Chapter 1

1. Chapter 1 Statistics, Data, and Statistical Thinking

2. The Science of Statistics • Statistics – the science of data. • This involves collection, evaluation, and interpretationof numerical information.

3. Types of Statistical Applications • Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data. • Statistical inference is the process of using data obtained from a small group of elements (the sample) to make estimates and test hypotheses about the characteristics of a larger group of elements (the population).

4. Types of Statistical Applications • Descriptive Statistics - describe collected data “Nearly 87% of players participating ina Speed Training Program improved their sprint times.” “Only about 3% of players participating in a Speed Training Program had decreased times.”

5. Types of Statistical Applications • Inferential Statistics - make generalizations about a group based on a subset (sample) of that group “Based on exit polls, more people voted for Candidate A.”

6. Fundamental Elements of Statistics • Experimental Unit – object of interest Example: Graduating senior • Population – the set of units we are interested in learning about Example: All 1450 graduating seniors at “State U” • Variable – characteristic of an individual population unit Example: Age at graduation

7. Fundamental Elements of Statistics • Sample – subset of population Example: 100 graduating seniors at “State U” • Statistical Inference – generalization about a population based on sample data Example: The average age at graduation is 21.9 (based on sample of 100) • Measure of reliability – statement about the uncertainty associated with an inference

8. Fundamental Elements of Statistics • Elements of Descriptive Statistical Problems • population/sample of interest • investigative variables • numerical summary tools (charts, graphs, tables) • pattern identification in data

9. Fundamental Elements of Statistics • Elements of Inferential Statistical Problems • population of interest • investigative variables • sample taken from population • inference about population based on sample data • reliability measure for the inference

10. Fundamental Elements of Statistics:Example • “Cola wars” is the popular term for the intense competition between Coca-Cola and Pepsi. Their marketing campaigns have featured movie stars, rock videos, athletic endorsements, and claims of consumer preference based on taste tests. Suppose, as part of a Pepsi marketing campaign, 1000 cola consumers are given a blind taste test. Each consumer is asked to state a preference for brand A or brand B.

11. Fundamental Elements of StatisticsExample (continued) Identify the following: • Describe the population. • Describe the variable of interest. • Describe the sample. • Describe the inference.

12. Types of Data • Data can be classified as being qualitative or quantitative. • The statistical analysis that is appropriate depends on whether the data for the variable are qualitative or quantitative. • In general, there are more alternatives for statistical analysis when the data are quantitative.

13. Types of Data • Quantitative Data • indicate either how many or how much • measured on a naturally occurring scale • quantitative data are always numeric • ordinary arithmetic operations are meaningful only with quantitative data

14. Types of Data • Qualitative Data • measured by classification only • non-numerical in nature • meaningfully ordered categories identify ordinal data (best to worst ranking, age categories) • categories without a meaningful order identify nominal data (political affiliation, industry classification, ethnic/cultural groups)

15. Types of DataExample • Classify the following examples of data as either qualitative or quantitative: a. The bacteria count in the water at each of 30 city swimming pools b. The occupation of each of 200 shoppers at a supermarket c. The martial status of each person living on a city block d. The time (in months) between auto maintenance for each of 100 used cars

16. Collecting Data • Data Sources • Published source (books, journals, abstracts) • Primary vs. secondary • Designed Experiment • Often used for gathering information about an intervention • Survey • Data gathered through questions from a sample of people • Observational Study • Data gathered through observation, no interaction with units

17. Collecting Data • Sampling • Sampling is necessary if inferential statistics are to be used • Samples need to be representative • Random Sampling • Most common sampling method to ensure sample is representative • Ensures that each subset of fixed size is equally likely to be selected

18. The Role of Statistics in Critical Thinking • Statistical literacy is necessary today to make informed decisions both at work and at home. • Requires statisticalthinking to critically assess data and the inferences drawn from it. • Statistical thinking assists you in identifying research resulting from unethical statistical practices.

19. The Role of Statistics in Critical Thinking • Common Sources of Error in Survey Data: • Selection bias – exclusion of a subset of the population of interest prior to sampling • Non-response bias – introduced when responses are not gotten from all sample members • Measurement error – inaccuracy in recorded data. Can be due to survey design, interviewer impact, or a transcription error