Data day2012 barboza_data_storytelling

1. Storytelling with
Data
Gia Elise Barboza, JD, PhD
Assistant Professor
Department of African American Studies and Health Science
Northeastern University

2. The Research Approach
• The scientific method
o Theory (rational choice theory)
o Hypothesis (a deficit approach)
o Data Analysis (incorrect method)
o Empirical Observation (cognitive bias)
o Research Conclusions (illogical conclusion)
• Reclaim our story using data
o When?
o Why?
o How?

3. Take-Aways
• Disaggregation leads to very different conclusions
(this is Simpson’s Paradox)
• Numbers are social constructs, the same data can
be “used” to show the exact opposite results (this is
NOT lying with stats)
o Know which method leads to invariance
• You must not rely on one data source to tell a story,
stories are woven together via multiple sources of
data
o Quantitative (census, surveillance) and qualitative data (focus group,
interview)

4. Why Reclaim Your Story?
• Existing uses of, lack of access to and manipulation of
data harms communities particularly on the basis of
o Race;
o Gender; and/or
o Sexual orientation?
• Research & data analyses often …
o Are biased
o Ignore community input
• Research is done “on” the “community” not in it
o Manipulated and (mis)used for political purposes
• To reclaim our story its essential to be numerate and to
understand limitations of research and data
o Policy outcomes

5. When to Reclaim Your
Story?
• When to reclaim
1. The data shows no disparity but I want to use the same data to
show that a disparity indeed exists
2. The data seem accurate but there is another side to the story
(similar to (1) but different data are used)
3. My intuition does not match the data & the story being told is
inaccurate (the data is being manipulated)

6. How to Reclaim?
• Understand data “issues”
• What is the story you are trying to reclaim? Three basic
story lines to reclaim
o Story 1 [the data shows no disparity but I want to use the same data
to show that a disparity indeed exists]: State accounts of the impact
of health care reform legislation do not address the needs of certain
groups and disparities in access to insurance coverage remain
o Story 2 [the data is reasonable but there is another side to the story]:
Unravel the image of the welfare queen as an inaccurate portrayal
of unwed motherhood and teenage pregnancy (among other
things)
o Story 3 [my intuition does not match the data]: Reclaiming the real
story behind the Boston “miracle” by arguing that youth
empowerment was responsible for the decrease in crime

7. Story 1
• Story 1 [The data shows no disparity but I want to
use the same data to show disparity exists]
• In order to understand this story, we have to
understand proportions, percents, odds and odds
ratios and how they are easily manipulated
o They are also the most misunderstood and misapplied
o Helps get a sense of how data are social constructs
o Involves understanding different interpretations of disparity using
proportions, percents, odds and odds ratios

8. Data Issues: Is there a Disparity?
• Many issues involve a comparison
between two percents (or proportions/
probabilities). Consider the example of a
test taken by men and women on which
men are observed to have a higher pass
rate.
• How would you describe the disparity in
pass (or fail) rates (and what are the pros
and cons of each way)?
1. The difference in pass (fail) rates (the “gap”)
2. The ratio of the pass (fail) rates
3. The odds ratio

9. The difference in pass(fail) rates
• Assume that the passage rate for men is 97% and the
passage rate for women is 90%
o What is the difference in pass rates?; What is the difference in
fail rates?
o If 100 persons take the test, 70% of them female, how would
you compute the number of women adversely affected by
the exam?
• Using a 7% difference I can show you that there will be
about 5 women adversely affected (.07 * 70)
• If there are 1000 people who take the exam, 50 women
are adversely affected
• If 10000 people take the exam, 500 women are affected
o When impact is an issue, this is the best method to use
o The problem is that a 7% difference between 97% and 90%
should not be treated the same as a 7% point difference
between 10% and 3% since the latter evinces a much larger
disparity (the next slide shows why)

10. The ratio of the pass/fail
rates
• Assume that the passage rate for men is 97%
and the passage rate for women is 90%
o What is the ratio of the pass rates?
• Men are 1.07 times as likely to
pass?
.97
= 1.07
.90
o What is the ratio of the fail rates?
• Interpretation?
.10
= 3.33
.03
Interpretation? Which statistic would you use to
show disparate impact?

