Chapter One Getting Started

1. Understandable StatisticsSeventh EditionBy Brase and BrasePrepared by: Lynn SmithGloucester County College Chapter One Getting Started

2. Statistics is The study of how to: • collect • organize • analyze • interpret numerical information from data

3. Individuals and Variables • Individual: a person or object included in a study • Variable: a characteristic of the individual to be measured or observed

4. Quantitative and Qualitative Data • Quantitative variable has a value or numerical measurement • example: number of siblings • Qualitative variable places an individual in a category or group • example: brand of computer

5. Population Variable is taken from every individual of interest Example: incomes of all residents of a county

6. Sample Variable is taken from only some of the indiviuals Example: incomes of selected residents

7. Levels of Measurement • Nominal • Ordinal • Interval • Ratio

8. Nominal Measurement Data is put into categories only. Example: eye color

9. Ordinal Measurement Data can be ordered. Differences cannot be calculated or interpreted. Example: class rank

10. Interval Measurement Data can be ordered. Differences between data values can be compared. Example: temperature

11. Ratio Measurement Data can be ordered. Differences and ratios between data values can be compared. Example: time

12. Branches of Statistics • Descriptive: methods of organizing, picturing, and summarizing information • Inferential: methods of using information from a sample to draw conclusions regarding the population

13. Methods of Producing Data • Sampling: drawing subsets from the population • Experimentation: impose a change and measure the result • Simulation: numerical facsimile of real-world phenomena • Census: using measurements from entire population • Survey: asking questions

14. Simple Random Sample of n measurements: • every sample of size n has equal chance of being selected • every item in the population has equal chance of being included

15. Not random sampling: asking for volunteers to respond to a survey choosing the first five customers in a store

16. Random sampling: • drawing names “from a hat” • using a random number table to select sample • using a random number generator

17. Simulation • Provides arithmetic imitation of “real” phenomenon • Random number table may be used

18. Sampling with replacement The same number may be selected for a sample more than one time.

19. Other sampling techniques • Stratified Sampling • Systematic Sampling • Cluster Sampling • Convenience Sampling

20. Stratified Sampling Population is divided into groups (“strata”) Random samples are drawn from each group

21. Systematic Sampling Population is arranged in sequential order. Select a random starting point. Select every “kth” item.

22. Cluster Sampling Population is divided into sections Some sections are randomly selected Every item in selected sections is included in sample

23. Convenience Sampling Use whatever data is readily available. Risk severe bias.

24. Which sampling technique is described? College students are waiting in line for registration. Every eighth person in line is surveyed. Systematic sampling

25. Which sampling technique is described? College students are waiting in line for registration. Students are asked to volunteer to respond to a survey. Convenience sampling

26. Which sampling technique is described? In a large high school, students from every homeroom are randomly selected to participate in a survey Stratified sampling

27. Which sampling technique is described? An accountant uses a random number generator to select ten accounts for audit. Simple random sampling

28. Which sampling technique is described? To determine students’ opinions of a new registration method, a college randomly selects five majors. All students in the selected majors are surveyed. Cluster sampling

29. Experimental Design Statistical studies are used to obtain reliable information.

30. Planning a Statistical Study • Identify individuals or object of interest • Specify variables and protocols for observations • Decide whether to use a census or a sample and determine viable sampling method • Collect data • Make decisions • List concerns and recommendations

31. Census Measurements or observations from entire populations are used.

32. Sample Measurements or observations from a representative part of the population are used.

33. Simulation A numerical facsimile of real-world phenomena

34. Experiments and Observation • Observational Study: no change is made in the responses or variable being studied • Experiment: a treatment is imposed in order to observe a possible change in the response or variable being measured

35. Randomized two-treatment experiment • Subjects are randomly assigned to one of two groups • One group receives treatment under study • Control group receives placebo • Results are compared • Randomization prevents bias • Replication on many subjects assures changes not caused by random chance

36. Surveys Data is gathered by asking people questions.

37. Problems with data collection • Some individuals do not respond. • People with strong opinions may be over-represented in voluntary response samples. • There may be a hidden bias in the data collection process. • There may be hidden effects of other variables. • There is no guarantee that results can be generalized.