ratio is 9.7512 and the p-value is 0.00, so you can reject the null hypothesis since the
difference is significant. The regions are different when compared on the amount of money they
per student. The ANOVA results (F = 9.7512, p = 0.0) indicates that the difference among the
regions is statistically significant (table 1.1). Such amount of variance in teacher/pupil ratio can
be accounted for by regional location (partial eta squared = .38). This is a small effect size. To
locate the source of the difference a post hoc test was conducted. The results of the Tukey HSD
test (table 1.3) show that region 4 spent significantly more than regions 1 and 2. Region 4
spends between $3696 and $4356 more per pupil than the other regions. Finding the range for
expenditure per pupil in each region can also be helpful when comparing amounts. Region 1
SPSS/Excel Project 14
spends between $5,960 and $12,861 per pupil. Region 2 spends between $8,487 and $10,872 per
pupil. Region 3 spends between $7,642 and $18,339 per pupil. Region 4 spends between
$10,975 and $16,511 per pupil. When we look at the ranges for each region, it is clear that
region 1 and region 2 spend the least amounts per pupil. Their maximum amounts are smaller
than the maximum amounts of region 3 and region 4. A student in region 3 could potentially
have the most amount of money spent on him because the maximum amount is the highest in
region 3 at $18,339. However, there is a possibility that a student could only have $7,642 spent
on him. Since the range, difference between the maximum and minimum, of region 3 is greater
than the range of region 4; it makes it less reliable to find a steady average amount per pupil in
the region. The higher range of region 3 brings the average amount per pupil down. If I were a
student, my chances of having the most amount of money spent on me are greatest in region 4.
In region 4, the average expenditure is the highest per pupil and the range between minimum and
maximum amounts is only $5536. This gives me the greatest odds to have an ample amount of
money spent on me.
The regions differ in pupil/teacher ratio for 2005.
ANOVA Table 2.1 5%
Source SS df MS F Fcritical
p-value
Between 146.88 3 48.96
13.081
2.8024
0.0000
Reject
Within175.91
7 473.742
9
Total322.79
7 50
Estimates of Group Means Table 2.2
Group Confidence Interval
A17.807
7 ±1.0795 95%
B14.808
3 ±1.1235 95%
C14.864
7 ± 0.944 95%D 12.733 ± 1.297 95%
SPSS/Excel Project 15
3 3
Tukey test for pairwise comparison of group means Table 2.3 A
r 4 B Sig B n - r 47 C Sig C q0 4.04 D Sig D
T2.6053
5
The F ratio is 13.081 and the p-value is 0.0, so you can determine that the difference is
significant. The regions compared on the student/teacher ratio to have a significant difference.
The ANOVA results (F = 13.081, p = 0.0) indicate that the difference among the regions is
statistically significant (table 2.1). Such amount of variance in teacher/pupil ratio can be
accounted for by regional location (R Squared = .455). This is a small to medium effect size. To
locate the source of the difference a post hoc test was conducted. The results of the Tukey HSD
test (table 2.3) show that regions 1, 2, and 3 had significantly more students for every teacher
than region 4. Region 4 had the lowest pupil/teacher ratio which means that approximately 13
students can receive instruction from a teacher in a small group compared to the other regions
where a teacher has a larger group, on average, to instruct with between 14 and 18 students.
When I look at the maximum number of pupils/teacher in each region, I also find that region 4
has the lowest number of students all around. The maximum number of pupils/teacher in region
4 is 15. This maximum is lower than the other regions’ maximum. The minimum is also lower
than the other regions’ minimum. If I were a student in region 4, I could expect to be instructed
in small groups of 10-15 students.
The regions differ in teacher average salary.
ANOVA Table 3.1 5%
Source SS df MS F Fcritical
p-value
Betwee 4.3E+0 3 1E+0 3.450 2.802 0.023 Rejec
SPSS/Excel Project 16
n 8 8 5 4 8 t
Within 2E+09 474E+0
7
Total2.4E+0
9 50
Estimates of Group Means Table 3.2
Group Confidence Interval
A47223.
4 ±3616.6 95%
B46312.
5 ±3764.3 95%
C45717.
4 ±3162.6 95%
D53864.
