student opinion survey

Student Opinion SurveyAP Stat Final Project byJohn GrazianoRyan GuthierLydia Keener

Background• American School System

▫ Unlike that in many other countries. Education is primarily the responsibility of state and local government, little standardization. States have great control over what is taught in their schools and over the requirements that a student must.

▫ Some common points: division of the education system into three levels: elementary/primary education, secondary education, and postsecondary/higher education

• Grade point average, why do we use it?▫ GPA ensures that a student’s performance is easily understood by the

many other institutions around the world that rely on GPA in the assessment of the performance of students. GPA allows you to keep track of your performance throughout your degree program. This will enable your faculty to identify your academic needs and provide advice and guidance.

• Average SAT score in the country is 1511• 71% of students graduate high school• 68.1% of 2010 high school graduates were enrolled in colleges or

universities

Description of Project• We wanted to see whether there is a relationship

between certain variables like academic performance, school type, and gender versus opinions about school and aspects of your education

• Created a survey asking a number of questions about school performance and opinion▫ Conducted from 5/27 – 6/1

• Posted survey on Facebook on different academic pages▫ College pages of three group members▫ General facebook status

• 168 people responded to our survey▫ 56 people chosen with systematic procedure

Procedure•While it was a voluntary response survey,

we only took every third piece of data•This made it a systematic random sample•Ensures randomness and sample

Student Opinion•Our population is high school students in

the country•Opinion of school was measured in:

▫Enjoyment▫How well school educated you▫Personal connection with teachers▫Usefulness of schooling▫Preparedness for post-high school life

Student Opinion Cont.•Academic Performance was measures in:

▫SAT scores▫GPA (weighted)▫ACT scores▫Grad school or not▫# of AP/Honors courses▫Special Awards of Achievements

5

10

15

20

25

30

35

40

What_is_your_genderFemale Male

count

Collection 1 Bar Chart

Distribution by Gender

66.1%

33.9%

Voluntary Response Bias created discrepancy in gender, females more likely to voluntarily take our survey

Distribution by Age

• 98% of people in 17-18 range indicates successful focus on outgoing high school students

5

10

15

20

25

30

35

40

45

What_is_your_age16 17 18 19 20

Collection 1 Histogram

71.4%

26.8%

1.8%

Distribution by State

5

10

15

20

25

What_state_do_you_live_in

Cal

iforn

ia

Col

orad

o

Con

nect

icut

Del

awar

e

Dis

tric

t of C

olum

bia

Flor

ida

Geo

rgia

Mar

ylan

d

Mas

sach

uset

ts

New

Jer

sey

New

Yor

k

Penn

sylv

ania

Texa

s

Virg

inia

Wis

cons

in

count

1.786% 1.786% 1.786% 1.786% 1.786%3.571%

1.786%

5.357%3.571%

12.5%

16.071%

39.286%

3.571% 3.571% 1.786%

Cleary PA was highest proportion, however around 60% of our data was from other states all over the country.

Distribution by Public/Private High School

• Fairly accurate distribution of public vs. private (actual is 63% public, 37% private)

5

10

15

20

25

30

35

40

45

What_type_of_schooling_do_youdid_you_receivePrivate School Public School

count


73.21%

26.79%

2

4

6

8

10

12

14

16

18

20

22

If_you_took_the_SATs_what_was_your_highest_score

I did

not

take

the

SAT

s

Less

than

120

0

1200

-140

0

1401

-160

0

1601

-180

0

1801

-200

0

2001

-220

0

2201

-240

0

count


Distribution by SAT score

• Center at 1800-2000• Unimodal, symmetric• Small spread with most data above 1600

Distribution by ACT score

• Center at 28, left skewed, unimodal• Gap at 31• Wider spread than SAT scores• Range- 22-32• IQR: 6

1

2

3

4

5

6

If_you_took_the_ACTs_what_was_your_score20 22 24 26 28 30 32 34 36 38

Collection 1 Histogram

• Mean- 28.3667• Min- 22• Q1-26• Median- 28.5• Q3- 32• Max- 34• Standard Deviation of 3.508

Conclusions about Population•People who responded to the survey were in

general relatively smart (3.8 GPA, around 1800 SATs). More females took this survey than males, because voluntary response, females were more willing to answer survey. Around 40% of respondents are from PA, but survey included people from 15 states all around the country. Also, around 70% of respondents attend/attended public school. This sample likely produced similar results due most people beings from our group members’ 3 colleges.

