1. Slide Slide 1 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Lecture Slides Essentials of Statistics Third Edition by Mario F. Triola

2. Slide Slide 2 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Chapter 1 Introduction to Statistics 1-1 Overview 1-2 Types of Data 1-3 Critical Thinking 1-4 Design of Experiments

3. Slide Slide 3 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Created by Tom Wegleitner, Centreville, Virginia Section 1-1 Overview

4. Slide Slide 4 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Overview A common goal of studies and surveys and other data collecting tools is to collect data from a small part of a larger group so we can learn something about the larger group. In this section we will look at some of the ways to describe data.

5. Slide Slide 5 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Data observations (such as measurements, genders, survey responses) that have been collected Definition

6. Slide Slide 6 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Statistics a collection of methods for planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data Definition

7. Slide Slide 7 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Definition  Population the complete collection of all elements (scores, people, measurements, and so on) to be studied; the collection is complete in the sense that it includes all subjects to be studied

8. Slide Slide 8 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Definitions  Census Collection of data from every member of a population  Sample Subcollection of members selected from a population

9. Slide Slide 9 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Chapter Key Concepts  Sample data must be collected in an appropriate way, such as through a process of random selection.  If sample data are not collected in an appropriate way, the data may be so completely useless that no amount of statistical torturing can salvage them.

10. Slide Slide 10 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Created by Tom Wegleitner, Centreville, Virginia Section 1-2 Types of Data

11. Slide Slide 11 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Key Concept The subject of statistics is largely about using sample data to make inferences (or generalizations) about an entire population. It is essential to know and understand the definitions that follow.

12. Slide Slide 12 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Parameter a numerical measurement describing some characteristic of a population. population parameter Definition

13. Slide Slide 13 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Definition  Statistic a numerical measurement describing some characteristic of a sample. sample statistic

14. Slide Slide 14 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Definition  Quantitative data numbers representing counts or measurements. Example: The weights of supermodels

15. Slide Slide 15 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Definition  Qualitative (or categorical or attribute) data can be separated into different categories that are distinguished by some nonnumeric characteristic Example: The genders (male/female) of professional athletes

16. Slide Slide 16 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Working with Quantitative Data Quantitative data can further be described by distinguishing between discrete and continuous types.

17. Slide Slide 17 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Discrete data result when the number of possible values is either a finite number or a ‘countable’ number (i.e. the number of possible values is 0, 1, 2, 3,...) Example: The number of eggs that a hen lays Definition

18. Slide Slide 18 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps Definition Example: The amount of milk that a cow produces; e.g. 2.343115 gallons per day

19. Slide Slide 19 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Levels of Measurement Another way to classify data is to use levels of measurement. Four of these levels are discussed in the following slides.

20. Slide Slide 20 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Nominal level of measurement characterized by data that consist of names, labels, or categories only, and the data cannot be arranged in an ordering scheme (such as low to high) Example: Survey responses yes, no, undecided Definition

21. Slide Slide 21 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Ordinal level of measurement involves data that can be arranged in some order, but differences between data values either cannot be determined or are meaningless Example: Course grades A, B, C, D, or F Definition

22. Slide Slide 22 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Interval level of measurement like the ordinal level, with the additional property that the difference between any two data values is meaningful, however, there is no natural zero starting point (where none of the quantity is present) Example: Years 1000, 2000, 1776, and 1492 Definition

23. Slide Slide 23 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Ratio level of measurement the interval level with the additional property that there is also a natural zero starting point (where zero indicates that none of the quantity is present); for values at this level, differences and ratios are meaningful Example: Prices of college textbooks ($0 represents no cost) Definition

24. Slide Slide 24 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Summary - Levels of Measurement  Nominal - categories only  Ordinal - categories with some order  Interval - differences but no natural starting point  Ratio - differences and a natural starting point

25. Slide Slide 25 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Recap  Basic definitions and terms describing data  Parameters versus statistics  Types of data (quantitative and qualitative)  Levels of measurement In this section we have looked at:

26. Slide Slide 26 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Created by Tom Wegleitner, Centreville, Virginia Section 1-3 Critical Thinking

27. Slide Slide 27 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Key Concepts  Success in the introductory statistics course typically requires more common sense than mathematical expertise.  This section is designed to illustrate how common sense is used when we think critically about data and statistics.