9 ±4346.6 95%
Tukey test for pairwise comparison of group means Table 3.3 A
r 4 B B n - r 47 C C q0 4.04 D D
T8728.8
7
The F ratio is 3.4505 and the p-value is 0.0238, so you can determine that the null hypothesis
should be rejected because there is a significant difference. The regions compared on the
teacher’s salary amount to be significantly different. The ANOVA results (F = 3.4505, p =
0.0238) indicate that the difference among the regions is statistically significant (table 3.1). Such
amount of variance in teacher salary can be accounted for by regional location (partial eta
squared = .18). This is a small effect size. Region 4 has the highest teacher salary per state
which means that, on average, each teacher in each state makes $53,864.89, which means that
teachers make more money in region 4 compared to the other regions where teachers make an
average of only between $45,717.35 and $47,223.38. When I look at the maximum teacher
salary, I find that region 1 has the highest paid teacher salary of $61,372. However, there are
enough teacher salaries lower than that in the region, that the mean average is brought down.
SPSS/Excel Project 17
There are many possible reasons for the higher teacher salary in region 4. Perhaps there are a
higher number of experienced teachers in region 4. Perhaps the state salary wages are higher in
region 4. Perhaps there are more school districts that can offer salary incentives in region 4.
The regions differ in percentage of eligible students taking the SAT for 2006-07.
ANOVA Table 4.1 5%
Source SS df MS F Fcritical
p-value
Between
24959.3 3
8319.8
16.659
2.8024
0.0000
Reject
Within 23472 47 499.4
Total48431.
3 50
Estimates of Group Means Table 4.2
Group Confidence Interval
A33.461
5 ±12.469 95%
B12.666
7 ±12.978 95%
C40.352
9 ±10.904 95%
D81.444
4 ±14.986 95%
Tukey test for pairwise comparison of group means Table 4.3 A
r 4 B B n - r 47 C C q0 4.04 D Sig Sig D
T30.094
4
The F ratio is 16.659 and the p-value is 0.0, so you can determine that the difference is
significant and the null hypothesis should be rejected. The regions compared on eligiblility are
significantly different. The ANOVA results (F = 16.659, p = 0.0) indicate that the difference
among the regions is statistically significant (table 4.1). Such amount of variance can be
accounted for by regional location (R Squared = .515). This is a medium to large effect size
because the adjusted R Squared is only .484. To locate the source of the difference a post hoc
SPSS/Excel Project 18
test was conducted. The results of the Tukey HSD test (table 4.3) show that region 4 had
significantly more eligible students than regions 1 and 2. In region 1, the minimum percentage
of students taking the SAT was 6% for a state. The maximum was 61% for a state. In region 2,
the minimum percentage of students taking the SAT was 3% for a state. The maximum was 62%
for a state. In region 3, the minimum percentage of students taking the SAT was 64% for a state.
The maximum was 78% for a state. In region 4, the minimum percentage of students taking the
SAT was 67% for a state. The maximum was 100% for a state. Region 4 clearly had more
students per state taking the SAT for 2006-07. Based on percentages, region 4 had more than
50% of its students taking the exam in every state while the other regions had minimum
percentages fall into single digit percentages. This means that region 4 had the highest
percentage of students taking the SAT placement test for college in 2006-07. On average, region
4 had 81% of students taking the SAT in each state compared to the other regions that had an
average per state of between 12% and 41%. Perhaps the students in region 4 come from families
that value college and education more than the other regions. Perhaps trade schools are more
popular in the other three regions. Perhaps the SAT test is offered at a low cost in region 4.
Perhaps there is an incentive for students in region 4 to take the SAT other than to get into
college. Perhaps students in region 4 have easier access to take the SAT. The test may be
offered at the high school where the students attend classes.
The regions differ in performance on the SAT.
SPSS/Excel Project 19
Tests of Between-Subjects Effects Table 5.1
Dependent Variable:average verbal SAT score 2005-06
SourceType III Sum of Squares df
Mean Square F P
Partial Eta Squared
region 30986.00 3 10328.67 12.00 .00 .43
Error 40450.83 47 860.66
Total 14665702.00 51
Corrected Total 71436.82 50
a. R Squared = .434 (Adjusted R Squared = .398)
The F ratio is 12.0 and the p-value is 0.0, so you can determine the difference is significant. The
regions compared on verbal SAT scores are significantly differnet. The ANOVA results (F =
12.0, p = 0.0) indicate that the difference among the regions is statistically significant (table 5.1).
Such amount of variance in verbal SAT scores can be accounted for by regional location (η2
= .43). This is a small to medium effect size. From the data, we can see that region 2 had the
highest reading performance score on average per state. However, the range of scores from 498
to 610 is the highest range of 112 points. That means that there were 112 points difference from
the lowest to the highest score on the reading SAT. Region 4 had a smaller range of only 27
points. This means that the reading scores were more consistent from state to state on the
reading SAT. Region 4’s average score per state of 504 is a more accurate score for the region
than the 576.5 average score for region 2. Region 4 had the most consistent reading SAT scores
per state than the other regions, followed by region 1 with a range of 78, region 3 with a range of
89, and region 2 with its range of 112.
