Using Statistics To Make Inferences 5

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Using Statistics To Make Inferences 5

• Summary
•   Graphical presentation of data
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• Goals
•   To review graphical methods covered in semester
  1 applied to real data
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• Practical
•   To examine the Vuyanich data, what tests might
  be appropriate?

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Background

• 723 F.2d 1195, Vuyanich v. Republic Nat. Bank of
  Dallas
• Joan Vuyanich began working as an agent contact
  clerk in Republic National Bank's ... Shortly
  thereafter, her supervisor told Vuyanich she
  should resign. ...

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Background

• Joan Vuyanich began working as an agent contact
  clerk in Republic National Bank's Money Order
  Department on April 29, 1969. She was the only
  black employee in that department. Shortly after
  beginning her job, she began having problems with
  two white female co-workers. She complained to
  her supervisors, and the situation was
  temporarily rectified.

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Background

• On June 29, 1969, Vuyanich married a white male.
  One month later, her supervisors met her husband.
  Shortly thereafter, her supervisor told Vuyanich
  she should resign. The supervisor gave as reasons
  her clashes with her co-workers, her complaints
  about her workload, and her not being suitable
  for the job. When Vuyanich inquired about a
  transfer, her supervisor replied that she
  probably did not need a job since her husband was
  white. Vuyanich was discharged on July 28, 1969.

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Background

• Less than two weeks later, Vuyanich filed a race
  discrimination charge against the Bank with the
  Equal Employment Opportunity Commission. She
  alleged a violation of Title VII of the Civil
  Rights Act of 1964, 42 U.S.C. Secs. 2000e to
  2000e-17. The EEOC issued a finding that a
  reasonable basis existed to believe that a Title
  VII violation may have occurred. Conciliation
  efforts were unsuccessful, and the EEOC issued a
  statutory right-to-sue letter. On March 22, 1973,
  Vuyanich filed suit in the district court.

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Bank Employee Survey

• Information on 474 employees hired by a
  midwestern bank between 1969 and 1971. Created
  for an Equal Employment Opportunity (EEO) court
  case involving wage discrimination, the file
  includes salary, job category and several other
  human resource variables.

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Questionnaire
Whats missing?
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Data
The key claimant was Vuyanich, you will find
further details on the web.   Some typical data
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Categories
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Whats missing?
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Charts

• Always look at your data first.
• Are charts a good idea?
• We will concentrate on sex for the charts. You
  can repeat this analysis or perform similar
  calculations for minority.

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Bar Chart
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Or?

• Tally for Discrete Variables SEX
• SEX Count Percent
• female 216 45.57
• male 258 54.43
• N 474

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Pie Chart
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Histogram
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Cumulative Frequency Polygon - Ogive
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Boxplot
Outlier
Minimum Lower Quartile Median Upper
Quartile Maximum
Upper Quartile Q3
Upper Limit Q3 1.5 (Q3-Q1)
Median
Lower Quartile Q1
Lower Limit Q1 - 1.5 (Q3-Q1)
Inter Quartile Range Q3 Q1
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Boxplot
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Dotplot
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Descriptive Statistics
Descriptive Statistics SALNOW Variable SEX
N N Mean SE Mean StDev Minimum SALNOW
female 216 0 10413 206 3023
6300 male 258 0 16577 486
7800 7860 Variable SEX Q1 Median
Q3 Maximum SALNOW female 8595 9720
11400 23250 male 11220 13140
20290 54000
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Tables

• Tabulated statistics SEX, JOBCAT
• Rows SEX Columns JOBCAT
• 1 2 3 4 5 6 7 All
• female 117 89 0 7 2 1 0 216
• male 110 47 27 34 30 4 6 258
• All 227 136 27 41 32 5 6 474
• Cell Contents Count

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Or A Plot?
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Or A Plot?
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What variables might we test?
Current salary versus Minority
Beginning salary versus Minority
Salary rise versus Minority
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What variables might we test?
Relative Salary rise versus Minority
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What variables might we test?
Relative Salary rise versus Minority
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What other factor might be relevant?
Salary rise given Job seniority versus Minority
What about Sex?
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Practical 5

• This material is available from the module web
  page.
• http//www.staff.ncl.ac.uk/mike.cox

Module Web Page
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Practical 5

• This material for the practical is available.

Instructions for the practical Practical 5
Material for the practical Practical 5
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There are three kinds of Lies Lies, Damned Lies
and Statistics

• Mark Twain or Benjamin Disraeli!

actually Leonard Henry Courtney 1832 to 1918
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Bullet Holes

• The bullet holes were all over the place on the
  R.A.F. planes -- in the wings and the fuselage,
  and seemingly distributed randomly on the
  undersides. So, where did the R.A.F.
  mathematician recommend extra armour, to save
  future missions?
• "A method of estimating plane vulnerability based
  on damage of survivors" by Abraham Wald

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Bullet Holes
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Bullet Holes
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Singleton BoomSingleton boom ... the number of
single-person households has doubled in the last
30 years - The Sun, 13 July, 2004
Critique!
J J J J J J j
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Singleton Boom Singleton boom ... the number of
single-person households has doubled in the last
30 years - The Sun, 13 July, 2004
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Polls Need Careful Reading to Work Out What's
Going On The Times October 26, 2006
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Polls Need Careful Reading to Work Out What's
Going On The Times October 26, 2006
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Age Structure