“What is your weighted GPA?”

mean = 3.83344min = 3Q1 = 3.7median = 3.87

Q3 = 4.001max = 4.36s = .306222

Please_estimate_your_cumulative_weighted_GPA_throughout_all_4_ye3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

Unimodal, symmetric, Mean of 3.833. Two outliers below 3.2. Range of 3-4.36 including outliers. IQR: .301

Goodness of Fit Test for Distribution of GPA

Ho: Observed distribution of GPA’s fits expected distribution of GPA’s

Ha: Observed distribution of GPA’s does not fit expected distribution of GPA’s

1. Categorical Data2. SRS3. All Expected Counts

≥ 5

1. GPA range is categorical2. Assumed representative and

systematic random sample3. All Expected Counts ≥ 5

State & Check

Conditions Met –χ2 distribution – χ2 GOF Test

Work Test of Collection 1 Goodness of Fit

Attribute: (categorical): GPA

Attribute: GPANumber of categories: 3Alternative hypothesis: Categories of GPA are not equally likely

The test statistic, chi-square, is 15.46. There are 2 degrees of freedom (one less than the number of categories).

If it w ere true that the categories of GPA were equally likely (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be 0.00044.

Column Summary

Count

3.0-3.49

3.5-3.99

4.0-4.49

GPA

7

31

18

56x2 = ∑ (obs-exp)

2/ exp

x2 = ∑ (7-18.66)

2/ 18.6 + (31-18.6)

2 / 18.6. . .

x2 = 15.46 df= 2

P(x2 > 15.46) = .00044

We reject the Ho because p-value of .00044 is less than the alpha of .05. We have sufficient evidence to conclude that the Observed distribution of GPA’s does not fit expected distribution of GPA’s

“Have you received any scholarships”

5

10

15

20

25

30

35

40

45

Have_you_recieved_any_scholarshipsno yes

count


73.2%

26.8%

Chi-Squared Test for IndependenceGender vs. Scholarships

Ho: Gender and receiving scholarships are independent of each otherHa: : Gender and receiving scholarships are not independent of each other

1. Categorical Data2. SRS3. All Expected Cell

Counts ≥ 5

1. GPA range and school enjoyment are categorical

2. Assumed representative and systematic random sample

3. All expected counts ≥ 5

State & Check

Conditions Met –χ2 distribution – χ2 Test for Independence

Work

x2 = ∑ (obs-exp)

2/ exp

x2 = ∑ (12-10.6)

2/ 10.6+ (25-26.4)

2 / 26.4 . . .

x2 =.7966 df= 1

P(x2 > .7966) = .37

We fail to reject the Ho because the P value of .37 is greater than the alpha of .05. We have sufficient evidence to conclude that gender and receiving scholarships are independent.

RowSummary

Column Summary

Have_you_recieved_any_scholarships

yes

Have_you_recieved_any_scholarships

no

Female

MaleWhat_is_your_gender

12 (10.6) 25 (26.4)

4 (5.4) 15 (13.6)

16 40

37

19

56

“Do you think you will be close with the friends you’ve made in high school in 10 years?”