SPSS/Excel Project 20
Tests of Between-Subjects Effects Table 5.2
Dependent Variable:average math SAT score 2005-06
SourceType III Sum of Squares df
Mean Square F P
Partial Eta Squared
region 36447.57 3 12149.19 16.94 .00 .52
Error 33708.78 47 717.21
Total 14974174.00 51
Corrected Total 70156.35 50
a. R Squared = .520 (Adjusted R Squared = .489)
The F ratio is 16.94 and the p-value is 0.0, so you can determine the difference is significant.
The regions compared on math SAT scores are significantly differnet. The ANOVA results (F =
16.94, p = 0.0) indicate that the difference among the regions is statistically significant (table
5.2). Such amount of variance in math SAT scores can be accounted for by regional location (η2
= .52). This is a large effect size. From the data, we can see that region 2 had the highest math
performance score on average per state. However, the range of scores from 509 to 617 is the
highest range of 108 points. That means that there were 108 points difference from the lowest to
the highest score on the math SAT. Region 4 had a smaller range of only 24 points. This means
that the math scores were more consistent from state to state on the math SAT. Region 4’s
average score per state of 512.33 is a more accurate score for the region than the 586.92 average
score for region 2. Region 4 had the most consistent math SAT scores per state than the other
regions, followed by region 1 with a range of 56, region 3 with a range of 78, and region 2 with
its range of 108. For writing, region 1 produced an average score of 515 per state in the region.
SPSS/Excel Project 21
Tests of Between-Subjects Effects Table 5.3
Dependent Variable:average writing SAT score 2005-06
SourceType III Sum of Squares df
Mean Square F P
Partial Eta Squared
region 26942.23 3 8980.74 9.62 .00 .38
Error 43857.69 47 933.14
Total 14147632.00 51
Corrected Total 70799.92 50
a. R Squared = .381 (Adjusted R Squared = .341)
The F ratio is 9.62 and the p-value is 0.0, so you can determine the difference is significant. The
regions compared on writing SAT scores are significantly differnet. The ANOVA results (F =
9.62, p = 0.0) indicate that the difference among the regions is statistically significant (table 5.3).
Such amount of variance in writing SAT scores can be accounted for by regional location (η2
= .38). This is a small effect size. From the data, we can see that region 2 had the highest writing
performance score on average per state. However, the range of scores from 591 to 486 is the
highest range of 105 points. That means that there were 105 points difference from the lowest to
the highest score on the writing SAT. Region 4 had a smaller range of only 28 points. This
means that the writing scores were more consistent from state to state on the writing SAT.
Region 4’s average score per state of 497.22 is a more accurate score for the region than the
564.17 average score for region 2. Region 4 had the most consistent writing SAT scores per
state than the other regions, followed by region 1 with a range of 78, region 3 with a range of 92,
and region 2 with its range of 105. The consistency of scores in region 4 can predict that the
instruction in the region is consistent and the students are learning at a comparable level. Region
2’s high averages can be attributed to some students’ high performance scores. The fact that
region 2 produced the highest average for each section on the SAT, suggests that students in
region 2 are being taught at a high level. They may have opportunities available to them that the
SPSS/Excel Project 22
other regions do not have. There is obviously some quality teaching and learning that is
happening in region 2. It would be worth the time to investigate what curriculum is used in
region 2 that helps the students to produce high scores on the SAT.
The regions differ in terms of SES as measured by percent of students on free/reduced
lunch.
ANOVA Table 6.1 5%
Source SS df MS F Fcritical
p-value
Between
2732.83 3
910.94
14.871
2.8068
0.0000
Reject
Within 2817.7 4661.25
4
Total5550.5
3 49
Estimates of Group Means Table 6.2
Group Confidence Interval
A39.566
7 ±4.5478 95%
B 34.425 ±4.5478 95%
C49.135
3 ±3.8209 95%
D29.777
8 ±5.2513 95%
Tukey test for pairwise comparison of group means Table 6.3 A
r 4 B B n - r 46 C Sig C q0 4.04 D Sig D
T10.539
7
The F ratio is 14.871 and the p-value is 0.0, so you can determine that the difference is
significant and the null hypothesis should be rejected. The regions compared on SES to be
significantly differnet. The ANOVA results (F = 14.871, p = 0.0) indicate that the difference
among the regions is statistically significant (table 6.1). Such amount of variance in SES can be
accounted for by regional location (R Squared = .492). This is a small to medium effect size. To
SPSS/Excel Project 23
locate the source of the difference a post hoc test was conducted. The results of the Tukey HSD
test (table 6.3) show that region 3 has significantly more students eligible for free/reduced lunch
than regions 2 and 4. Region 1 produced an average percentage of 39.57% per state in the
region. Region 2 produced an average percentage of 34.43% per state in the region. Region 3
produced an average percentage of 49.14% per state in the region. Region 4 produced an
average percentage of 25.8% per state in the region. From the data, we can see that region 4 had
the lowest percentage of students per state that received free/reduced lunch. This means that the
students in region 4 have more money in their families compared to the other regions. More
money can mean that the students in region 4 have more opportunities available to them than the
others. More money typically means healthier lifestyles and more access to learning at home
which can increase the learning that happens in the classroom.
