Introduction to Statistics: Understanding Data, Samples, and Variables

1. Chapters 1 and 2 Week 1, Monday

2. 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

3. 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” Chapter 2: Data

4. Sample VS Population “Often, the cases are a sampleof 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

5. 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) Chapter 2: Data

6. 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 Chapter 2: Data

7. 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 Chapter 2: Data

8. 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) Chapter 2: Data

9. Chapter 3 Week 1, Wednesday and Friday

10. 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

11. Frequency Table 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

12. 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

13. 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

14. 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

15. Contingency Table 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

16. Contingency Table Marginal Distribution– Can be obtained from the contingency table by observing row (or column) percents. Chapter 3: Displaying and Describing Categorical Data

17. Contingency Table Marginal Distribution– Can be obtained from the contingency table by observing row (or column) percents. Chapter 3: Displaying and Describing Categorical Data

18. Contingency Table 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

19. Contingency Table 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

20. Contingency Table 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

21. Contingency Table 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

22. Contingency Table 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

23. Contingency Table 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