Statistics onAmerican TV Habits

Kevin Englebert, Jordan Goodreau,

Don Li

Description of topic

1. We wanted to determine whether the number of viewers of a show and the critic rating of the show are related

2. Also we wanted to figure out if viewers of a show relate to the number of Google hits that show gets

3. Finally, we wanted to find out if the network a show is on affects its number of viewers

Background• Google

– Founded September 4 1998– Larry Page– Worth $23 billion– Internet search, e-mail, online mapping, office

productivity, video sharing, social networking• Nielsen Ratings

– Audience measurement systems – Gather Data through the extensive use of surveys

• TV.com– Critic Ratings– Staff Writers – Scale of 1-10

Procedure of Data Collection1. We performed a stratified random sample by

randomizing lists from Nielsen site then randomly selecting two shows per list for the two linear regression tests (Tests 1 and 2)

2. We then found critics rating (as determined by a scale from 1-10 on tv.com) and Google hits (as results generated by searching “name of show” TV show) for each of the shows

3. We performed a test on each of the sets of data and then constructed a confidence interval for the slope of the pop reg line

Procedure of Data Collection1. For the chi squared test we randomly

selected 10 shows for each of the three major networks with more than 30 shows (ABC, CBS, NBC)

2. We collected the number of viewers in millions for each of the shows from the Nielson rating site.

3. Finally, we performed the chi squared test on the data set.

Scatter plot Test DataIn Format of Show – Viewers in Millions

– Rating – Google Hits

As The World Turns - 2.744 - 8.2 - 291,000BIG BANG THEORY, THE – 10.200- 9.0- 432,000THE BIGGEST LOSER – 11.923- 8.1 - 397,000COLD CASE – 11.509- 8.9- 534,000CSI - 15.778 -9.1- 677,000DESPERATE HOUSEWIVES – 6.907-8.8- 2,290,000Eleventh Hour - 5.514- 7.8- 361,000FAMILY GUY – 5.970-9.1- 3,380,000FRIENDS -  3.574-9.2- 19,800,000FRINGE -  4.011-8.5- 816,000GHOST WHISPERER – 10.644- 8.7- 697,000Grey’s Anatomy - 12.9- 9.0- 1,750,000HEROES -  6.614-9.2- 7,800,000HOUSE -  6.032- 9.2- 34,300,000HOW I MET YOUR MOTHER 6.595- 9.1- 1,010,000

HOWIE DO IT – 7.777- 4.7- 520,000ICARLY – 3.901-8.6- 263,000

JUDGE JUDY -  6.071- 7.8- 112,000KNIGHT RIDER – 5.736- 8.0- 934,000

Late Night with Conan O’Brien- 1.033- 9.1- 194,000Late Show with David Letterman – 1.355- 8.3- 1,750,000

LAW AND ORDER – 10.259- 8.9 - 658,000LIFE – 4.745- 9.0- 52,600,000

MOMMA’S BOYS -  4.746- 6.4- 98,600ONE TREE HILL - 1.813- 9.0- 1,660,000PRISON BREAK -  4.574- 9.1- 5,980,000

PRIVATE PRACTICE -  6.077 - 8.7- 623,000PUSHING DAISIES -  4.323- 8.9- 711,000

SCRUBS – 4.169-9.2- 534,000SPONGEBOB – 4.070- 8.6- 1,190,000

STYLISTA – 1.323 - 6.9- 172,000The Office - 8.346- 9.1- 7,170,000

TWO AND A HALF MEN – 4.686- 9.0- 542,000WITHOUT A TRACE -  14.062- 9.0- 478,000

Chi Squared Test DataNBC ABC CBS

BIGGEST LOSER 14,860 GREY’S ANATOMY 13,866 TWO AND A HALF MEN 11,559

LAW AND ORDER 10,259 SCRUBS 4,531 MENTALIST, THE 19,617

HOWIE DO IT 7,777 UGLY BETTY 7,535 GHOST WHISPERER 10,644

KNIGHT RIDER 5,736 AMER FUNN HOME VIDEOS 8,016 ELEVENTH HOUR 7,645

MY NAME IS EARL 5,601 DESPERATE HOUSEWIVES 13,787 COLD CASE 12,300

CRUSOE 2,810 BACHELOR, THE 8,742 WITHOUT A TRACE 13,133

OFFICE 4,134 PRIVATE PRACTICE 4,338 BIG BANG THEORY, THE 8,505

SUPERSTARS OF DANCE 9,666 PUSHING DAISIES 4,674 CSI 9,760

MOMMA’S BOYS 5,323 SUPERNANNY 3,780 GARY UNMARRIED 8,778

E.R. 7,342 ELI STONE 3,841 60 MINUTES 14,110

Viewers vs Critic Rating

R2= .015 (only 1.5% of the critic

rating plays a role on viewers)