11. Odds Ratio of the Pass (Fail) Rates
• The odds ratio of the pass rates is defined as the odds of
passing for men divided by the odds of passing for women.
• Calculate the odds ratio in pass rates
o First calculate the odds of passing for men
pM .97 .97
Odds = = = = 32.3: 1
1  pM 1  .97 .03
• Interpretation?
o Second calculate the odds of passing for women
pW .90 .90
Odds = = = = 9: 1
1  pW 1  .90 .10
Divide the two
• Odds ratio = 32.3/9 = 3.6

12. Odds Ratio of the Pass (Fail) Rates
• The odds ratio of the fail rates is defined as the odds
of failing for women divided by the odds of failing for
men.
• Calculate the odds ratio in fail rates
o First calculate the odds of failing for women
pW .10 .10 1
Odds = = = =  1: 9
1  pW 1  .10 .90 9
• Interpretation?
o Second calculate the odds of failing for men
pM .03 .03 3
Odds = = = =  3 : 97
1  pM 1  .03 .97 97
o Divide the two 1
• Odds ratio = 9 = 97 = 3.6
3 27
97

13. Two Quick Examples
• MCAS proficiency rates
• Infant Mortality rates

14. MCAS proficiency by Race/Ethnicity

15. Infant Mortality Survival Ratio
Year White Black Ratio (B/W) White Black (B/W)
1992 5.9 19 3.22 994.1 981 0.99
1993 5.9 15 2.54 994.1 985 0.99
1994 7.2 12.5 1.74 992.8 987.5 0.99
1995 4.7 11.9 2.53 995.3 988.1 0.99
1996 6.7 9.9 1.48 993.3 990.1 1.00
1997 9.5 12.8 1.35 990.5 987.2 1.00
1998 4 12 3.00 996 988 0.99
1999 5.6 13.5 2.41 994.4 986.5 0.99
2000 2.8 13.6 4.86 997.2 986.4 0.99
2001 5.1 13.5 2.65 994.9 986.5 0.99

16. Health Insurance
Disparity
• Massachusetts is often touted as having the lowest
uninsurance rate in the nation
o This is true!
o BUT, I want to show disparity remains by race using the same data the
state uses, in particular that
• Coverage for some groups is as bad as it is in the state with the worst
coverage rate, Texas
• For some groups, things are actually worse after the legislative reforms
in 2006
• The health care gap has at best remained the same for some groups

17. Empirical evidence for the success of health care reform
in MA in 2006

18. “Among major subpopulations, the largest increases were observed among Hispanics (14.2%),
persons with less than a high school diploma (12.0%), and persons making <$25,000 (11.9%).”
Based on Number Insured Based on Number Uninsured
Pre-law Post-law % change Pre-law Post-law % change
White, non-Hispanic 93 97.3 4.6 7 2.7 61.4
Black, non-Hispanic 88.2 92.7 5.1 11.8 7.3 38.1
Hispanic 77.9 89 14.2 22.1 11 50.2
Asian 90.5 98.4 8.7 9.5 1.6 83.2
English 84.6 93.3 10.2 15.4 6.7 56.5
Spanish 69.1 81.8 18.4 30.9 18.2 41.1
Less than high school diploma or GED 79.1 88.6 12.0 20.9 11.4 45.5
At least high school diploma or GED 92.2 96.8 5.0 7.8 3.2 59.0
< $25,000 79.5 89 11.9 20.5 11 46.3
$25,000 – $74,999 91 96.2 5.7 9 3.8 57.8
>= $75,000 97.4 99.4 2.1 2.6 0.6 76.9

19. Recall Hispanics had the largest gains!
Table 1. Persons Aged 18 – 64 by Health Insurance Coverage and
In 2010, the Health Status by Latino Origin, Massachusetts, 2003 & 2010 (Annual
percent of Social and Economic Supplement (ASEC))
foreign-
No Health Health Status:
born non-
citizens Insurance (%) Poor (%)
without Massachusetts 10.8 1.6
insurance Non-Latino 10.1 1.5
coverage is 2003 All Latino 17.9 2.6
actually Foreign Born 27.9 3.6
greater than
US Born 8.1 1.7
it was in
Foreign Born Non-Citizen 41.0 3
Texas,
which is the
state with Massachusetts 5.2 1.8
the lowest Non-Latino 4.4 1.4
overall 2010 All Latino 12.5 5.4
coverage Foreign Born 15.5 9.6
rate.
US Born 9.8 1.5
Foreign Born Non-Citizen 30.4 8.7