The regions differ in terms of percentage of students with disabilities.
ANOVA Table 7.1 5%
Source SS df MS F Fcritical
p-value
Between
89.7784 3
29.926
10.252
2.8024
0.0000
Reject
Within137.18
9 472.918
9
Total226.96
7 50
Estimates of Group Means Table 7.2
Group Confidence Interval
A12.407
7 ±0.9533 95%
B 14.9 ±0.9922 95%
C13.988
2 ±0.8336 95%
D16.344
4 ±1.1457 95%
Tukey test for pairwise comparison of group means Table 7.3 A
SPSS/Excel Project 24
r 4 B Sig B n - r 47 C C q0 4.04 D Sig D
T2.3007
6
The F ratio is 10.252 and the p-value is 0.0, so you can determine that the difference is
significant and the null hypothesis should be rejected. The regions compared on percentage of
students with disabilitis to be significant. The ANOVA results (F = 10.252, p = 0.0) indicate that
the difference among the regions is statistically significant (table 7.1). Such amount of variance
in percentage of students with disabilities can be accounted for by regional location (R Squared =
.396). This is a small effect size. To locate the source of the difference a post hoc test was
conducted. The results of the Tukey HSD test (table 7.3) show that region 1 has significantly
fewer students with disabilities than regions 2 and 4. Region 1 produced an average percentage
of 12.41% of students with disabilities per state in the region. Region 2 produced an average
percentage of 14.9% of students with disabilities per state in the region. Region 3 produced an
average percentage of 13.99% of students with disabilities per state in the region. Region 4
produced an average percentage of 16.34% of students with disabilities per state in the region.
On average, each state has between 12% and 16.34% of students with disabilities. This spread
from region to region is quite small. Even though region 4 produced the largest percentage of
students with disabilities, the percentage is only about 4% greater than the percentage of region 1
which had the lowest percentage of students with disabilities. Across all states, there is a
possibility of about 12 to 16 students per every 100 that have a disability. Statistically, this
average is higher in region 4 than the other regions, but that may change over time. It would be
interesting to know how the students are tested for disabilities in the different regions. I think
this may make a difference in the final percentages of students that qualify as having disabilities.
The regions do not differ in terms of total revenues for the year.
SPSS/Excel Project 25
ANOVA Table 8.1 5%
Source SS df MS F Fcritical
p-value
Between
1.4E+14 3
5E+13
0.2979
2.8024
0.8267
Within7.3E+1
5 472E+1
4
Total7.5E+1
5 50
Estimates of Group Means Table 8.2
Group Confidence Interval
A878548
6 ±7E+06 95%
B968018
1 ±7E+06 95%
C984209
7 ±6E+06 95%
D1.4E+0
7 ±8E+06 95%
Tukey test for pairwise comparison of group means Table 8.3 A
r 4 B B n - r 47 C C q0 4.04 D D
T1.7E+0
7
The F ratio is 0.2979 and the p-value is 0.8267, so you can determine that the difference is not
significant and the null hypothesis should be accepted. The regions compared on revenues to be
not significant. The ANOVA results (F = 0.2979, p = 0.8267) indicate that the difference among
the regions is not statistically significant (table 8.1). Such amount of variance in revenues can be
described as having a small effect size (partial eta squared = .02). Region 4 produced greater
revenues than the other regions by over 3 million dollars, but this is not a significant amount
according to statistical analysis. This could be a general indicator that there could be more
money generated by families in region 4 compared to the other regions. Students that come from
wealthier families often have better learning experiences in school because they have fewer
SPSS/Excel Project 26
issues to deal with at home. Issues that may not be a problem for students in region 4 are
transportation, food, clothing, shelter, supplies, resources, and opportunities for learning in the
community (access to libraries, zoos, aquariums, museums, etc.). I wish I knew how the
revenues had actually been generated.
