Sampling

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Sampling
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Todays Objectives

• Describe how base rates can fluctuate in relation
  to the sample frame
• Define regression to the mean
• Explain why it it is difficult to compare
  performance across time in a sample that has been
  selected based on its extremity.

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Perils of Cross Race Identification
From EXONERATIONS IN THE UNITED STATES 1989
THROUGH 2003 Gross et al. (2004)
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Perils of Cross Race Identification

• According to Gross et al. (2004), there is an
  overrepresentation of Black defendants among rape
  exoneration cases due to the cross race effect.

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Perils of Cross Race Identification

• The evidence
• A majority of rape prisoners in 2002 were white,
  58 only 29 were black and 13 were Hispanic.
• But for rape exonerations the proportions are
  reversed almost two thirds of the defendants are
  black, 65 only 27 are white and 8 are
  Hispanic.

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Perils of Cross Race Identification

• The evidence
• The race of the victim was known for 75 of the
  69 rape exonerations in 75 of those cases the
  victim was white.
• Most women who are raped are victimized by
  members of their own racial or ethnic groups.
• Inter-racial rape is uncommon, and rapes of white
  women by black men in particular account for well
  under 10 of all rapes.
• But among rape exonerations for which we know the
  race of both parties, almost exactly half (39/79)
  involve a black man who was falsely convicted of
  raping a white woman.

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Perils of Cross Race Identification

• The evidence
• In 88 of rapes the victim and the offender are
  of the same race, and
• Victims of rape are approximately evenly divided
  between whites and blacks.
• It follows then that the rate of interracial rape
  should be between 4-5

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Perils of Cross Race Identification

• the most obvious explanation for this racial
  disparity i.e., 50 versus 4-5 is probably
  also the most powerful the perils of
  cross-racial identification.
• p. 24

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My Neighborhood
UC San Diego
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How prevalent social factor x is depends on how
you sample.

• An illustration How prevalent is rape? The
  answer depends on where you sample
• Victimization Survey Findings
• National Crime Victimization Survey (NCVS)
• College samples e.g., Koss (1987)
• Arrest and Clearance Rates
• Uniform Crime Reports (UCR, collected by the FBI)
• Conviction Rates
• Imprisonment Rates

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Case Flow in CJS
Felony Crime Committed Police, Victim, or Witness
Reports Arrest is Made 12 Released lt--Police
Review ---gt 88 Sent to DA 15 Complaint Denied
lt-- DA Review --gt 40 Misdemeanor 45 of Cases DA
Reviews are Sent to Lower Court 15 Judge
Dismisses lt-- Lower Court --gt 27 Misdemeanor 58
of Cases Reviewed in Lower Courts Sent to
Superior Court 7 Judge Dismisses lt-- Superior
Court --gt 1 Acquitted Felony Conviction in 92
of Cases Sent to Superior Court
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Reconsideration of Cross Race Explanation

• Inter-racial rape is uncommon, and rapes of white
  women by black men in particular account for well
  under 10 of all rapes.

• Source
• Criminal Victimization in the United States,
  1996-2002

• The base rate of black on white victimizations is
  27 among stranger cases reported to the police.

• Source
• NCVS 1992-2004 data

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Reconsideration of Cross Race Explanation

• A majority of rape prisoners in 2002 were white,
  58 only 29 were black and 13 were Hispanic.

• Source
• Sourcebook, 2002

• 35 of prisoners in 2002 were white, 37 were
  black, and 23 hispanic

• Source
• Bureau of Justice Statistics, Prisoners in 2002

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Reconsideration of Cross Race Explanation

• And
• Black males are more likely to be convicted for
  raping white females because the probability of
  prosecution is reduced in cases that involve
  black women as complainants.

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Reconsideration of Cross Race Explanation

• Bottom line All things considered, should we
  really expect that the base rate for Black on
  White rape convictions resulting in prison time
  to be 4-5?

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Some people hate the very name of statistics but
I find them full of beauty and interest. Whenever
they are not brutalized, but handled by higher
methods, and are warily interpreted, their power
of dealing with complicated phenomena is
extraordinary.
Regression to the Mean

• Sir Francis Galton

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Regression to the Mean

• Many parents think that punishment improves bad
  behavior, and rewards do not sustain good
  behavior. (Kahneman Tversky, 1973.)
• Rookies of the year in major league baseball seem
  to suffer from a sophomore jinx. (Taylor Cuave,
  1994)
• Some children assigned to remedial programs do
  not seem to belong in such programs.

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Regression to the Mean

• Some very depressed people spontaneously become
  much less depressed.
• The sequel to a movie is usually not as good as
  the original movie.
• High school students who do poorly on the SAT
  seem to improve remarkably after taking an SAT
  preparation course.

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Regression to the Mean

• Regression toward the mean defined
• Statistical reality in which performance declines
  for those who do the best and improves for those
  who have done the worst.

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Regression to the Mean

• The Offset Effect of Psychotherapy
• Medical services usage declines once
  psychotherapy begins.

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Regression to the Mean

• The Offset Effect of Psychotherapy
• Medical services usage declines once
  psychotherapy begins.

Psychotherapy
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Regression to the Mean

• The Trick
• Many individual time series have been averaged
  after being co-aligned around the onset of
  therapy.
• The period prior to the onset of therapy is a
  sample of extreme scores! That is, an extreme
  point in time was selected to begin therapy.

Psychotherapy
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Regression to the Mean

• The Solution
• Examine time series for individual people (pink
  dots)

Psychotherapy
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Regression to the Mean

• Incorporate a control into the design
• That is, find people who are at the height of
  their medical usage, and look at what happens to
  them afterwards without having exposure to
  psychotherapy.

Psychotherapy