20. How many additional Latinos actually need to be covered to achieve parity with the
general population?
Table 4. Total Population, Total Population Uninsured, Percentage and Number of Individuals needed to
achieve parity with State Overall Coverage Rate by Ethnicity, 2003 to 2010
Number of
Percentage of
Additional
Additional Number
Individuals
Coverage Needed to
Number Who Need
Total Population (Drop in Achieve
Uninsured Coverage in
Percent State
order to
Uninsured Percent
achieve state
since 2003)
drop in %
2003 2010 2003 2010
Massachusetts 5,615,372 5,621,910 606,460 292,339 0.482 -- --
Non-Latino 5,123,402 5,076,744 517,464 223,377
Latino 491,970 545,166 88,063 68,146 0.774 42,449 25,695
US born 248,274 285,810 20,110 28,009 1.390 9,693 18,315
Foreign born 243,696 259,357 67,991 40,200 0.591 32,774 7,425
Foreign born non-
citizen 131,574 95,170 53,945 28,932 0.536 26,003 2,927

21. If the red line is above the blue line the gap relative to whites
is worse in the post-law period! The health care gap is worse for blacks compared
to whites

22. Story 2: The demonization
of black female sexuality
• This is a story about how we use outliers to represent
a group BUT the value we assign to the outlying
behavior differs according to race (& gender)
o When behavior is done by blacks is bad, we conclude all blacks do it, and
engage the blame frame to impute moral failure
o When behavior done by whites is bad, we excuse it as an aberration
• Popular notions regarding black women, sexuality,
and welfare are hypocritical at best
o I want reclaim the story by exposing the hypocrisy around this issue. But
how?
• Juxtapose popular images; and
• Disaggregate data around this issue
• Flip the script on morality

23. “Tangle of Pathology?” Who
Do We Value?
72% of black babies are born to
unwed mothers

24. Who’s the Baby Daddy?
• As of 2010…
o “The black community's 72 percent rate eclipses that of most other
groups: 17 percent of Asians, 29 percent of whites, 53 percent of Hispanics
and 66 percent of Native Americans were born to unwed mothers in 2008,
the most recent year for which government figures are available. The rate
for the overall U.S. population was 41 percent.”
• In the 60s, when Moynihan characterized black
family life as a “tangle of pathology” the black
“illegitimacy” rate was 24%! (29 > 24!)
o Logic dictates that the pathology still exists today… and includes whites.

25. Reinforcing the Blame Frame
71.4%, 54.6% and 16.3% of
black, Hispanic and white
women, respectively, who
were pregnant were not
married
The percentage of white
pregnant women aged 18
– 24 who have either never
been married or who are
unmarried but in a
relationship is
approximately the same as
that for black pregnant
women overall, 70%!
The right question…
Blaming one group for their
own failure seems to be a
constant theme…

26. Same behavior, different result?
• Next, consider the percentage of
women who have either never been
married or who are unmarried but in a
relationship who report having EVER
used contraception after having
unprotected sex.
• More than 50% of white women used
contraception after unprotected sex
compared to only 16% of black
women.
• Whites engage in the same behavior,
they just have different observable
results
o But what is more immoral? Having a baby out
of wedlock or using the morning after pill to
induce abortion. Other arguments suggest
abortion is worse…

27. • In another story the
Boston Globe reported
the teen birthrate fell to
a record low, dropping
6% from 2008 to 39.1
births per 1000 in 2009.
• “The decline in teen
births is really quite
amazing”!!! Let’s see just
how amazing it is…
“Rates fell significantly for all race and Hispanic origin groups between 2008 and
2009, with declines ranging from 4 to 6 percent (for non-Hispanic white, non-
Hispanic black, and ASIAN teenagers). The rate for Hispanic teenagers aged 15-19
fell 10 percent in 2009 to 70.1 births per 1,000, the lowest rate ever reported for this
group in the two decades for which rates for Hispanic teenagers are available. The
rate for API teenagers dropped 10 percent. Rates for all groups reached historic
lows [2].” http://www.cdc.gov/nchs/data/nvsr/nvsr59/nvsr59_03.pdf

28. Dispositionism, Situationism or Some Combination of Both?: Whites’
Perceptions of Welfare Policy and Attitudes towards the Poor, Barboza
(2011).
Table 2. Attitudes Towards Welfare Recipients Among Individuals Who Believe That Most Welfare
• There is a significant relationship between the
Recipients Are Black
Most Welfare Most Welfare Recipients Are
perceived welfare recipients race and Recipients Are Black White
In your opinion, do you think that most people who receive money from welfare today could get
• A belief that people on welfare are morally different
along without it if they tried, or do you think that most of them really need this help?
than those not on welfare.
Get along without it 50.2 45.5
Really need the help 49.8 54.5
o Individuals who perceive welfare recipients as black are significantly more
likely to claim that welfare recipients have lower moral values
In general, do you think people on welfare have higher, lower, or about the same moral values as
• A belief that welfare recipients do not really want to
other Americans?
Higher 2.3 2.9
work.
Lower 35.5 24.3
o Individuals who perceive welfare recipients as black are more likely to
About the same 62.2 72.8
P = .001 claim that welfare recipients don’t want to work.
Do you think that most welfare recipients today really want to work or not?
Yes 42.6 59.4
No 57.4 40.6
P < .000