28. Slide Slide 28 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Misuses of Statistics

29. Slide Slide 29 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Misuse # 1- Bad Samples  Voluntary response sample (or self-selected sample) one in which the respondents themselves decide whether to be included In this case, valid conclusions can be made only about the specific group of people who agree to participate.

30. Slide Slide 30 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Misuse # 2- Small Samples Conclusions should not be based on samples that are far too small. Example: Basing a school suspension rate on a sample of only three students

31. Slide Slide 31 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. To correctly interpret a graph, you must analyze the numerical information given in the graph, so as not to be misled by the graph’s shape. Misuse # 3- Graphs

32. Slide Slide 32 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Part (b) is designed to exaggerate the difference by increasing each dimension in proportion to the actual amounts of oil consumption. Misuse # 4- Pictographs

33. Slide Slide 33 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Misuse # 5- Percentages Misleading or unclear percentages are sometimes used. For example, if you take 100% of a quantity, you take it all. 110% of an effort does not make sense.

34. Slide Slide 34 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Loaded Questions  Order of Questions  Refusals  Correlation & Causality  Self Interest Study  Precise Numbers  Partial Pictures  Deliberate Distortions Other Misuses of Statistics

35. Slide Slide 35 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Recap  Reviewed 13 misuses of statistics  Illustrated how common sense can play a big role in interpreting data and statistics In this section we have:

36. Slide Slide 36 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Created by Tom Wegleitner, Centreville, Virginia Section 1-4 Design of Experiments

37. Slide Slide 37 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Key Concept  If sample data are not collected in an appropriate way, the data may be so completely useless that no amount of statistical tutoring can salvage them.

38. Slide Slide 38 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Observational study observing and measuring specific characteristics without attempting to modify the subjects being studied Definition

39. Slide Slide 39 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Experiment apply some treatment and then observe its effects on the subjects; (subjects in experiments are called experimental units) Definition

40. Slide Slide 40 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Cross sectional study data are observed, measured, and collected at one point in time  Retrospective (or case control) study data are collected from the past by going back in time  Prospective (or longitudinal or cohort) study data are collected in the future from groups (called cohorts) sharing common factors Definitions

41. Slide Slide 41 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Confounding occurs in an experiment when the experimenter is not able to distinguish between the effects of different factors Definition

42. Slide Slide 42 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Controlling Effects of Variables  Blinding subject does not know he or she is receiving a treatment or placebo  Blocks groups of subjects with similar characteristics  Completely Randomized Experimental Design subjects are put into blocks through a process of random selection  Rigorously Controlled Design subjects are very carefully chosen

43. Slide Slide 43 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Replication repetition of an experiment when there are enough subjects to recognize the differences from different treatments Replication and Sample Size  Sample Size use a sample size that is large enough to see the true nature of any effects and obtain that sample using an appropriate method, such as one based on randomness

44. Slide Slide 44 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Random Sample members of the population are selected in such a way that each individual member has an equal chance of being selected Definitions  Simple Random Sample (of size n ) subjects selected in such a way that every possible sample of the same size n has the same chance of being chosen

45. Slide Slide 45 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Random Sampling selection so that each individual member has an equal chance of being selected

46. Slide Slide 46 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Systematic Sampling Select some starting point and then select every k th element in the population

47. Slide Slide 47 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Convenience Sampling use results that are easy to get

48. Slide Slide 48 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Stratified Sampling subdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)

49. Slide Slide 49 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Cluster Sampling divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters

50. Slide Slide 50 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Random  Systematic  Convenience  Stratified  Cluster Methods of Sampling - Summary

51. Slide Slide 51 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.  Sampling error the difference between a sample result and the true population result; such an error results from chance sample fluctuations  Nonsampling error sample data incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly) Definitions

52. Slide Slide 52 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Recap In this section we have looked at:  Types of studies and experiments  Controlling the effects of variables  Randomization  Types of sampling  Sampling errors