Age Structure Of College Enrolment American
Education Magazine
Why 3D?
Why colour?
Why reflect?
How much data?
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Heavy Drinking Kills Twice As Many People As In
1991The Times November 08, 2006
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Heavy Drinking Kills Twice As Many People As In
1991 The Times November 08, 2006
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Pie Chart
www.bbc.co.uk/skillswise/ 2004
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Pie Chart
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Online Casinos 'Used To Launder Cash' The Times
November 01, 2006
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Online Casinos 'Used To Launder Cash' The Times
November 01, 2006
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Online Casinos 'Used To Launder Cash' The Times
November 01, 2006
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Online Casinos 'Used To Launder Cash' The Times
November 01, 2006
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Online Casinos 'Used To Launder Cash' The Times
November 01, 2006
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Cost of Salad
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http//www.elainevigneault.com/why-does-a-salad-co
st-more-than-a-big-mac.html
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Fig 1
MSOR ConnectionsVolume 7 Number 4 November
2007 Chalkboard to smartboard maths going
green? Susan Starkings and Larry Krause
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University Challenge

• Presenter Jeremy Paxman
• 'In statistics, in data which are binomially
  distributed, individual values may be placed in
  one of two mutually exclusive categories such
  that the sum of the probabilities of occurring in
  the categories is what value?'
• Answer given 'Unity'
• Presenter
• 'No, it's one, or a hundred percent'
• University Challenge BBC222 October 2007

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Public loses faith in ability of politicians to
deal with crime The Sunday Telegraph By John
Curtice 02/07/2006
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Public loses faith in ability of politicians to
deal with crime The Sunday Telegraph By John
Curtice 02/07/2006
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Public loses faith in ability of politicians to
deal with crime
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Take a deep breath, the search for tranquillity
is over Sally Pook Telegraph 23 October 2006
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Hot Dog!
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Prison Figures Show A Link Between Sex Crime And
Religion
The Times Dominic Kennedy 25 November 2006
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Prison Figures Show A Link Between Sex Crime And
Religion
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Shrinking
Los Angeles Times 3 August 1979
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Shrinking
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Shrinking
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Poor put off college by fee rise
Comment? The Times 19-10-2006
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Poor put off college by fee rise
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Poor put off college by fee rise
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Poor put off college by fee rise
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Giuliani

• Presidential Candidate Giulianis New Hampshire
  radio advertisement, October 29, 2007.
• I had prostate cancer, five, six years ago. My
  chances of surviving prostate cancer and thank
  God I was cured of it, in the United States, 82
  percent. My chances of surviving prostate cancer
  in England, only 44 percent under socialized
  medicine.
• It is not completely clear here what is being
  compared here. It is probably meant to be the
  survival rate.

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Giuliani
The Giuliani campaign reports that these
percentages came from an article in the City
Journal a publication of the Manhattan Institute,
a conservative research organization. This
article entitled The Ugly Truth About Canadian
Health Care, was written by Dr. Lavid Gratzer, a
senior fellow at the Manhattan Institute and an
adviser for the Giuliani campaign. While the
article did not say where the numbers came from,
Dr. Gratzer has now explained that they came from
a Commonwealth Fund article Multination
Comparisons of Health Systems Data, 2000 by
Gerard F. Anderson and Peter S. Hussey of Johns
Hopkins University. Specifically they came from
the graphic in the Commonwealth Fund article
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Giuliani
Unfortunately incidence and mortality cannot give
survival rate!
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Supposedly shown at an FBI training program
Reproduced in a Wired magazine article 14
September 2011
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Supposedly shown at an FBI training program
The gap between 610 and 622 A.D. seems to be
about the same as the previous 600 years, and
only a little less than the 1400 years before
that.
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Supposedly shown at an FBI training program
Pious and devout Jews are portrayed as having
steadily increased in nonviolence up to the
present day.
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Supposedly shown at an FBI training program
I assume the line labelled Bible is referring
to Christians? Were pious and devout Christians
maximally violent at the beginning?
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Supposedly shown at an FBI training program
Pious and devout Christians in 1492 or 1618, were
much more peaceful than Jesus and his disciples.
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Supposedly shown at an FBI training program
The graph is itself an expression of religious
fundamentalism! Look at the Torah line
carefully. It starts in 1400 B.C.!
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One in four lap dancers has a degree, study finds
The Independent 27 August 2010
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Religious Outlier
The New York Times
The New York Time 3 September 2010
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Religious Outlier
Results are based on telephone and face-to-face
interviews conducted in 2009 with approximately
1,000 adults in each country.
The New York Times 3 September 2010
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Religious Outlier
For results based on the total sample of national
adults, one can say with 95 confidence that the
maximum margin of sampling error ranges from 5.3
percentage points in Lithuania to 2.6 percentage
points in India.
The New York Times 3 September 2010
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Religious Outlier
In addition to sampling error, question wording
and practical difficulties in conducting surveys
can introduce error or bias into the findings of
public opinion polls.
The New York Times 3 September 2010
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Religious Outlier
1. Does the United States look like an outlier to
you? Are there any other outliers on this graph?
New York Times 3 September 2010
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Religious Outlier
2. Why would there be a relationship between GDP
and percentage of people who call themselves
religious? Does a higher GDP cause lower
religiosity? Does a lower religiosity cause a
higher GDP? What sort of data could you collect
that might help answer this question?
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Religious Outlier
3. Do you like how Mr. Blow presented this data?
What would you change, if anything, in this
graph?
The New York Times 3 September 2010
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Religious Outlier
What might be "practical difficulties in
conducting surveys"? "wording difficulties"? What
effect might these have on the findings?
The New York Times 3 September 2010
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