29. It’s all really smoke and mirrors…
Living with mother ‘This is a defining time for
• 291 75.2
America,” says Mitt Romney.
In labor force President Barack Obama, he78.7
229
Not in labor force argues, wants to turn
62 21.3
America into a “European-
Source: 2005-2009 American Community Survey 5-Year Estimatessociety” in
like entitlement
which “government provides
Survey: American Community Survey Geographic Area: Census Tract 902, Suffolk
County, Massachusetts every citizens with the same
or similar rewards.” In
contrast, Romney supports
“an opportunity society, free
people living under a limited
government.”
• Read more:
http://www.politico.com/new
“I come from a single family household. My mother was a single mother of 3 and
she had 3 jobs. She was able to go to RCC so we s/stories/0112/71791.html#ixzz
grew up a lot by ourselves. I started
1ka0UKvU3 extremely
working at the age of 13. I worked all through college…. I was
independent.” (Focus group, January, 2011).

30. Story 3
• Story 3: Based on your experience, the “data”
being presented is wrong, I want the data to reflect
my intuition
• Story 3 illustrates:
o How to use qualitative data to validate quantitative findings
o That relying on existing data leads to the reification of misinformation
o How overly simple analyses and a lack of depth leads to incorrect
conclusions

31. The Problem of Youth
Violence
• We are retelling the story of the Boston miracle
o Operation ceasefire & the 10-point coalition
o In reclaiming the story, we show that these factors usually
attributed to the decrease in youth violence in the 1990s
are actually responsible for increases in youth violence
today
o but how?

32. Steps used in reclaiming
the story
• Define the crisis
o Start at the beginning and the end -- with existing accounts of the decline in
youth violence in the 1990s and the upsurge in youth violence in the 2000s
o Use data in a way that is impactful
• Reframe the issue as something to be solved by using a
positive youth development framework
o Focus on prevention
• Show the impact of PYD on the problem of youth
violence both
o Show how PYD impacted crime in the 1990s
o Show how it impacts crime today using community level inputs
• Private funding is essential
o Argue that the reason for the increase is the lack of federal funding and that
we need private foundation money in order to solve the problem

33. The :: Miracle
• Between 1996 and 2003, Boston experienced a drop
of almost 90% in violent acts among youth, with
shootings decreasing from a high of 550 in 1990 to a
low of 133 in 1997.
• Then, in 2003 a reversal in this pattern began. By
2004, there were almost three times as many
shootings as there had been in 1997.
• Where are we now?

34. Defining the Problem of
Youth Violence
• Homicide ranks as the 7th leading cause of
death for both blacks and Hispanics but only
30th among whites.
o The death rate from firearms is more than five times higher for
black males than it is for white males (23.5 per 100,000 vs. 4.3 per
100,000).

35. Youth* Violence in Boston
1 Young Black Male Dies
Every Two Weeks in
Young Blacks
Boston
* Ages 15 - 24

36. Youth Development in the
Workplace
Mentoring
1. Mentoring
Public
2. Youth Workforce Development andand Supports Education
Family
Awareness &
Policy
3. Family Supports and Mental Health
Initiatives
Mental Health
4. Conflict Resolution and Social Skill Development
5. Community Capacity-Building
Community
Conflict
Youth
Resolution and
6. Public Awareness & Policy
Capacity- Workforce Initiatives
Social Skill
Building Development
Development
But where’s the leverage point??

