Chapter 1:Statistics: The Art and Science of Learning from Data

1. Chapter 1:Statistics: The Art and Science of Learning from Data 1.1: How Can You Investigate Using Data? 1.2: We Learn about Populations Using Samples 1.3: What Role Do Computers Play in Statistics?

2. Section 1.1 Learning Objectives How Can You Investigate Using Data? • Data and examples of collecting data • Define Statistics • Identify three aspects of a study

3. Learning Objective 1:Data • Data is information we gather with experiments and with surveys. • Example: Experiment on the 5:2 diet • Data could be measurements on subjects before and after the experiment • Example: Survey on effectiveness of a TV ad • Data could be percentage of people who went to Starbucks since the ad aired

4. Learning Objective 2:Define Statistics • Statistics is the art and science of: • Designing studies • Analyzing data • Translating data into knowledge and understanding

5. Learning Objective 3:Statistical Methods • Design: Planning how to obtain data • Description: Summarizing the data • Inference: Making decisions and predictions

6. Learning Objective 3:Examples of Design Statistics • Design questions: • How to conduct the experiment, or • How to select people for the survey to insure trustworthy results • Examples: • Planning the methods for data collection to study the effects of Vitamin E on athletic strength • For a marketing study, how do you select people for your survey to provide proper coverage

7. Learning Objective 3:Examples of Descriptive Statistics • Description: • Summarize the raw data and present it in a useful format (e.g., average, charts or graphs) • Examples: • A meteorologist constructs a graph showing the total precipitation in Bloomington, IL for each of the months of 2005. • The average age of the students in a statistics class is 25 years.

8. Learning Objective 3:Inference • Methods of making decisions or predictions about a populations based on information obtained from a sample.

9. Learning Objective 3:Examples of Inferential Statistics • Inference: Make decisions or predictions based on the data • Examples: • There is a relationship between smoking cigarettes and getting emphysema. • From past figures, it is predicted that 47% of the registered voters in Illinois will vote in the primary.

10. Section 1.2 Learning Objectives We Learn about Populations Using Samples • Subjects • Population and sample • Descriptive statistics and inferential statistics • Sample Statistics and Population Parameters • Randomness and Variability

11. Learning Objective 1:Subjects • Subjects • The entities that we measure in a study • Subjects could be individuals, schools, rats, counties, widgets

12. Learning Objective 2:Population and Samples • Population: All subjects of interest • Sample: Subset of the population for whom we have data Population Sample

13. Learning Objective 2:Example: The Sample and the Population for an Exit Poll • In California in 2003, a special election was held to consider whether Governor Gray Davis should be recalled from office. • An exit poll sampled 3160 of the 8 million people who voted. Define the sample and the population for this exit poll. • The population was the 8 million people who voted in the election. • The sample was the 3160 voters who were interviewed in the exit poll.

14. Learning Objective 3Descriptive vs. Inferential Statistics • Descriptive Statistics refers to methods for summarizing the data. Summaries consist of graphs and numbers such as averages and percentages • Inferential statistics refers to methods of making decisions or predictions about a population based on data obtained from a sample of that population.

15. Learning Objective 3:Descriptive Statistics Example Types of U.S. Households

16. Learning Objective 3:Inferential Statistics Example Calculating a confidence interval: • By surveying 1000 likely voters, we find a sample proportion of 39% who approve of the job President Bush is doing. • We are 95% confident that the population proportion of likely voters who approve of the job President Bush is doing is between 36% and 42%.

17. Learning Objective 4:Sample Statistics and Population Parameters • A parameter is a numerical summary of the population • Mean (µ) number of cigarettes smoked by all teenagers • Proportion (p) of all teenagers who smoked in the last month

18. Learning Objective 4:Sample Statistics and Population Parameters • A statistic is a numerical summary of a sample taken from the population • Mean number of cigarettes smoked per day by a sample of students • Proportion of a sample of students who smoked in the last month

19. Learning Objective 5:Randomness • Simple Random Sampling, SRS: Each subject in the population has the same chance of being included in the sample • Randomness is crucial to insuring that the sample is representative of the population so that powerful inferences can be made

20. Learning Objective 5:Variability • Measurements may vary from subject to subject, and • Measurements may vary from sample to sample Predictions will therefore be more accurate for larger samples.

21. Section 1.3What Role Do Computers Play in Statistics? • Using Technology • You, not technology, must select valid analyses • Data files • Large sets of data are typically organized in a spreadsheet format known as a data file • Each row contains measurements for a particular subject • Each column contains measurements for a particular characteristic • Databases • An existing archive collection of data files Sources should always be checked for reliability