5

10

15

20

25

30

35

40

Do_you_think_you_will_be_close_w ith_the_friends_youve_made_inNo Yes

count


31.25%

68.75%

Chi-Squared Test for IndependenceGender vs. Closeness to High School Friends

Ho: Gender and being close with your high school friends in 10 years are independent of each otherHa: Gender and being close with your high school friends in 10 years are not independent of each other


Counts ≥ 5

1. Gender and close with friends or not is categorical


3. All expected counts ≥ 5

State & Check


Work

x2 = ∑ (obs-exp)

2/ exp

x2 = ∑ (10-11.2)

2/ 11.2 + (27-25.8)

2 / 25.8 . . .

x2 =.572 df= 1

P(x2 > .572) = .45

We fail to reject the Ho because the P value of .45 is greater than the alpha of .05. We have sufficient evidence to conclude that gender and being close with your high school friends in 10 years are independent

First attribute: Do_you_think_you_will_be_close_with_the_friends_youve_made_in Number of categories: 2Second attribute: What_is_your_gender Number of categories: 2 Alternative hypothesis: There is an association betw een Do_you_think_you_w ill_be_close_w ith_the_friends_youve_made_in and What_is_your_gender

The test statistic, chi-square, is 0.572. There are 1 degrees of freedom (the number of row s minus one times the number of columns minus one).

If it w ere true that Do_you_think_you_w ill_be_close_w ith_the_friends_youve_made_in w ere independent of What_is_your_gender (the null hypothesis), and the sampling process w ere performed repeatedly, the probability ofgetting a value for chi-square this great or greater w ould be 0.45.

The numbers in parentheses in the table are expected counts.

RowSummary

Column Summary

Do_you_think_you_will_be_close_w ith_the_friends_youve_made_in

Yes

Do_you_think_you_will_be_close_w ith_the_friends_youve_made_in

No

Female

MaleWhat_is_your_gender

10 (11.2) 27 (25.8)

7 (5.8) 12 (13.2)

17 39

37

19

56

“How much do you enjoy school?”

5

10

15

20

25

30

How_much_do_you_enjoy_schoolNot at all/ A little Somew hat A good deal

count


17.2%

34%

48.8%

Chi-Squared Test for IndependenceGPA vs. School Enjoyment

Ho: GPA and school enjoyment are independent of each otherHa: GPA and school enjoyment are not independent of each other


Counts ≥ 5

1. GPA range and school enjoyment are categorical


3. All but one ≥ 5

State & Check


WorkFirst attribute (categorical): GPA

Second attribute (categorical): How _much_do_you_enjoy_school

RowSummary

Column Summary

GPAGPA

3.5-3.99 4.0-4.49

GPA

3.0-3.49

A good deal

Not at all/ A little

Somew hat

How_much_do_you_enjoy_school

3 (3.4) 17 (14.9) 7 (8.7)

2 (1.2) 5 (5.5) 3 (3.2)

2 (2.4) 9 (10.5) 8 (6.1)

7 31 18

27

10

19

56x2 = ∑ (obs-exp)

2/ exp

x2 = ∑ (3-3.4)

2/ 3.4+ (17-14.9)

2 / 14.9 . . .

x2 =2.03 df= 4

P(x2 > 2.03) = .73

We fail to reject the Ho because the P value of .73 is greater than the alpha of .05. We have sufficient evidence to conclude that GPA and How Much you enjoy school are independent.

“What type of schooling have you received?”

5

10

15

20

25

30

35

40

45

What_type_of_schooling_do_youdid_you_receivePrivate School Public School

count


73.21%

26.79%

Chi-Squared Test for Independence•Public/Private HS vs. School Enjoyment

Ho: Public and Private School attendance and school enjoyment are independent of each otherHa: Public and Private School attendance and school enjoyment are not independent of each other

1. Categorical Data2. SRS3. All Expected cell

counts ≥ 5

1. Type of school and school enjoyment are categorical


3. All but one cell count ≥ 5

State & Check


Work•x2

= ∑ (obs-exp)2/ exp

•x2 = ∑ (20-18.3)

2/

18.3+ (7-8.7)2 / 8.7 . . .