Expenditure and Reading SAT Scores Figure 1.1
4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,0000.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
Series2Series4Series6
Expenditure
SAT S
core
s
Expenditure and Math SAT Scores Figure 1.2
SPSS/Excel Project 27
4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,0000
100
200
300
400
500
600
700
Series2Series4Series6
Expenditure
SAT S
core
s
Expenditure and Writing SAT Scores Figure 1.3
4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,0000
100
200
300
400
500
600
700
Series2Series4Series6
Expenditure
SAT S
core
s
Theses scatterplots show a negative correlation between pairs.
SPSS/Excel Project 28
What I can say about the relationship between these pairs is that the highest SAT scores
were from students whose school expenditure was at least $10,000 per pupil. The students who
scored the highest scores on the SAT were not the students whose school had the largest
expenditure. The correlation coefficient is -0.4155; -0.3935; and -0.3969. These correlation
coefficients are for the reading, math, and writing SAT scores respectively.
Figure 1.4
verbal SAT score
2005-06
math SAT score
2005-06
writing SAT score
2005-06
Expenditure/ pupil 2005-06 Pearson r -0.42** -0.39** -0.40**
p 0.00 0.00 0.00
n 51 51 51
Figure 1.5
Model R R Square
Std. Error of the
Estimate
1 .39a .16 34.79
The statistical and practical significance of the relationship is that since the p value is 0.0
(figure 1.4), then there is no relationahip between the expenditure per pupil and SAT scores. In
this case, we can accept the null hypothesis that there is no correlation. When we look at the
coefficient of determination, .16 (figure 1.5), we can see that it has a small indication that SAT
scores would be affected by expenditure per pupil. This shows that schools should spend the
most amount of money per pupil that they can, but not expect more than reasonable results on
SAT scores because money isn’t the only factor that contributes to student success.
The corresponding regression equations are for reading, math, and writing SAT scores
respectively:
Y=-0.0063x + 599.76
Y=-0.0059x + 601.42
Y=-0.006x + 587.02
SPSS/Excel Project 29
Conclusions that I have found about my analysis is that when more money is spent per
pupil, reading and math SAT scores benefit, but not significantly. Students in schools that make
it a priority to spend money on their education can benefit by being given opportunities to gain
knowledge that may be tested on the SAT, but should be aware that money is not a strong
indicator for success.
Pupil/Teacher Ratio and Reading SAT Scores Figure 2.1
10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.000
100
200
300
400
500
600
700
Series2Series4
Pupil/Teacher Ratio
Read
ing S
AT Sc
ores
This scatterplot shows a slight negative correlation between pairs. The correlation is so
slight that we can determine there to be a zero correlation.
Figure 2.2
average writing SAT
score 2005-06
average verbal SAT
score 2005-06
average math SAT
score 2005-06
average pupil/teacher ratio Fall 2006 Pearson r -.07 -.03 -.03
p .64 .82 .85
n 51 51 51
Figure 2.3
SPSS/Excel Project 30
Model R R Square
Std. Error of the
Estimate
1 .03a .00 38.16
What I can say about the relationship between these pairs is that the fewer students there
are per teacher, the greater the reading SAT scores. The correlation coefficient is -0.0145. This
correlation coefficient is for the reading SAT scores. The practical significance of the
relationship is that teachers should try to hold classes with as few students as possible because
the data shows that students in classes of 10-15 performed higher on the reading SAT than those
students in larger classes. The statistical significance of the relationship is that since the p value
is.82 (figure 2.2) then there is a relationship between the average pupil/teacher ratio and SAT
scores. In this case, we can reject the null hypothesis since there is a correlation. When we look
at the coefficient of determination, .00 (figure 2.3), we can see that it has a small indication that
SAT scores would be affected by pupil/teacher ratio.
However, the correlation is so slight that there could be no statistical proof that a smaller
class size did in fact help students to perform on the reading SAT.
The corresponding regression equation is for reading SAT scores respectively:
Y=-0.2154x + 538.22
The conclusions that I can draw from my anaysis is that smaller class size does affect
student performance positively, but only slightly in this instance. When we teachers negotiate
our contracts for class size, we should really think about the benefits to our students that are
continuing on to college. To better their careers, our curriculum, and for the greater good of
education, we should push for smaller class size. There were still students that did well on the
SAT that were in larger classes. This tells me that those students may work very well in noisier
SPSS/Excel Project 31
situations, group situations, or even situations with higher stress. So, even though class size
doesn’t determine every student’s success, small classes do fair a bit better on the reading SAT.
Pupil/Teacher Ratio and Math SAT Scores Figure 3.1
10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.000
100
200
300
400
500
600
700
Series2Series4
Pupil/Teacher Ratio
Mat
h SA
T Sco
res
This scatterplot shows a zero correlation between pairs.