R=.123 (weak correlation)

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

8

9

10

f(x) = 0.0309155881088944 x + 8.33526935330051

Viewers Vs Critics Rating

Series1Linear (Series1)Linear (Series1)Linear (Series1)

Viewers in Millions

Criti

cs ra

ting

(from

1-1

0)

Assumption

1. two Independent SRS

2. True relationship is linear

1. Assumed for the purpose of the analysis

2. Assumed for the purpose of the analysis

Test• Ho: β=0• Ha: β>0

T=b/Seb= .701P(t>.701 I Df=32)= .2443

We fail to reject ho in favor of ha because the p-value is greater than .05. We have sufficient evidence that the slope of the population regression line is zero. As the rating increases the number of viewers remains the same. Therefore critics rating and number of viewers for a show are not related.

B – Confidence interval

b t*SEb=(-.9321, 1.9097)We are 95% confident that the slope of the

population regression line lies between -.9321 and 1.9097.

This interval contains zero thus as critics rating increases, the number of viewers of the show stays the same so there is no linear relationship between viewers and Google hits.

Viewers vs Google Hits

Graph of Viewers vs Hits

0 2 4 6 8 10 12 14 16 180

10,000,000

20,000,000

30,000,000

40,000,000

50,000,000

60,000,000

google hits Linear (google hits )

Viewers in Millions

Goog

le H

itsr sq=.012

Only about a percent of the

variation in Google hits can be

explained by the change in viewers

of the show.

r= -.109Very weak association

Viewers vs. Google Hits

• Ho: β=0

• Ha: β>0

• n= 34

• y = a+bx → y=6611920.29+ -347302.62x

Example of what we call a Google hit

Assumption

1. two Independent SRS

2. True relationship is linear

1. Assumed for the purpose of the analysis

2. Assumed for the purpose of the analysis

Viewers vs. Google Hits

• We fail to reject Ho in favor of Ha• Sufficient Evidence that slope of population regression line β=0

• As number of viewers Increases, the number of Google hits stays the same.

• Therefore there is no linear relationship between viewers and Google hits.

Confidence Interval

We are 95% confident that the slope of the population regression line lies between -1,500,000 and 791,428.

Since this interval contains zero there is no relation between critic rating and viewers because a slope of 0 on the population regression line means that Google hits does not change as viewers change.

= (-1500000 , 791428)

IQR Test

• 1.5 x IQR Test• Q3-Q1=IQR• 1.5 x 1318000= 1977000• 1977000+1750000=3,727,000• Outliers : 6 outliers

Viewers vs Hits (New Data)

0 2 4 6 8 10 12 14 16 180

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

google hits Linear (google hits )

Viewers in Millions

Goog

le H

itsr sq.= 2.58 x 10^-5

Less than a tenth of a percent of the variation in

Google hits can be explained by the

change in viewers of the show.

r= -.0051 Scattered

Viewers vs. Google Hits (New Data)

• Ho: β=0

• Ha: β>0

• N=28

• y=a +bx→ y= 830682.87+ -1028.44x

Assumption

1. two Independent SRS

2. True relationship is linear

1. Assumed for the purpose of the analysis

2. Assumed for the purpose of the analysis

Viewers vs. Google Hits (New Data)

• We fail to reject Ho in favor of Ha• Sufficient Evidence that slope of population regression line

β=0• As number of viewers Increases, the number of Google hits

stays the same.• Therefore there is no linear relationship between viewers

and Google hits.

Confidence Interval (New Data)

We are 95% confident that the slope of the population regression line lies between -82,612 and 80,555.

