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 1 in 8 women (12.5%) of women get breast
cancer, so P(breast cancer if female) = 0.125
 1 in 800 (0.125%) of men get breast cancer, so
P(breast cancer if male) = 0.00125
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Two-Way Table
 Create a two-way table, with 1000 each of
males and females.
Gender/C Breast Cancer
ancer
No Breast Total
Cancer
Female
Male
Total
875
998.75
1873.75
0.125*1000 = 125
0.00125*1000 = 1.25
126.25
1000
1000
2000
 What’s the overall (unconditional) probability
of breast cancer?
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Conditional Probability
Gender/ Breast Cancer No Breast Total
Cancer
Cancer
Female
Male
Total
125
1.25
126.25
875
998.75
1873.75
1000
1000
2000
 What’s P(breast cancer if female)?
 What’s P(female if breast cancer)?
 P(A if B) is NOT the same as P(B if A)!!!
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Odds Ratio
 The odds ratio (OR) is the ratio of the odds of
an event in one group to the odds of an event
in another group
 Odds ratio for breast cancer comparing
females to males:
odds of getting breast cancer for males
OR =
odds of getting breast cancer for females
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Odds Ratio
odds of getting breast cancer for males
OR =
odds of getting breast cancer for females
P(breast cancer if female)
1- P(breast cancer if female)
=
P(breast cancer if male)
1- P(breast cancer if male)
1/ 8
1/ 7
11
/
8
=
=
= 114.14
1 / 800
1 / 799
1- 1 / 800
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Unit A
Essential Synthesis
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The Big Picture
Population
Sampling
Sample
Statistical
Inference
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Descriptive
statistics
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Chapter 1: Data Collection
Was the sample
randomly selected?
Yes
No
Possible to
generalize to
the population
Should not
generalize to
the
population
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Was the explanatory
variable randomly
assigned?
Yes
Possible to
make
conclusions
about causality
No
Can not make
conclusions
about causality
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Chapter 2: Descriptive Statistics
 Type of summary statistics and visualization
methods depend on the type of variable(s) being
analyzed (categorical or quantitative)
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Variable(s)
Visualization
Summary Statistics
Categorical
bar chart,
pie chart
frequency table,
relative frequency table,
proportion, odds
Quantitative
dotplot,
histogram,
boxplot
mean, median, max, min,
standard deviation,
z-score, range, IQR,
five number summary
Categorical vs
Categorical
side-by-side bar chart, two-way table, difference
segmented bar chart
in proportions, odds
ratio
Quantitative vs
Categorical
Overlaid histograms,
parallel dotplots,
side-by-side boxplots
statistics by group,
difference in means
Quantitative vs
Quantitative
scatterplot
correlation
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Descriptive Statistics
Think of a topic or question you would like to
use data to help you answer.

What would the cases be?

What would the variables be?
(Limit to one or two variables)
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Descriptive Statistics
How would you visualize and summarize the
variable or relationship between variables?
a) bar chart/pie chart, proportions, frequency
table/relative frequency table, odds
b) dotplot/histogram/boxplot, mean/median,
sd/range/IQR, five number summary
c) side-by-side or segmented bar charts, difference in
proportions, two-way table, odds ratio, conditionals
d) side-by-side boxplot, difference in means
e) scatterplot, correlation
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