What I can say about the relationship between these pairs is that Math SAT scores are
most consistent around 15 students per teacher. As the student to teacher ration increases from
10 to 15, the math SAT scores also increase. The scores decrease as the class size increases
above 15 pupils per teacher. The correlation coefficient is -0.0076. This correlation coefficient
is for the math SAT scores. Its statistical and practical significance is that students taking math
classes should register for any class size because student scores were consistent from class sizes
of 10 to 25.
The statistical significance of the relationship is that since the p value is.85 (figure 2.2)
then there is a relationship between the average pupil/teacher ratio and SAT scores. In this case,
we can reject the null hypothesis since there is a correlation. When we look at the coefficient of
determination, .00 (figure 2.3), we can see that it has a small indication that SAT scores would
be affected by pupil/teacher ratio. They are bound to have a more rewarding learning experience
SPSS/Excel Project 32
in a class size of 15 than a class size larger than 15. Student math SAT scores should also
benefit from the individualized attention that can be gained in a smaller class. However, the
significance cannot be granted as huge because of the small correlation of the scatterplot.
The corresponding regression equation is for math SAT scores:
Y=-0.1117x + 542.29
The conclusions that can be drawn from the scatterplot are conclusions that can benefit
student learning. Smaller class size does affect student performance positively when we
compare individual state scores. There were still students that did well on the SAT that were in
larger classes. However, they did not do as well as those in smaller class sizes. So, even though
class size doesn’t determine every student’s success, small classes do fair better on the math SAT
only slightly.
Pupil/Teacher Ratio and Writing SAT Scores Figure 4
10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.000
100
200
300
400
500
600
700
Series2Series4
Pupil/Teacher Ratio
Writi
ng SA
T Sco
res
SPSS/Excel Project 33
This scatterplot shows a zero correlation between pairs.
What I can say about the relationship between these pairs is that students in classes of
about 15 do the best on the writing SAT consistently. The correlation coefficient is -0.0467.
This correlation coefficient is for the writing SAT scores. Its statistical and practical significance
that the scores for the writing SAT were very tightly plotted around scores of 550 and class sizes
of 15 pupils per teacher. The statistical significance of the relationship is that since the p value
is.64 (figure 2.2) then there is a relationship between the average pupil/teacher ratio and SAT
scores. In this case, we can reject the null hypothesis since there is a correlation. When we look
at the coefficient of determination, .00 (figure 2.3), we can see that it has a small indication that
SAT scores would be affected by pupil/teacher ratio. This consistency implies that class sizes of
about 15 are ideal for students to get a score of about 550 on the writing SAT. The
corresponding regression equation is for SAT scores:
Y=-0.6917x + 535.9
The conclusions that I can draw from my anaysis is that smaller class size does affect
student performance positively, but size isn’t the only factor for success. Specifically, a class
size of about 15 consistently allows for students to perform above 500 on the Writing SAT. The
benefits to students getting quality writing education are consistent with a small class size. There
were still students that performed above 500 on the SAT that were in larger classes. However,
their scores were below the 550 mark consistently. This tells me that those students may work
very well with more students in a class, but could still increase their writing SAT score to meet
the average. So, even though class size doesn’t determine every student’s success, small classes
do fair better on the writing SAT only slightly.
Salary and Math SAT Scores Figure 5.1
SPSS/Excel Project 34
30,000.00 35,000.00 40,000.00 45,000.00 50,000.00 55,000.00 60,000.00 65,000.000
100
200
300
400
500
600
700
Series2Series4Series6
Salary
SAT S
core
s
Salary and Reading SAT Scores Figure 5.2
30,000.00 35,000.00 40,000.00 45,000.00 50,000.00 55,000.00 60,000.00 65,000.000.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
Series2Series4Series6
Salary
SAT S
core
s
SPSS/Excel Project 35
Salary and Writing SAT Scores Figure 5.3
30,000.00 35,000.00 40,000.00 45,000.00 50,000.00 55,000.00 60,000.00 65,000.000
100
200
300
400
500
600
700
Series2Series4Series6
Salary
SAT S
core
s
These scatterplots show a negative correlation between pairs.
What I can say about the relationship between these pairs is that when the salary
increases, the SAT scores decrease. The correlation coefficient is -0.4748; -0.4068; and -0.4472.
These correlation coefficients are for the reading, math, and writing SAT scores respectively.
The statistical and practical significance is that salary may not extrinsically motivate teachers to
teach better since the student SAT scores actually went down as teachers were paid more.
