Chapters 1 and 2 Week 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 2 Involves: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 NameStudent IDGenderAgeStatusGPA Joe00001Male23Grad4.0 Amy00002Female19Ugrad3.5 Bob00003Male32Ugrad3.0 “variables” “cases” “records”

Chapter 2: Data Sample VS Population NameStudent IDGenderAgeStatusGPA Joe00001Male23Grad4.0 Amy00002Female19Ugrad3.5 Bob00003Male32Ugrad3.0 “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

Chapter 2: Data Types of Variables NameStudent IDGenderAgeStatusGPA Joe00001Male23Grad4.0 Amy00002Female19Ugrad3.5 Bob00003Male32Ugrad3.0 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 NameStudent IDGenderAgeStatusGPA Joe00001Male23Grad4.0 Amy00002Female19Ugrad3.5 Bob00003Male32Ugrad3.0 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 NameStudent IDGenderAgeStatusGPA Joe00001MaleOlderGrad4.0 Amy00002FemaleYoungerUgrad3.5 Bob00003MaleOlderUgrad3.0 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 NameStudent IDGenderAgeStatusGPA Joe00001Male23Grad4.0 Amy00002Female19Ugrad3.5 Bob00003Male32Ugrad3.0 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 3 Week 1, Wednesday and Friday

Chapter 3: Displaying and Describing Categorical Data 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 GradeCount A2 B3 C2 D1 Grade% A25 B37.5 C25 D12.5 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 Contingency Table GRADE GENDER ABCD Male03115 Female 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 ABCD Male03115 Female Grade A2/825% B3/837.5% C2/825% D1/812.5% 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 ABCD Male03115 Female Gender M5/862.5% F3/837.5% 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 ABCD Male03115 Female 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 ABCD Male03115 Female 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 ABCD Male03115 Female 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 ABCD Male03115 Female 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 ABCD Male03115 Female 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 ABCD Male03115 Female 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%