37. Table 4: Predicted Probability of Youth Employment By Selected
Characteristics Holding Parental Work, School Enrollment and Poverty
Status Constant
Black White Hispanic
Male Female Male Female Male Female
Overall (16-24) .35 .38 .51 .54 .45 .48
16 .15 .16 .25 .27 .21 .23
17 .19 .21 .31 .33 .26 .28
18 .24 .26 .38 .41 .33 .35
Below Poverty .23 .26 .37 .40 .32 .34
Line
Above Poverty .38 .41 .54 .57 .48 .51
Line
Source: 2008-10 American Community Survey, Census Bureau

38. Newt is Right!
“Inner city” youth should be working!
Clean Toilets? Research Assistant at NEU?

41. Perceptions of Positive Role Models
Table ES.6 Categories of Positive Role Models in Youth Lives
• Youth who perceive
Gang
Professionals
Family &
Members & professionals and
Friends
Drug Dealers
family & friends to
Peers .488
Mother .825 be positive
Father .762
influences are
Teacher .633
Pastor or Church Leaders .552 significantly less
The Police .602
likely to engage in
Health Care Professionals .693
Social Workers .817 bad behavior
Street Workers .714
Drug Dealers .880
Gang Members
Extraction Method: Principal Component Analysis.
.887
• Youth who perceive
Rotation Method: Varimax with Kaiser Normalization. gang members to be
positive influences
are significantly
more likely to
engage in bad
behavior.

42. Can’t just remove negative you must replace it with positive behaviors
Kaplan-Meier Survival Estimate of Gang Membership Kaplan-Meier Survival Estimate Gang Exit
1
1
.75
.75
Survivorsip Probability
.5
.5
.25
.25
0
0
0 5 10 15 20 0 5 10 15 20
Analysis Time (Age Became Gang Member) Analysis Time (Age Left Gang)
95% CI Survivor function 95% CI Survivor function
Why get involved with a gang? “There are constant let down[s]. If I can’t resort to the people around me, why have them around
me? Frustrated, don’t know who to turn to, so I turn to the street, someone owes me…”
Why turn to the street? Because “being part of something is better than not being a part of anything.” This theme of wanting to belong was
echoed by many, gang involved or not. Survey results indicate that 16.3% of youth feel the need to rep their hood to others, 11% said they have
been or currently are involved in a gang, and 22% said they are associated with a gang. 1 in 4 current or former gang members said they
became involve between the ages of 8 and 10 years old.
And this story by a former gang member corroborates the empirical evidence, “I joined a gang at 9 years old, I had my first tattoo at 9 years old,
I always wanted to be a part of something, they took care of
picked up my first gun at 9 years old.
me, made sure I had sneakers, made sure I went to school and had money in my
pocket.” When I commented that the gang had a positive role despite the fact it came with negative behaviors, his response to me was,
“Nothing is free. That’s what I learned at an early age.”

43. How did employment change behavior?
Post-survey Findings
In general, do you think this In general, do you think this
program has helped you?... program has helped community 60% of youth say that
either their age or having
Open up new doors for by?... a CORI is the biggest
84% barrier the y face in
your future? Providing People with acquiring employment
60%
Learn about others’ Opportunities and only 13% say that
experiences and how to there are a lot of high
88% Providing Role Models for quality jobs available for
respect differences of 25% teens. Nevertheless, only
opinion Children and Young Adults 11% of youth taking the
Approach a problem by post-survey believed that
the application process
communicating without Giving People Money 19% was “extremely hard”
79% while 42% claimed it was
anger to come up with a
“not too hard” or “not
good solution Providing the Labor to hard at all.” Moreover,
14% the majority of youth
From hanging around in Clean up the Community
received a job offer
the street and being 76% Making People in the within 3 months.
13%
unsafe Community Safer
Providing new Providing people in the Connecting the
experiences, empathy, community with Disconnected to
problem solving, opportunities and a Job quickly
providing a safe place access to role models and easily

44. The 6C’s of Youth Development
Connection Competence Character Confidence Caring Contribution
Organizational Opportunities to Sense of belonging Community
Mentoring Empathy
Decision-making learn and grow and responsibility participation
Constant Meaning of Hard Positive identity Learning about Civic
Skill building Responsibility
supervision Work development others’ experiences
Efficacy, self- Three-tiered
Community Higher levels of Understanding
worth, positive mentoring
Engagement thriving “self”
view of the future
“I learned
School Engagement
how to get
with
“I need to “Makes me feel others” “Being a
“Being part of it.”
work on my good to help role model
patience in people who need for a
“I was told dealing with it.” younger
I'm good in work tasks.” girl.”
math and I
never was
before.”

