1. Chapter 1: Statistics, Data, and Statistical Thinking

2. Where We’re Going Introduction to the field of statistics
How statistics applies to real-world problems
Establish the link between statistics and data
Differentiate between population and sample data
Differentiate between descriptive and inferential statistics
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

3. 1.1: The Science of Statistics
Statistics is the science of data. This involves collecting, classifying, summarizing, organizing, analyzing, and interpreting numerical information.
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

4. 1.2: Types of Statistical Applications
Statistics
Descriptive Statistics
Inferential Statistics
McClave, Statistics, 1th ed. Chapter 1: Statistics, Data and Statistical Thinking

5. 1.2: Types of Statistical Applications
Descriptive statistics utilizes numerical and graphical methods
to look for patterns in a data set, to summarize the information revealed in a data set and
to present that information in a convenient form.
Average, spread, range, frequency, histogram, median, scatter plot, mode, interquartile range,…
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

6. 1.2: Types of Statistical Applications
Inferential statistics utilizes sample data to make estimates, decisions, predictions or other generalizations about a larger set of data (i.e., population).
Hypothesis test, z. ANOVA, confidence interval, ordinary least squares, σ2, margin of error, t, …
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

7. 1.3: Fundamental Elements of Statistics
An experimental unit is an object about which we collect data.
Examples:
Person
Place
Thing
Event
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

8. 1.3: Fundamental Elements of Statistics
A population is a set of all units in which we are interested.
Typically, there are too many experimental units in a population to consider every one.
If we can examine every single one, we conduct a census.
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

9. 1.3: Fundamental Elements of Statistics
A variable is a characteristic or property of an individual unit.
Not surprisingly, the values of these characteristics will vary (i.e., change)!
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

10. 1.3: Fundamental Elements of Statistics
A sample is a subset of the population.
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

11. 1.3: Fundamental Elements of Statistics
A measure of reliability is a statement about the degree of uncertainty associated with a statistical inference.
Based on our analysis, we think 56% of soda drinkers prefer Pepsi to Coke, ± 5%.
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

12. 1.3: Fundamental Elements of Statistics
Descriptive Statistics
Inferential Statistics
The population or sample of interest
One or more variables to be investigated
Tables, graphs or numerical summary tools
Identification of patterns in the data
Population of interest
One or more variables to be investigated
The sample of population units
The inference about the population based on the sample data
A measure of reliability of the inference
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

13. 1.4: Types of Data
Quantitative Data are measurements that are recorded on a naturally occurring numerical scale.
Age
GPA
Salary
Cost of books this semester
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

14. 1.4: Types of Data
Qualitative Data are measurements that cannot be recorded on a natural numerical scale, but are recorded in categories.
Class standing (freshman, sophomore, senior, junior)
Live on/off campus
Major
Gender
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

15. 1.5: Collecting Data Published Source Designed Experiment Survey
You can obtain data in 4 different ways:
Published Source
Designed Experiment
Survey
Observational Study
SOURCE: United States Department of Agriculture Foreign Agricultural Service
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

16. 1.5: Collecting Data Published Source Journal Book Newspaper Magazine
(Reliable) Web Site
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

17. 1.5: Collecting Data Designed Experiment
Strict control over the experiment and the units in the experiment
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

18. 1.5: Collecting Data Survey Gallup, Harris, and other polls Nielsen
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

19. 1.5: Collecting Data Observational Study
Observe units in natural settings
No control over behavior of units
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

20. 1.5: Collecting Data
A representative sample exhibits characteristics typical of those possessed by the target population.
A random sample of n units is selected in such a way that every different sample of size n has the same chance of being selected.
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

21. 1.6: The Role of Statistics in Critical Thinking
Statistical thinking involves applying rational thought and the science of statistics to critically assess data and inferences.
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

22. 1.6: The Role of Statistics in Critical Thinking
Selection bias results when a subset of the experimental units in the population have been excluded so that these units have no chance of being selected in the sample.
LANDON IN A LANDSLIDE
In 1936 The Literary Digest predicts Governor Alf Landon of Kansas would defeat President Roosevelt with 57% of the popular vote and 370 electoral votes, the result of polling primarily affluent voters.
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

23. 1.6: The Role of Statistics in Critical Thinking
Nonresponse bias results when the researchers conducting a survey or study are unable to obtain data on all experimental units selected for the sample.
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking

24. 1.6: The Role of Statistics in Critical Thinking
Measurement error refers to inaccuracies in the values of the data recorded. In surveys, this kind of error may be due to ambiguous or leading questions and the interviewer’s effect on the respondent.
“Do you prefer Candidate X, father of three and decent family guy,
or Candidate Y, who got the nomination despite his shady past?”
McClave, Statistics, 11th ed. Chapter 1: Statistics, Data and Statistical Thinking