Transcript CHAPTER 1 STATISTICS

CHAPTER 1
STATISTICS
Statistics is a way of reasoning, along
with a collection of tools and methods,
designed to help us understand the
world
READ THE BOOK
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Think
Show
Tell
For Example
Step-by-Step
What can go wrong*
What have we learned?
CHAPTER 2
DATA
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Information together with its context
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Numerical
Names
Labels
Five W’s
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Who, What, When, Where, Why
How
WHO
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Respondents: Individuals who answer a
survey
Subjects or Participants: People on
whom we experiment. (Experimental
Units)
Records or Cases: Rows in a database
or data table. Individuals about whom
or about which, we have the data.
WHAT
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Variables
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Characteristics recorded about each
individual. These are usually columns in a
data table, and they should have a name
that identifies what has been measured.
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Categorical (or Qualitative)
Quantitative (Numerical values with
measurement units)
Ordinal
…more W’s
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Where and When?
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How?
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Country? Year?
How the data was collected?
Why?
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Reason for the study
Exercise
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Investments. According to an article in
Fortune (Dec.28, 1992), 401(K) plans permit
employees to shift part of their before-tax
salaries into investments such as mutual
funds. Employers typically match 50% of the
employees’ contribution up to about 6% of
salary. One company, concerned with what it
believed was a low employee participation
rate in its 401(k) plan, sampled 30 other
companies with similar plans and asked for
their 401(k) participation rates.
Identify the W’s
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Who ?
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30 Companies
What ?
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Participation Rates
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Quantitative (Units : Percent)
When ?
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Sometime after 1992
Identify the W’s (cont.)
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Where ?
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Why ?
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USA
The company was concerned with its
participation rate compared with other
companies
How ?
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Companies were sampled using an
unspecified method
Exercise
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Flowers. In a study appearing in the journal
Science a research team reports that plants in
southern England are flowering earlier in the
spring. Records of the first flowering dates for
385 species over a period of 47 years indicate
that flowering has advanced an average of 15
days per decade, an indication of climate
warming according to the authors.
Identify the W’s
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Who ?
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385 species of flowers over 47 years
What ?
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First flowering date
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Quantitative (Units : days)
When ?
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Not specified
Identify the W’s (cont.)
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Where ?
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Why ?
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Southern England
Researchers associate this behavior with
climate warming
How ?
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Observation. ( Method not specified)
Chapter 3. Displaying and
Describing Categorical Data
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Make a picture
First Make piles
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Organize the counts by categories in a
frequency table (counts) or a relative
frequency table (percentages)
Both types of tables describe the
distribution of the categorical variable
because they name the possible categories
and tell how frequently each occurs
The Area Principle
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The area occupied by a part of the
graph. It should correspond to the
magnitude of the value it represents
Bar Charts
A bar chart displays the distribution of a
categorical variable, showing the counts for
each category next to each other for easy
comparison.
Bar Chart
1000
800
Frequency
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600
400
200
0
First
Second
Third
Class
Crew
Pie Charts
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Relative proportion
(percentages instead
of counts).
Pie charts show the
whole group of cases
as a circle, each of the
pieces has a size
proportional to the
fraction of the whole
in each category.
Pie Chart
15%
40%
13%
First
Second
Third
Crew
32%
Contingency Tables
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Two categorical variables
Class
Survival
First
Second
Third
Crew
Total
Alive
Dead
202
123
118
167
178
528
212
673
710
1491
Total
325
285
706
885
2201
Marginal and Conditional
distributions
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Marginal Distribution
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Conditional Distribution
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Distribution of either variable alone (at the margin
of the table)
A distribution in one variable for only those
individuals satisfying some condition on another
variable.
Note : If the distribution of one variable is the
same for all categories of another we say that
the variables are independent.
Exercises
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Step-by-Step page 31
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What can go wrong
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Check the charts on pages 34
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Simpson’s Paradox (page 35)