Figure 5.4
average writing SAT
score 2005-06
average verbal SAT
score 2005-06
average math SAT
score 2005-06
estimated ave salary
2005-2006
Pearson r -.45** -.48** -.41**
P .00 .00 .00
N 51 51 51
Figure 5.5
SPSS/Excel Project 36
Model R R Square
Std. Error of the
Estimate
1 .41a .17 34.57
The statistical and practical significance of the relationship is that since the p value is 0.0
(figure 5.4), then there is no relationship between the teacher’s salary and SAT scores. In this
case, we can accept the null hypothesis that there is no correlation. When we look at the
coefficient of determination, .17 (figure 5.5), we can see that it has a small indication that SAT
scores would be affected by teacher’s salary.
The corresponding regression equations are for reading, math, and writing SAT scores
respectively:
Y=-0.0026x + 658.2
Y=-0.0022x + 645.24
Y=-0.0024x + 640.96
Conclusions that I can draw from my analysis are that teachers are intrinsically motivated
people. This is supported by the scatterplot that shows that being paid less made a better impact
on student SAT scores. We cannot assume that teachers getting paid higher wages aren’t
teaching well, but we do know that higher paid teachers are usually more experienced teachers.
Perhaps it is the newer, lesser paid teachers, that have the newest training to succesfully impact
student learning. Perhaps there is a need for training of established teachers. There is also the
correlation of individual state salary wages and student performance that is not present in this
scatterplot. I would like to know how individual states performed on the SAT compared to their
teachers’ salary schedule.
Revenues and Math SAT Scores Figure 6.1
SPSS/Excel Project 37
0.00 20,000,000.00 40,000,000.00 60,000,000.00 80,000,000.000
100
200
300
400
500
600
700
Series2Series4Series6
Revenues
SAT S
core
s
Revenues and Reading SAT Scores Figure 6.2
SPSS/Excel Project 38
0.00 20,000,000.00 40,000,000.00 60,000,000.00 80,000,000.000.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
Series2Series4Series6
Revenues
SAT S
core
s
Revenues and Writing SAT Scores Figure 6.3
0.00 20,000,000.00 40,000,000.00 60,000,000.00 80,000,000.000
100
200
300
400
500
600
700
Series2Series4Series6
Revenues
SAT S
core
s
These scatterplots show a negative correlation between pairs.
What I can say about the relationship between these pairs is that higher revenue does not
make for higher scores on the SAT. The correlation coefficient is -0.2932; -0.1986; and -0.2525.
These correlation coefficients are for the reading, math, and writing SAT scores respectively.
The statistical and practical significance of the relationship is the higher the revenue the less
likely that SAT scores are affected.
SPSS/Excel Project 39
Figure 6.4
writing SAT score
2005-06
verbal SAT score
2005-06
math SAT score
2005-06
Total revenues for the
year 2005-06 (in
thousands)
Pearson r -.25 -.29* -.20
p .07 .04 .16
N 51 51 51
Figure 6.5
Model R R Square
Std. Error of the
Estimate
1 .29a .09 36.50
The statistical and practical significance of the relationship is that since the p values
are .07, .04, and .16 (figure 6.4), then there is a relationship between revenues and SAT scores.
In this case, we can reject the null hypothesis since there is a correlation. When we look at the
coefficient of determination, .09 (figure 6.5), we can see that it has a small indication that SAT
scores would be affected by revenues. According to the scatterplots, the students that did the best
on the SAT had the lowest revenues for the state. The corresponding regression equations are
for reading, math, and writing SAT scores respectively:
Y=-9E-07x + 544.2
Y=-6E-07x + 546.8
Y=-8E-07x + 533.31
The conclusions that I can draw from this analysis is that states should worry less about
revenues impacting student performance and focus their attention on more important matters.
When revenues were up in the scatterplot, the students actually performed lower, so the
correlation between the two shouldn’t raise red flags for schools or states.
SES and Math SAT Scores Figure 7.1
SPSS/Excel Project 40
10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.000
100
200
300
400
500
600
700
Series2Series4Series6
SES
SAT S
core
s
SES and Reading SAT Scores Figure 7.2
10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.000.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
Series2Series4Series6
SES
SAT S
core
s
SES and Writing SAT Scores Figure 7.3
SPSS/Excel Project 41
10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.000
100
200
300
400
500
600
700
Series2Series4Series6
SES
SAT S
core
s
These scatterplots shows a zero correlation between pairs for the math and reading SAT
scores compared with SES, but a slightly positive correlation for the writing SAT scores and
SES.
