Chapters 1 and 2
Week 1, Monday
What is Statistics?
“Statistics is a way of reasoning, along with a collection of tools
and methods, designed to help us understand the world”
-- Textbook, page 2
Involves: 1) Collecting, analyzing, presenting, interpreting data
2) Making decisions
Chapter 1: Stats Starts Here
What are Data?
“Data are values along with their context”
-- Textbook, page 2
“We can make the meaning clear if we organize the values into
a data table”
-- Textbook, page 8
“variables”
“cases”
“records”
Name Student ID Gender Age
Status GPA
Joe
00001
Male
Grad
4.0
Amy
00002
Female 19
Ugrad
3.5
Bob
00003
Male
Ugrad
3.0
Chapter 2: Data
23
32
Sample VS Population
“Often, the cases are a sample of cases selected from some
larger population that we’d like to understand”
– Textbook, page 9
Example: The data set below is a sample of three students from
the population “All University of Akron Students”
Goal: A sample that is representative of the population
Name Student ID Gender Age
Status GPA
Joe
00001
Male
Grad
4.0
Amy
00002
Female 19
Ugrad
3.5
Bob
00003
Male
Ugrad
3.0
Chapter 2: Data
23
32
Types of Variables
Categorical:
“When a variable names categories and
answers questions about how cases fall into
those categories” (Gender, Status)
Quantitative:
“When a measured variable with units
answers questions about the quantity of what
is measured” (Age, GPA)
Name Student ID Gender Age
Status GPA
Joe
00001
Male
Grad
4.0
Amy
00002
Female 19
Ugrad
3.5
Bob
00003
Male
Ugrad
3.0
Chapter 2: Data
23
32
Types of Variables
Pitfalls: 1) Often numeric values are quantitative, but not
always! (Student ID is not a “measured variable with
units”)
2) We could turn Age into a categorical variable by
assigning labels: “younger” for students under 22 and
“older” for students over 22
Name Student ID Gender Age
Status GPA
Joe
00001
Male
Grad
4.0
Amy
00002
Female 19
Ugrad
3.5
Bob
00003
Male
Ugrad
3.0
Chapter 2: Data
23
32
Types of Variables
Pitfalls: 1) Often numeric values are quantitative, but not
always! (Student ID is not a “measured variable with
units”)
2) We could turn Age into a categorical variable by
assigning labels: “younger” for students under 22 and
“older” for students over 22
Name
Student ID Gender Age
Status
GPA
Joe
00001
Male
Grad
4.0
Amy
00002
Female Younger
Ugrad
3.5
Bob
00003
Male
Ugrad
3.0
Chapter 2: Data
Older
Older
Types of Variables
Identifier:
A unique value for each case (“[When] there
are as many categories as individuals and
only one individual in each category”) whose
value is not “useful”
-- Textbook, page 12
(Student ID)
Name Student ID Gender Age
Status GPA
Joe
00001
Male
Grad
4.0
Amy
00002
Female 19
Ugrad
3.5
Bob
00003
Male
Ugrad
3.0
Chapter 2: Data
23
32
Chapter 3
Week 1, Wednesday and Friday
Data Set for Chapter 3 Slides
Data is from a sample of 8
students from a graduate
level Statistics class
An identifier (Name)
Three categorical variables:
Gender (male, female)
Handed (right, left)
Grade (A, B, C, D, F)
Chapter 3: Displaying and Describing Categorical Data
Frequency Table
Grade
Count
Grade
%
A
2
A
25
B
3
B
37.5
C
2
C
25
D
1
D
12.5
Frequency Table – displays counts for each category
Relative Frequency Table – displays percentages/proportions
(describes the distribution – names the possible categories
and tells how frequently they occur)
Chapter 3: Displaying and Describing Categorical Data
Graphing Categorical Data
Bar Chart– Displays the distribution of a categorical variable,
showing the counts for each category next to each other for
easy comparison.
Chapter 3: Displaying and Describing Categorical Data
Graphing Categorical Data
Pie Chart– Shows the whole group of cases as a circle, slicing it
into pieces whose size is proportional to the fraction of the
whole in each category.
Chapter 3: Displaying and Describing Categorical Data
Graphing Categorical Data
Area Principle– The area occupied by a part of the graph should
correspond to the magnitude of the value it represents.
Chapter 3: Displaying and Describing Categorical Data
GENDER
Contingency Table
Male
Female
A
0
2
2
GRADE
B
C
3
1
0
1
3
2
D
1
0
1
Contingency Table – A two-way table for categorical variables
showing how the individuals are distributed along each
variable.
Chapter 3: Displaying and Describing Categorical Data
5
3
8
Grade
A 2/8
25%
B 3/8
37.5%
C 2/8
25%
D 1/8
12.5%
GENDER
Contingency Table
Male
Female
A
0
2
2
GRADE
B
C
3
1
0
1
3
2
D
1
0
1
Marginal Distribution– Can be obtained
from the contingency table by
observing row (or column) percents.
Chapter 3: Displaying and Describing Categorical Data
5
3
8
Gender
M 5/8
62.5%
F 3/8
37.5%
GENDER
Contingency Table
Male
Female
A
0
2
2
GRADE
B
C
3
1
0
1
3
2
D
1
0
1
Marginal Distribution– Can be obtained
from the contingency table by
observing row (or column) percents.
Chapter 3: Displaying and Describing Categorical Data
5
3
8
GENDER
Contingency Table
Male
Female
A
0
2
2
GRADE
B
C
3
1
0
1
3
2
D
1
0
1
In future assignments you’ll have to answer the following types
of questions from a contingency table:
1) What is the percent of students that earned an A?
2/8 = 25%
Chapter 3: Displaying and Describing Categorical Data
5
3
8
GENDER
Contingency Table
Male
Female
A
0
2
2
GRADE
B
C
3
1
0
1
3
2
D
1
0
1
In future assignments you’ll have to answer the following types
of questions from a contingency table:
2) What is the percent of students that are female?
3/8 = 37.5%
Chapter 3: Displaying and Describing Categorical Data
5
3
8
GENDER
Contingency Table
Male
Female
A
0
2
2
GRADE
B
C
3
1
0
1
3
2
D
1
0
1
In future assignments you’ll have to answer the following types
of questions from a contingency table:
3) What is the percent of females that earned an A?
(Called a “conditional probability”)
2/3 = 66.7%
Chapter 3: Displaying and Describing Categorical Data
5
3
8
GENDER
Contingency Table
Male
Female
A
0
2
2
GRADE
B
C
3
1
0
1
3
2
D
1
0
1
In future assignments you’ll have to answer the following types
of questions from a contingency table:
4) What is the percent of students that earned an A or B?
5/8 = 62.5%
Chapter 3: Displaying and Describing Categorical Data
5
3
8
GENDER
Contingency Table
Male
Female
A
0
2
2
GRADE
B
C
3
1
0
1
3
2
D
1
0
1
In future assignments you’ll have to answer the following types
of questions from a contingency table:
5) What is the percent of students that earned an A and B?
0/8 = 0%
Chapter 3: Displaying and Describing Categorical Data
5
3
8
GENDER
Contingency Table
Male
Female
A
0
2
2
GRADE
B
C
3
1
0
1
3
2
D
1
0
1
5
3
8
In future assignments you’ll have to answer the following types
of questions from a contingency table:
6) What is the percent of students that are female and earned C?
1/8 = 12.5%
Chapter 3: Displaying and Describing Categorical Data