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Chapters 1 and 2 Week 1, Monday
Chapters 1 and 2Week 1, Monday
Chapter 1: Stats Starts Here
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 2Involves: 1) Collecting, analyzing, presenting, interpreting data
2) Making decisions
Chapter 2: Data
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
Name
Student ID
Gender
Age
Status
GPA
Joe 00001 Male 23 Grad 4.0Amy 00002 Femal
e19 Ugra
d3.5
Bob 00003 Male 32 Ugrad
3.0
“variables”
“cases”“records”
Chapter 2: Data
Sample VS Population
Name
Student ID
Gender
Age
Status
GPA
Joe 00001 Male 23 Grad 4.0Amy 00002 Femal
e19 Ugra
d3.5
Bob 00003 Male 32 Ugrad
3.0
“Often, the cases are a sample of cases selected from some larger population that we’d like to understand”
– Textbook, page 9Example: 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
Chapter 2: Data
Types of Variables
Name
Student ID
Gender
Age
Status
GPA
Joe 00001 Male 23 Grad 4.0Amy 00002 Femal
e19 Ugra
d3.5
Bob 00003 Male 32 Ugrad
3.0
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)
Chapter 2: Data
Types of Variables
Name
Student ID
Gender
Age
Status
GPA
Joe 00001 Male 23 Grad 4.0Amy 00002 Femal
e19 Ugra
d3.5
Bob 00003 Male 32 Ugrad
3.0
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
Chapter 2: Data
Types of Variables
Name
Student ID
Gender
Age Status GPA
Joe 00001 Male Older Grad 4.0Amy 00002 Femal
eYounger
Ugrad 3.5
Bob 00003 Male Older Ugrad 3.0
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
Chapter 2: Data
Types of Variables
Name
Student ID
Gender
Age
Status
GPA
Joe 00001 Male 23 Grad 4.0Amy 00002 Femal
e19 Ugra
d3.5
Bob 00003 Male 32 Ugrad
3.0
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)
Chapter 3Week 1, Wednesday and Friday
Chapter 3: Displaying and Describing Categorical Data
Data Set for Chapter 3 SlidesData 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 TableGrade
Count
A 2B 3C 2D 1
Grade
%
A 25B 37.
5C 25D 12.
5Frequency Table – displays counts for each
categoryRelative 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
Contingency Table
GRADE
GENDER
A B C D Male 0 3 1 1 5Female 2 0 1 0 3 2 3 2 1 8
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
Contingency Table
GRADE
GENDER
A B C D Male 0 3 1 1 5Female 2 0 1 0 3 2 3 2 1 8Grade
A 2/8 25%B 3/8 37.5
%C 2/8 25%D 1/8 12.5
%
Marginal Distribution– Can be obtained from the contingency table by observing row (or column) percents.
Chapter 3: Displaying and Describing Categorical Data
Contingency Table
GRADE
GENDER
A B C D Male 0 3 1 1 5Female 2 0 1 0 3 2 3 2 1 8Gender
M 5/8 62.5%
F 3/8 37.5%
Marginal Distribution– Can be obtained from the contingency table by observing row (or column) percents.
Chapter 3: Displaying and Describing Categorical Data
Contingency Table
GRADE
GENDER
A B C D Male 0 3 1 1 5Female 2 0 1 0 3 2 3 2 1 8
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
Contingency Table
GRADE
GENDER
A B C D Male 0 3 1 1 5Female 2 0 1 0 3 2 3 2 1 8
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
Contingency Table
GRADE
GENDER
A B C D Male 0 3 1 1 5Female 2 0 1 0 3 2 3 2 1 8
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?2/3 = 66.7% (Called a “conditional
probability”)
Chapter 3: Displaying and Describing Categorical Data
Contingency Table
GRADE
GENDER
A B C D Male 0 3 1 1 5Female 2 0 1 0 3 2 3 2 1 8
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
Contingency Table
GRADE
GENDER
A B C D Male 0 3 1 1 5Female 2 0 1 0 3 2 3 2 1 8
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
Contingency Table
GRADE
GENDER
A B C D Male 0 3 1 1 5Female 2 0 1 0 3 2 3 2 1 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%