What I can say about the relationship between these pairs is that SES didn’t negatively
affect the general SAT scores. In writing, the higher the SES, the greater the scores were. The
correlation coefficient is 0.02; -0.08; and 0.08. These correlation coefficients are for the reading,
math, and writing SAT scores respectively. Its statistical and practical significance of the
relationship is that the students that fit into the category of SES, had SAT scores that were
impressive.
Figure 7.4
writing SAT score
2005-06
verbal SAT score
2005-06
math SAT score
2005-06
% of students eligible
for free/reduced lunch
2006-07
Pearson r .08 .02 -.08
p .58 .87 .57
n 50 50 50
Figure 7.5
SPSS/Excel Project 42
Model R R Square
Std. Error of the
Estimate
1 .08a .01 37.80
The statistical and practical significance of the relationship is that since the p values
are .58, .87, and .57 (figure 7.4), then there is a relationship between SES and SAT scores. In
this case, we can reject the null hypothesis since there is a correlation. When we look at the
coefficient of determination, .01 (figure 7.5), we can see that it has a small indication that SAT
scores would be affected by SES. As the SES increased, the scores in writing did too slightly
while the reading and math scores did not substantially suffer at all due to SES.
The corresponding regression equations are for reading, math, and writing SAT scores
respectively:
Y=0.111x + 530.99
Y=-0.2706x + 551.79
Y=0.3129x + 513.52
The conclusions that I can draw from the analysis is that SES can positively affect SAT
scores. Surprisingly, the more students categorized as SES, the better the SAT scores. This tells
me that the students are performing very well given that they may be underprivileged or come
from disadvantaged homes. I wonder if these students are receiving benefits from extra funding.
Because these students are qualifying for free/reduced lunches, I can assume that eating lunch at
school is helping them to focus on their academics and improve their learning in class as shown
on the SAT.
Students with Disabilities and Math SAT Scores Figure 8.1
SPSS/Excel Project 43
10.00 12.00 14.00 16.00 18.00 20.00 22.000
100
200
300
400
500
600
700
Series2Series4Series6
IDEA (Students with Disabilities)
SAT S
core
s
Students with Disabilities and Reading SAT Scores Figure 8.2
10.00 12.00 14.00 16.00 18.00 20.00 22.000.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
Series2Series4Series6
IDEA (Students with Disabilities)
SAT S
core
s
Students with Disabilities and Writing SAT Scores Figure 8.3
SPSS/Excel Project 44
10.00 12.00 14.00 16.00 18.00 20.00 22.000
100
200
300
400
500
600
700
Series2Series4Series6
IDEA (Students with Disabilities)
SAT S
core
s
These scatterplots show a negative correlation between pairs. The correlation is small,
but it is slightly negative. For the writing SAT scores compared with IDEA, the negative
correlation is very close to a zero correlation.
What I can say about the relationship between these pairs is that when there are higher
numbers of students with disabilities, the SAT scores go down. The correlation coefficient is
-0.0652; -0.0723; and -0.0531. These correlation coefficients are for the reading, math, and
writing SAT scores respectively. Its statistical and practical significance of the relationship is
what I expected.
Figure 8.4
average writing SAT
score 2005-06
average verbal SAT
score 2005-06
average math SAT
score 2005-06
% of students with
disabilities 2006-07
Pearson Correlation -.05 -.07 -.07
Sig. (2-tailed) .71 .65 .61
N 51 51 51
SPSS/Excel Project 45
Figure 8.5
Model R R Square
Std. Error of the
Estimate
1 .07a .00 38.10
The statistical and practical significance of the relationship is that since the p values
are .71, .65, and .61 (figure 8.4), then there is a relationship between the percentage of students
with disabilities and SAT scores. In this case, we can reject the null hypothesis since there is a
correlation. When we look at the coefficient of determination, .00, we can see that it has a zero
indication that SAT scores would be affected by students with disabilities. Students with
disabilities often have learning disabilities that make test-taking challenging. Because of this, I
expect SAT scores for students with disabilities to be lower than the general population. As the
number of students with disabilities increases, I can only assume that the challenges also
increase. The data confirms that this theory may be true.
The corresponding regression equations are for reading, math, and writing SAT scores
respectively:
Y=-1.1568x + 551.39
Y=-1.271x + 558.66
Y=-0.9371x + 538.69
What conclusions that I can draw from my analysis is that students with disabilities need
one-on-one time away from other students with disabilities. According to the scatterplot, the
fewer students with disabilities, the higher the SAT score. So, when there are fewer students that
are trying to overcome challenges, the SAT seems to be an easier feat to overcome. States
should try to reduce the number of students with disabilities in their classrooms to increase the
opportunities for learning for those students that may have more challenges to face than the
general population.
SPSS/Excel Project 46