Since this interval contains zero there is no relation between critic rating and viewers because a slope of 0 on the population regression line means that Google hits does not change as viewers change.

Network Relate to Viewers

Descending DataNBC ABC CBS14,860 13,866 19,61710,259 13,787 14,1109,666 8,742 13,1337,777 8,016 12,3007,342 7,535 11,5595,736 4,674 10,6445,601 4,531 9,7605,323 4,338 8,7784,134 3,841 8,5052,810 3,780 7,645

1 2 3 4 5 6 7 8 9 100

5,000

10,000

15,000

20,000

25,000

Viewers per show in Networks

NBCABCCBS

Descending Show Number

Num

ber o

f Vie

wer

s In

Thou

sand

s

1 2 3 4 5 6 7 8 9 10

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

20,000

NBCABC

CBS

Viewers per show by network

NBCABCCBS

Descending Show Number

Num

ber o

f Vie

wer

s In

Thou

sand

s

NBC Show PercentagesBIGGEST LOSERLAW AND ORDERHOWIE DO ITKNIGHT RIDERMY NAME IS EARLCRUSOEOFFICESUPERSTARS OF DANCEMOMMA’S BOYSE.R. ABC Show Percentages

GREY’S ANATOMY

SCRUBS

UGLY BETTY

AMER FUNN HOME VIDEOS

DESPERATE HOUSEWIVES

BACHELOR, THE

PRIVATE PRACTICE

PUSHING DAISIES

SUPERNANNY

ELI STONE

CBS Show PercentagesTWO AND A HALF MENMENTALIST, THEGHOST WHISPERERELEVENTH HOURCOLD CASEWITHOUT A TRACEBIG BANG THEORY, THECSIGARY UNMARRIED60 MINUTES

Chi Squared TestObserved NBC ABC CBS

X< 5 million 2 5 0

5 million< X<

10 million

6 3 4

X< 10 Million 2 2 6

Expected NBC ABC CBSX< 5 million 2.333 2.333 2.333

5 million< X<

10 million

4.333 4.333 4.333

X< 10 Million 3.333 3.333 3.333

Assumption

1. SRS

2. Sample size large enough so that all expected counts are ≥ 5

1. Assumed for the purpose of the analysis

2. Assumed (sure, why not….. Catch 22 for this one)

Chi Squared TestH0 : There is no association between the network that a show is

on and the number of viewers of that show.HA : There is an association between the network that a show is

on and the number of viewers of that show.

X2 = Σ = = 9.7

P(X2 > 9.7 | df = 4) = .0457

(observed – expected)2

expected

(2 – 2.333)2

2.333(5 – 2.333)2

2.333 …...+ +

We reject H0 in favor of HA because our P value of .0457 is less than α = .05. We have sufficient evidence that

there is an association between the network that a show is on and the number of viewers of that show.

Overall Breakdown

NBCABCCBS

Personal opinion

These tests were very interesting. We learned many things about television and how critic ratings and viewers affect each other and also Google hits. I liked our tests and feel like I wouldn’t know some of these interesting stats if we wouldn’t have done these tests. This has also shown us that many people watch dumb shows for no reason just that they like them.

Bias/ Error• Population of TV Shows too small• Only more common shows data available• Unable to find data on all TV shows

– Ratings not available for all TV shows• Data Could be skewed

– Name of show could result in more Google hits – “Life” “House” “Friends” etc showed outlier

number of hits perhaps not all returns are of show– Also shows that have been running longer may

have gotten a boost simply for duration

Application to Population

• There is no relationship between viewers and rating

• Critic’s best shows are not necessarily what the public is watching

• Sophistication vs Amusement

Application to Population• There is no relationship between the

number of Google hits and the number of views of the show

• There is a possible confounding variable of hits that have common words not related to the TV show

• Should not be extrapolated to pop. • Perhaps there maybe more there then a

linear relationship but we are unsure

Application to Population• There is a relationship between viewers

of a show and the network it runs on• This may suggest that viewers perhaps

just go to a network for a show and stay for more than one show

• Due to some of the assumptions failing however this should not be definitively extrapolated to the population

Conclusion• There is no relationship

between viewers and rating or Google hits but there is a relationship btw viewers and network

• More loyal to networks than shows?

• Cannot be extrapolated