Transcript Comparative Qualitative Graphs

Warm-up
An investigator wants to study the effectiveness of two surgical
procedures to correct near-sightedness: Procedure A uses cuts from a
scalpel and procedure B uses a laser. The data to be collected are the
degrees of improvement in vision after the procedure is performed.
Design an experiment for this.
Comparitive Graphs
Section 1.1
Creating and Interpreting Comparative
Graphs
Learning Objectives
After this section, you should be able to…

CONSTRUCT and INTERPRET Comparative bar graphs

CONSTRUCT and INTERPRET Segmented bar graphs

CONSTRUCT and INTERPRET Two Way Tables

CALCULATE & INTERPRET marginal and conditional
distributions

ORGANIZE statistical problems
Two Way Table

Describes two categorical variables.

One variable is shown in the rows and the
other is in the columns.
Example of Two Way Table
Young adults by gender & chance of getting rich
Gender
Opinion
Female
Male
Total
Almost no chance
96
98
194
Some chance but probably not
426
286
712
A 50-50 chance
696
720
1416
A godd chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
Reading a Two-Way Table

Look at the distribution of each variable
separately.
 The
totals on the right are strictly the values
for the distribution of opinions about becoming
rich for all.
 The totals at the bottom are for gender
Marginal Distribution

The marginal distribution of one of the
categorical variables in a two-way table of
counts is the distribution of values of that
variable among all individuals described
by the table.

It’s the distribution of each category alone.
Percentages

Often are more informative

Used when comparing groups of different
sizes.
Find the percent of young adults who they
there is a good chance they will be rich.
Young adults by gender & chance of getting rich
Gender
Opinion
Female
Male
Total
Almost no chance
96
98
194
Some chance but probably not
426
286
712
A 50-50 chance
696
720
1416
A godd chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
Find the marginal distribution (in %) of
opinions. Make a graph to display the marginal
distribution.
Young adults by gender & chance of getting rich
Gender
Opinion
Female
Male
Total
Almost no chance
96
98
194
Some chance but probably not
426
286
712
A 50-50 chance
696
720
1416
A godd chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
Response
Percent
Almost no
chance
4.0%
Some chance but
probably not
14.8%
A 50-50 chance
29.3%
A good chance
29.4%
Almost certain
22.4%
Find the marginal distribution (in %) of gender.
Make a graph to display the marginal
distribution.
Young adults by gender & chance of getting rich
Gender
Opinion
Female
Male
Total
Almost no chance
96
98
194
Some chance but probably not
426
286
712
A 50-50 chance
696
720
1416
A godd chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
Response
Percent
Male
51%
Female
49%
Conditional Distribution

It describes the values of that variable
among individuals who have a specific
value of another variable.

To describe the relationship between the
two categorical variables
Conditional Distribution of young women and
men and their opinion.
Young adults by gender & chance of getting rich
Gender
Opinion
Almost no
chance
Female
96
Male
98
Some chance but
probably not
426
286
A 50-50 chance
696
720
A godd chance
663
758
Almost certain
486
597
Total
2367
2459
Side-by-Side Bar Graph
Response
Women
Men
Almost no
chance
4.1%
4%
Some chance
but
probably
not
18.0%
11.6%
A 50-50
chance
29.4%
29.3%
A good
chance
28%
30.8%
20.5%
24.3%
Almost certain
Segmented Bar Graph
Response
Women
Men
Almost no
chance
4.1%
4%
Some chance
but
probably
not
18.0%
11.6%
A 50-50
chance
29.4%
29.3%
A good
chance
28%
30.8%
20.5%
24.3%
Almost certain
Did we look at the right
conditional distribution?

Our goal was to analyze the relationship
between gender and opinion about
chances of becoming rich for these young
adults.
Hint: Does gender influence opinion or opinion influence gender?
Since gender influences opinion, then we want to consider the conditional
distribution of opinion for each gender.
Four-Step Process
State: What’s the question that you’re
trying to answer?
 Plan: How will you go about answering
the question? What statistical techniques
does this problem call for?
 Do: Make graphs and carry out needed
calculations.
 Conclude: Give your practical conclusion
in the setting of the real-world problem.

State

What is the relationship between gender
and responses to the question “What do
you think are the chances you will have
much more than a middle-class income at
age 30?”
Plan

We suspect that gender
might influence a young
adult’s opinion about the
chance of getting rich.
So we’ll compare the
conditional distributions of
response for men alone
and for women alone.
Response
Women
Men
Almost no
chance
4.1%
4%
Some chance
but probably
not
18.0%
11.6%
A 50-50 chance
29.4%
29.3%
A good chance
28%
30.8%
Almost certain
20.5%
24.3%
Do

We’ll make a side-by side bar graph to
compare the opinions of males and
females.
I
could have used a segmented as well!
Side-by Side Comparative
Bar Graph
Response
Women
Men
Almost no
chance
4.1%
4%
Some chance
but
probably
not
18.0%
11.6%
A 50-50
chance
29.4%
29.3%
A good
chance
28%
30.8%
20.5%
24.3%
Almost certain
Segmented Comparative Bar Graph
Response
Women
Men
Almost no
chance
4.1%
4%
Some chance
but
probably
not
18.0%
11.6%
A 50-50
chance
29.4%
29.3%
A good
chance
28%
30.8%
20.5%
24.3%
Almost certain
Conclude

Based on the sample data, men seem
somewhat more optimistic about their
future income than women. Men were
less likely to say that they have “some
chance but probably no” than women
(11.6% vs 18.0%). Men were more likely
to say that they have a “good chance”
(30.8% vs 28.0%) aor alre “almost certain”
(24.3% vs 20.5%) to have much more than
a middle-class income by age 30 than
women were.
Association

We say there is an association between
two variables if specific values of one
variable tend to occur in common with
specific values of the other.
 Be
careful though….even a strong association
between two categorical variables can be
influenced by other variables lurking in the
background.
Simpson’s Paradox

An association between two variables that
holds for each individual value of a thrid
variable can be changed or even reversed
when the data for all values of the third
variable are combined. This reversal is
called Simpson’s paradox.
Accident victims are sometimes taken by helicopter from
the accident scene to a hospital. Helicopters save taim.
Do they also save lives?
Helicopter
Road
Victim Died
64
260
Victim survived
136
840
Total
200
1100
32% of
helicopter
patients died,
but only 24% of
the others did.
This seems
discouraging!
Helicopter is sent mostly to
serious accidents.
Serious Accident
Helicopter
Less Serious Accident
Road
Helicopter
Road
Died
48
60
Died
16
200
Survived
52
40
Survived
84
800
Total
100
100
Total
100
1000
Titanic Disaster
Homework

Page 24
 (19,
21, 23, 24, 25, 27-32, 33, 35, 36)