45. Table 1. Quotations Demonstrating the Impact of Employment on Positive Youth
Development
Behaviors Youth Want to Program Impact on Youth Behaviors2
Change1
PYD Concept
“I'd change the people I hang “Being part of it!”; “
out with.” “Being a role model for a younger girl.”
Connection (a sense of
“We want people to listen to “On this job, you get to communicate with
safety, structure, and
us and hear our struggles.” new people.”
belonging; positive
“I’m on my own, have to do “Feels real good to get stuff off our chests
bonds with people and
it all myself.” and just vent”
social institutions)
“Taking time to know me”
“This job kept me off the streets.”
1Allparticipating youth were asked, “If you could change one thing about yourself, what would it be?” In addition, BHS youth were asked, “What do
you want to get out of this program?” 2 On the post-survey, all youth were asked to provide an open-ended response to the following, “What is the most
rewarding thing that happened to you this summer?” (q21). In addition, focus group respondents were asked to describe the mai n benefits of
employment.
Youth want to change, and the emphasis on PYD in an employment context
allows them to begin to change their attitudes and behaviors…

46. Relationship Between Meaningful
Employment and YVP
Causes of Youth Crime Positive Youth Development Quotations Illustrating
Concept the Relationship
between PYD, YVP and
MYE
Relationship issues “I think it’s the people
Negative Socialization they put in front of us…
Connection
w/out positive socialization my worksite supervisor,
or role models she’s been there…”
PYD concepts are linked directly to what the community attributes as being the
causes of youth crime.
All this to say that meaningful employment can change behaviors associated with
criminogenic risk, but what does this have to do with the Boston miracle?

47. Rethinking the “Miracle”: Finding Unity and Peace in
Boston – Replacing the Miracle with a Methodical
Approach to Reduce Youth Violence, Barboza, et al. (2012)
• It “ is not that the Boston model of the
1990s has failed, but rather that the City of
Boston and the Boston Police failed to
pursue the policies and practices that had
been so successful during the late 1990s.”
(Braga, et al. 2008).
o The largest influx of federal funds in the history of the
Commonwealth
o An economy conducive to youth employment
o An unprecedented amount of collaboration across all
sectors including religious, family, schools, criminal justice,
social service, health and non-profit organizations Massachusetts Arrest Rate for Violent Crime, 1986 – 2007 (Source: Fox)
o By 2003 there were “dramatic cuts in community
programs aimed towards at-risk children” (Fox, 2008).
o More arrests of youth under 18 during a 20 year period
o The number of black males incarcerated over this time
period skyrocketed
o This created a short-term moratorium on violence, the
large number of well-funded youth development
programs for at-risk youth -- is the real story behind the
Boston miracle.

48. A call for Public Funding…
• In a 2004 public opinion poll of African Americans,
respondents were asked their opinion on a variety of social
and political issues thought to be of particular salience to
blacks living in the United States.
o Not a single black respondent who was asked to describe the most pressing issue
that a presidential candidate should discuss during the presidential campaign
selected an answer that pertains to youth: youth crime/violence/gangs,
drugs/youth, youth (other), parenting or lack of discipline, or youth values/respect.
o Top responses included jobs/unemployment, the economy, health care, and war.
This is best attributed to the fact that 41% said they were “very concerned” that in
the next year they or someone in their household will be unemployed and looking for
a job
• These same adults were asked to state the one thing that
would be most impactful for reducing youth crime and
violence.
o Most often cited was the importance of community programs, followed by holding
parents legally responsible for their children’s actions.
o Programmatic activities and family support are clearly viewed as important to
reduce youth violence even though youth violence itself is not viewed as being an
important issue for government to address.
o Since politicians are responsive to their constituents, it seems likely that alternative
modes of funding are essential to combat youth violence in the long run.

49. A Primer: Odds and
Odds Ratios
• The odds of something occurring (versus not
occurring) is defined as the probability of it occurring
divided by the probability it does not occur
p
Odds=
1− p
• Example: Let the probability of rain be 1/4. What are
the odds of observing rain (vs. not rain)?

50. Odds and Odds Ratios
• Example: Let the probability of rain be 1/4.
What are the odds of observing rain (vs. not
rain)?
1 1
Odds
= 4 1 1
4 = == 3 :
 
1 3 3

1 
  4
4
• Interpretation: for every day it rains it will not
rain three days

51. Relationship between probability and odds
Probability:
Probability = 1/4
Number of days it will rain over
total number of days
Odds:
Number of days it will rain to the
number of days it will NOT rain
Rain Not rain

52. Odds and Odds Ratios
• Odds Ratio: the ratio of two odds
p1
Odds1 1− p1
Odds Ratio= =
Odds 2 p2
1− p 2
Interpretation: the odds of an event occurring in
Group 1 versus the odds of it occurring in
Group 2