keegaa.files.wordpress.com€¦ · Web viewThis study is about controversy over equity in expenditures of public schools across the nation. Some people think that the financing

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


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


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


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


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


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


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


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


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


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


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


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.


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


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%


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



A17.807

7 ±1.0795 95%

B14.808

3 ±1.1235 95%

C14.864

7 ± 0.944 95%D 12.733 ± 1.297 95%


3 3


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


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%


p-value

Betwee 4.3E+0 3 1E+0 3.450 2.802 0.023 Rejec


n 8 8 5 4 8 t

Within 2E+09 474E+0

7

Total2.4E+0

9 50



A47223.

4 ±3616.6 95%

B46312.

5 ±3764.3 95%

C45717.

4 ±3162.6 95%

D53864.

9 ±4346.6 95%


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.


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%


p-value

Between

24959.3 3

8319.8

16.659

2.8024

0.0000

Reject

Within 23472 47 499.4

Total48431.

3 50



A33.461

5 ±12.469 95%

B12.666

7 ±12.978 95%

C40.352

9 ±10.904 95%

D81.444

4 ±14.986 95%


r 4 B B n - r 47 C C q0 4.04 D Sig Sig D

T30.094

4


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


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.


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.



Dependent Variable:average math SAT score 2005-06


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



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.



Dependent Variable:average writing SAT score 2005-06


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



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


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%


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



A39.566

7 ±4.5478 95%

B 34.425 ±4.5478 95%

C49.135

3 ±3.8209 95%

D29.777

8 ±5.2513 95%


r 4 B B n - r 46 C Sig C q0 4.04 D Sig D

T10.539

7


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



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%


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



A12.407

7 ±0.9533 95%

B 14.9 ±0.9922 95%

C13.988

2 ±0.8336 95%

D16.344

4 ±1.1457 95%



r 4 B Sig B n - r 47 C C q0 4.04 D Sig D

T2.3007

6


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.


ANOVA Table 8.1 5%


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



A878548

6 ±7E+06 95%

B968018

1 ±7E+06 95%

C984209

7 ±6E+06 95%

D1.4E+0

7 ±8E+06 95%


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


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


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


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


Expenditure

SAT S

core

s

Theses scatterplots show a negative correlation between pairs.


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


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


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


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


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


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


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


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


Salary

SAT S

core

s


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


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


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


scores would be affected by teacher’s salary.


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


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


Revenues

SAT S

core

s

Revenues and Reading SAT Scores Figure 6.2


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


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


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.


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


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


10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.000

100

200

300

400

500

600

700


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


SES

SAT S

core

s

SES and Writing SAT Scores Figure 7.3


10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.000

100

200

300

400

500

600

700


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


Model R R Square

Std. Error of the

Estimate

1 .08a .01 37.80


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


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.


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


10.00 12.00 14.00 16.00 18.00 20.00 22.000

100

200

300

400

500

600

700


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



SAT S

core

s

Students with Disabilities and Writing SAT Scores Figure 8.3


10.00 12.00 14.00 16.00 18.00 20.00 22.000

100

200

300

400

500

600

700



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


Figure 8.5

Model R R Square

Std. Error of the

Estimate

1 .07a .00 38.10


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.


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.


Documents

keegaa.files.wordpress.com€¦ · Web viewThis study is about controversy over equity in expenditures of public schools across the nation. Some people think that the financing