•x2 =1.364 df= 2

•P(x2 > 1.364 ) = .51First attribute (categorical): If_you_plan_to_attend_college_is_that_school_public_or_private

Second attribute (categorical): How _much_do_you_enjoy_school

RowSummary

Column Summary

If_you_plan_to_attend_college_is_that_school_public_or_private

Public

If_you_plan_to_attend_college_is_that_school_public_or_private

Private

A good deal

Not at all/ A little

Somew hat

How_much_do_you_enjoy_school

20 (18.3) 7 (8.7)

7 (6.8) 3 (3.2)

11 (12.9) 8 (6.1)

38 18

27

10

19

56

We fail to reject the Ho because the P value of .51 is greater than the alpha of .05. We have sufficient evidence to conclude that : Public and Private School attendance and school enjoyment are independent of each other

Overall Conclusions• In all of our tests, we didn’t find a correlation

between any measurements of academic ability or other variables and opinions about school or aspects of your education. We believe that most of the survey respondents were fairly similar in nature and therefore, we did not find major differences in the answers. This is due to common mediums used to obtain responses (our college facebook groups and facebook statuses). We would have liked to have surveyed a more diverse sample of students that would give us more results to analyze. If possible, we would like to reach people through other places, rather than relying only on facebook.

Applications to population• Based on our data, high school students’ academic

ability does not have an impact on your enjoyment of school or your opinions of school. Also, your gender does not impact your achievement in school or opinions of school. Therefore, we think students should not worry about the factors that impact their academic careers, and focus more on you as an individual and your goals. Basically, we can say that all students have the power to achieve at the highest level, and regardless of your opinions or enjoyment of school, you can be successful.

Bias and Error• Voluntary response bias- Our data reflected a

discrepancy in gender ▫Significant amount of George Washington University

students responded▫Not so much University of Pittsburgh or James

Madison University▫The three schools are not an adequate

representation of college-bound seniors• Under coverage bias- Not everyone has Facebook

▫Of those who have Facebook, some people may not be ‘friends’ with us, therefore where not exposed to the survey

Bias and Error cont.•People have different scales for weighted

GPA in other states▫Some posted their GPA’s as a percent, we

converted them in order to have uniform data

Everybody Stand Up!!• If you have a Facebook, go to the right side of the

room, if not go to the left side of the room• Of those who have Facebook, if you are not friends

with any of us three, go to the left side of the room• If you did not check your Facebook between 5/27 –

6/1, go to the left side of the room• Those who remain on the right side of the room,

you were possible subjects, and it was up to you to respond▫Those on the left, you represent our under coverage

bias

You have questions? We have answers!

Bibliography• “The American School System.” Heildenburg. N.p., n.d. Web. 6 June 2011.

<http://www.rzuser.uni-heidelberg.de/ ~el6/ presentations/ pres_c2_uss/ TheAmericanSchoolSystem.htm>. ▫ We used this to gather background on the America Education System and Grade

Point Averages• “College Enrollment and Work Activity of 2010 High School Graduates.” Bureau

of Labor Statistics. N.p., n.d. Web. 6 June 2011. <http://www.bls.gov/ news.release/ hsgec.nr0.htm>. ▫ We used this to determine how many students go to college after high school.

• Facebook. N.p., n.d. Web. 6 June 2011. <http://www.facebook.com>. ▫ We used facebook in order to spread our survey to studenents around the country

through our college groups.• “High School Graduation Rates in the United States.” Manhattan Institute. N.p.,

n.d. Web. 6 June 2011. <http://www.manhattan-institute.org/ html/ cr_baeo.htm>. ▫ This site allowed us to know how many high schoolers graduate.

• “http://www.infoplease.com/ ipa/ A0883611.html.” Info Please. N.p., n.d. Web. 6 June 2011. <http://www.infoplease.com/ ipa/ A0883611.html>. ▫ We used this site to gather average SAT scores.

• Survey Gizmo. N.p., n.d. Web. 6 June 2011. <https://appv3.sgizmo.com/ login/ v1>. ▫ This was the site used to take our survey. It allowed us to collect our data and

export it to fathom.

student opinion survey

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