Comparing Demographics

Patricia JancovaPenny Hausher

Block:1

Background• The U.S. has taken a census

of its population every ten years since 1790

• The most recent census available to us at present is the 1930 census, due to a 72-year privacy restriction

• From 1790-1840, only the head of household is listed – The number of household

members are listed in selected age groups

• In U.S. census records the questions vary from year to year and in state censuses, from state to state

• Census records can provide the building blocks of your research, and confirm information

• Details provided are:– Names of family members– Ages– Birthplaces– Residence– Occupation– Immigration– Citizenship details– Marriage information– Military service

Why Demographics?

• We were inspired to explore this topic after seeing an insert from a recent National Geographic Magazine– A yearlong series on the global population

Data Collection

• Most of our data collection occurred in center-city Philadelphia• Three locations: Market East Station, Rittenhouse

Square, and City Hall• Tuesday after school~5-7• Systematic Sample: every other person• Variables: sex, age group, ethnicity, Philly’s gear

• Data on U.S., PA, and world statistics came from online sources

117117

Variable Specifics• Ethnicity:

• White• Black• Hispanic• Other

• Asian, Indian, Native American, mixed, etc.

• Age Structure:• Young: (1-14)• Middle: (15-64)• Old: (64+)

Ethnicity Data

117

51

17 15

Comparison of Ethnic Distributions

White59%

Black26%

His-panic9%

Other8%

Ethnicity Distribution of Philadelphia

White 65%

Black12%

Hispanic16%

Other7%

Ethnicity Distribution of the U.S.

Phila. U.S.White 117 196769100

Black 51 36795300

Hispanic 17 48828900

Other 15 20949900

Total: 200 303343200

Conclusion: the ethnicity of the entire Philadelphia population roughly matches the ethnicity distribution of the US

GOF of Ethnicity Distribution of Philadelphia

Check1. Ethnicities are

categorical2. Assume Representative3. All expected ≥ 5

State 1. Categorical data2. SRS3. All expected counts

are ≥ 5

:0H The distribution of ethnicity fits the expected distribution:AH The observed H distribution does not fit the expected distribution

Conditions:

P(x2 > 38.7777│df=3)=1.9344x10-8

14)1415(

32)3217(

24)2451(

130)130117( 2222

2

x

7777.382 x

We reject the Ho because the p-value of 1.9344x10-8 < α=.05. We have sufficient evidence that the distribution of ethnicity for

Philadelphia does not fit the expected distribution of the US.

GOF of Ethnicity Distribution of Philadelphia

Literacy Rate Data1. 13 Bahrain 88.8%2. 88 Kazakhstan 99.6%3. 9 Australia 99%4. 140 Poland 99.3%5. 161 Somalia 24%6. 122 Namibia 88%7. 157 Singapore 94.4%8. 103 Macedonia 97%9. 25 Brunei 94.9%10. 169 Sweden 99%11. 96 Lebanon 89.6%12. 111 Mauritania 55.8%13. 131 Norway 99%14. 126 New Zealand 99%15. 165 Sri Lanka 90.8%16. 86 Japan 99%17. 166 Sudan 60.9%18. 70 Guatemala 73.2%19. 152 Saudi Arabia 85%

Average Literacy Rate:86.121%*

*from an SRS of 19 from 194 countries

Claim: average world rate < US rate

Literacy Rate T-test

Check1. Assume Representative2. There are more than 190

countries 3. Assume distribution of all

literacy rates in the world is normal

99:99:0

AHH

State 1. SRS2. Pop ≥ 10n3. Normal Pop

or n ≥ 30

Conditions:

Literacy Rate T-test

We reject the Ho because the p-value of .0055 < α=.05. We have sufficient evidence that the true average literacy in

the sampled countries is less than that of the U.S.

8314.2

nsxt

P(t<-2.8314│df=18)=.0055

Age Structure Data

22

167

11

Comparison of Age Structure11%

84%

6%

Age Structure of Philadelphia

Young Middle Old

27%

65%

8%Age Structure of the World

Young Middle Old

Phila. World

Young 22 1829256297

Middle 167 4422699018Old 11 516212397

Total: 200 6768167712

Conclusion: the age structure of the entire Philadelphia population roughly matches the age structure of the World

GOF of Age Structure

:0H

:AH

Check1. Age groups are

categorical2. Assume Representative3. All expected counts ≥ 5

State 1. Categorical data2. SRS3. All expected counts

are ≥ 5

The distribution of age fits the expected distributionThe observed H distribution does not fit the expected distribution

Conditions:

GOF of Age Structure

P(x2 >31.0562│df=2)=1.804x10-7

0562.3116

)1611(130

)130167(54

)5422( 2222

x

We reject the Ho because the p-value of 1.804x10-7 < α=.05. We have sufficient evidence that the distribution of age for

Philadelphia does not fit the distribution of age for the world.

Philly’s Gear-1 Prop Z-test

20.:20.:0

pHpH

A

Check1. Assume Representative2. (200)(.2)= 40 ≥ 10

(200)(.8)= 160 ≥ 103. There are more than 2,000

people in Philadelphia

State 1. SRS2. np ≥ 10

nq ≥ 103. Pop ≥ 10n

Conditions:

045.2009ˆ p

• 9 out of the 200 people observed were wearing Philly’s gear

Philly’s Gear-1 Prop Z-test

4801.5)1(

ˆ

nppppz

We reject the Ho because the p-value of 2.1309x10-8 < α=.05. We have sufficient evidence that the true proportion of

people who wear Philly’s gear in Philadelphia is less than 20 percent.

P(Z<-5.4801│df=199)=2.1309x10-8

Overall Conclusions• The Philadelphia population matches the “Most

Typical Person” in terms of age (middle aged), but not in terms of race Will probably see changes in population makeup

• The ethnicity of the entire Philadelphia population matches the ethnicity distribution of the U.S.

Overall Conclusions Cont.• The age structure of the entire Philadelphia population matches

the age structure of the world population• Literacy in the world is less than that of the U.S.

Average world rate lowered by underdeveloped countries• Less than 20% of the Philadelphia population sports Philly’s

gear on a given Tuesday afternoon • Not much spirit?!

Project Opinions• We found this project to be interesting in terms of:

• Relevance to the world• Application of statistics skills to real data

Sources of Bias and Error• Some of our data comes from the internet so it may

not be completely reliable• Censuses do not account for every single person

and must be assumed representative of the population

• Undercoverage– Only people who walked past us had a chance of being

counted– We only went to three places

• Doesn’t necessarily account for the whole Philadelphia population