Chapter One Getting Started

1. Understandable StatisticsEighth 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 • Individuals: the people or objects included in the study • Variable: the characteristic of the individual to be measured or observed

4. Quantitative and Qualitative Data • Quantitative variable has a value or numerical measurement • example: height • Qualitative variable places an individual in a category or group • example: gender

5. Population Variable is taken from every individual of interest Example: the data from all individuals who have climbed Mt. Everest

6. Sample Variable is taken from only some of the individuals of interest Example: the data from just some of the climbers of Mt. Everest

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

8. Nominal Measurement Applies to data that consists of names, labels or categories. Example: names of ski resorts

9. Ordinal Measurement Data that may be arranged in order. Differences between data values either cannot be determined or are meaningless. Example: class rank

10. Interval Measurement Data that can be arranged in order. Differences between data values are meaningful. Example: body temperature

11. Ratio Measurement Data that can be arranged in order. Differences between data values and ratios of data values are meaningful. Example: temperature in degrees Kelvin

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. Simple Random Sample of n measurements are selected in a manner such that: • every sample of size n has equal chance of being selected • every member of the population has an equal chance of being included

14. Random sampling: • drawing cards “from a hat” • using a random-number table to select a sample • using a random-number generator

15. Example 1 of using a random number table We want to choose a random sample of 8 shirts out of a shipment of 300. We drop a pin on a random number table on page A13 and it falls on Column 3 row 15. Since we have 300 shirts we regroup the digits into groups of three. The digits are: 275, 924, 208, 999, 281, 596, 401, 522, 196, 079, 099, 610, 537, 129, 553, 184, ... The shirts we use in our sample are: 275, 208, 281, 196, 79, 99, 129, 184.

16. Example 2 using a random number table We want to use a random number table to simulate rolling a die 10 times. We drop a pin on the random number table and it lands on column 7 row 3. Since a die has numbers 1 through 6, we will use single digits as our possible rolls. The numbers from the table are: 2, 9, 2, 8, 1, 1, 8, 5, 4, 4, 5, 2, 4, ... The simulated outcomes are 2, 2, 1, 1, 5, 4, 4, 5, 2, 4.

17. Simulation • A numerical facsimile or representation of a real-world phenomenon • Random-number table may be used

18. Sampling with replacement A number that is selected for the sample is not removed from the population.

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

20. Stratified Sampling Groups or classes inside a population that share a common characteristic (“strata”) Random samples are drawn from each stratum

21. Systematic Sampling Members of the population are sequentially numbered. Select a random starting point. Select every “kth” item.

22. Cluster Sampling Population is divided into pre-existing clusters Some clusters are randomly selected Every member in selected sections is included in the sample

23. Convenience Sampling Use whatever data is readily available. Risk of being 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.