GUESS THE DISTANCE By Amanda Cunha and Ashley Kershaw

DESCRIPTION OF TOPIC

Depth perception- the ability to judge how far away an object is as well as how far away objects are from each other

With glasses depth perception can be impaired This is because everything is simulated to be at

the same distance It is also said contacts can affect ones depth

perception as well

BACKGROUND OF TOPIC

We decided to test and see if there was a significant difference in the depth perception of those who wear glasses, contacts or neither

We also wanted to test and see if there was a difference in the depth perception of females vs. males

PROCEDURE1. We put one cone next to us at Macy’s at the

Montgomery Mall2. We measured 30 feet from the first cone and put a

second cone there3. We stood next to the door of Macy’s and as people

entered or exited recorded… 1. Gender2. Glasses- if we could see that3. If no glasses were visible asked if they wore contacts4. If they did not wear contacts, we recorded neither

glasses nor contacts4. We asked them to stand at the first cone and

guess how far away the second cone was and recorded their answer

5. We went to Macy’s on Monday morning, Thursday afternoon, & Sunday evening

Contacts

1

2

3

4

5

6

7

C

0 10 20 30 40 50 60 70

Guess

Contact Histogram

Contact

Column Summary

Guess

CContacts

63

34.0635

15

27

34

42

60

10.0224

63

34.0635

15

27

34

42

60

10.0224

S1 = countS2 = meanS3 = minS4 = Q1S5 = medianS6 = Q3S7 = maxS8 = s

EXPLORATORY DATA: CONTACTS

The data is bimodal and slightly right skewed

The median is at 34ft and the IQR is 15ft

The range is 15ft to 60ft There is a gap at 22ft and 55ft

Neither_Glasses_nor_contacts

2

4

6

8

10

N

0 10 20 30 40 50 60 70

Guess

Nothing Histogram

Column Summary

NNeither_Glasses_nor_contacts

35.5972

15

26.5

34

43.5

59

11.5754

72

35.5972

15

26.5

34

43.5

59

11.5754

72

S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = sS8 = count

EXPLORATORY DATA: NEITHER CONTACTS NOR GLASSES

• The data is unimodal and right skewed

• The median is 34ft and the IQR is 17ft

• The range is 15ft to 59ft

Glasses

1

2

3

4

5

6

7

G

0 10 20 30 40 50 60 70

Guess

Glass Histogram

Glass

Column Summary

Guess

GGlasses

37.46

15

29

35

49

59

11.8187

50

37.46

15

29

35

49

59

11.8187

50

S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = sS8 = count

EXPLORATORY DATA: GLASSES

The data is unimodal with a right skew

The median is 35ft and the IQR is 20ft

The range is 15ft and 59 ft

SAMPLE POPULATION

20

40

60

80

100

120

Gender

F M

count

SIGHT Bar Chart

10

20

30

40

50

60

70

80

G_C_N

C G N

count

SIGHT Bar Chart

Females vs. Males at the Montgomery mall

Population of people with contacts, glasses,

or neither in Montgomery County

CONCLUSIONS POPULATION

In Montgomery County there is a greater population of people that wear neither glasses nor contacts. We then found that there is a greater number of people with contacts rather than glasses. The glasses population is the minority in Montgomery County.

We found that there are more females going to the mall than males, which was expected.

2 SAMPLE T-TEST

Ho: c/g = n Ha: c/g n

NV

Guess

0 10 20 30 40 50 60 70

SIGHT Box Plot

ASSUMPTIONS

1. Two independent SRS

2. Popg/c 10ng/c Popn 10nn

3. Two normal populations or ng/c and nv 30

1. They were not SRS but was the best sample and both were independent

2. There are more than 1130 people with glasses/contacts and 720 people with neither in Montgomery County

3. Ng/c (113) > 30Nv (72) > 30

StateCheck

Conditions Met – Student t-distribution -2 sample t-test

CALCULATIONS AND CONCLUSIONS

= 1.317

2 P(t>1.317 df=154.2590) = 0.19

Ho: c/g = v Ha: c/g v

-We fail to reject Ho because the p-value of 0.19 is greater than alpha 0.05. -We have sufficient evidence that the average distance guessed by those with glasses or contacts is equal to the average distance guessed by those without glasses or contacts.

2 SAMPLE T-TEST

Ho: c = g Ha: c g

CG

Guess

0 10 20 30 40 50 60 70

SIGHT Box Plot

ASSUMPTIONS

1. Two independent SRS

2. Popc 10nc Popg 10ng

3. Two normal populations or nc and ng 30

1. They were not SRS but was the best sample and both were independent

2. There are more than 500 people with glasses and 630 people with contacts in Montgomery County.

3. Nc (63) > 30Ng (50) > 30

State Check

Conditions Met – Student t-distribution -2 sample t-test

CALCULATIONS AND CONCLUSIONS Ho: c = g Ha: c g

= 0.303

2 P(t>0.303 df=105.931) = 0.76

-We fail to reject Ho because the p-value of 0.76 is greater than alpha 0.05. -We have sufficient evidence that the average distance guessed by those with contacts is equal to the average distance guessed by those without glasses.

2 SAMPLE T-TEST

Ho: m = f Ha: m f

GenderF M

FM

0 10 20 30 40 50 60 70

Guess

SIGHT Box Plot

ASSUMPTIONS

1. Two independent SRS

2. Popm 10nf Popm 10nf

3. Two normal populations or nm and nf 30

1. They were not SRS but was the best sample and both were independent

2. There are more than 110 females and 750 males inMontgomery County .

3. Nf (110) > 30Nm (75) > 30

State Check

Conditions Met – Student t-distribution -2 sample t-test

CALCULATIONS AND CONCLUSIONS

Ho: m = f Ha: m f

= -0.376

2 P(t<-0.376 df=81.7625) = 0.71

-We fail to reject Ho because the p-value of 0.71 is greater than alpha 0.05. -We have sufficient evidence that the average distance guessed by males is equal to the average distance guessed by females.

APPLICATION TO POPULATION

We conclude that regardless of wearing contacts, glasses, or neither the people of Montgomery County do not show a significant difference in depth perception.

We can also conclude that there is not a difference in the depth perception of males and females in Montgomery County.

BIAS/ ERROR We found that people in groups guessed

similar to each other, so they may not have been saying the distance that they actually felt.

Some people did not take us seriously and said a random number when we asked for the distance between the cones.

Since it was right after the holiday season, many people were in a rush and did not want to answer our questions.

We faced the problem of involuntary response because not everyone wanted to answer our questions.

PERSONAL OPINIONS/CONCLUSIONS

Our original hypothesis that there would be no difference in the depth perception of those with glasses, contacts, or neither was correct.

We felt that it was difficult to ask people to participate in our data collection when they were going in and out of the store.

Overall it was interesting to see the wide variety of response.