1. Section 4.1
Why Take Samples and

2. Why Take Samples and How Not To
Section 4.1
Why Take Samples and How Not To

3. Read Activity 4.1a on pages 220 – 222 before class tomorrow
Time in the Hospital
Read Activity 4.1a on pages 220 – 222 before class tomorrow

4. Population: set of people or things that you want to know something about.
Population changes depending on your particular interest

5. Population Changes
Issue Population
Presidential election ??

6. Population Changes Issue Population
Presidential election US citizens 18 & ↑

7. Population Changes Issue Population
Presidential election US citizens 18 & ↑
Gubernatorial election ??

8. Population Changes Issue Population
Presidential election US citizens 18 & ↑
Gubernatorial election state citizens 18 & ↑

9. Population Changes Issue Population
Presidential election US citizens 18 & ↑
Gubernatorial election state citizens 18 & ↑
Senior class election ??

10. Population Changes Issue Population
Presidential election US citizens 18 & ↑
Gubernatorial election state citizens 18 & ↑
Senior class election all seniors

11. Population Changes Issue Population
Presidential election US citizens 18 & ↑
Gubernatorial election state citizens 18 & ↑
Senior class election all seniors
Food for our class party ??

12. Population Changes Issue Population
Presidential election US citizens 18 & ↑
Gubernatorial election state citizens 18 & ↑
Senior class election all seniors
Food for our class party members of this class

13. Units are the individual elements of the population

14. Units are the individual elements of the population
Population size is the number of units

15. Census
What is a census?

16. Census
Census: when we collect data on the entire population

17. Census Census: when we collect data on the entire population
Often times, we can’t get data from whole population so we use a subset called a sample.
Sample is set of units you study

18. Parameter is the characteristic of the population in which we are interested
Examples: population mean, population standard deviation

19. Statistic is a numerical summary of the sample
Parameter is the characteristic of the population we are interested in
Examples: population mean, population standard deviation
Statistic is a numerical summary of the sample
Examples: sample mean, sample standard deviation

20. Why take a sample?
Taking a census would give us an accurate representation of the population’s characteristic in which we are interested
Why would we ever take a sample of the population rather than always using a census?

21. Why take a sample? Consider the following situations:
1) determining ratings for TV shows
2) who is favored to win an election
3) tensile strength of steel bars
4) quality control of chocolate chip cookies

22. Why take a sample? 1) 2) 3) 4)

23. Why take a sample?
1) sampling can save time 2) 3) 4)

24. Why take a sample? 1) sampling can save time
2) sampling can save money 3) 4)

25. Why take a sample? 1) sampling can save time
2) sampling can save money
3) testing sometimes destroys items 4)

26. Why take a sample? 1) sampling can save time
2) sampling can save money
3) testing sometimes destroys items
4) sampling can make it possible to collect more or better information on each unit

27. Page 220, D1

28. Page 220, D1 a. Census. Each new car is inspected.
This procedure is used because every
customer expects his or her new car to be
perfect.
Also, if a safety-related problem gets by in
even one car, the cost is high.

29. Page 220, D1 b. Sampling. Counting the chocolate chips in a cookie is
destructive, and counting all the chips in
every cookie is time-consuming.

30. Page 220, D1
c. Sampling.
Theoretically, elections in the United States
are a census of eligible voters, but because
not everyone who is eligible actually votes,
elections are in practice a nonrandom
sample.

31. Page 220, D1 d. Sampling. Not every movie theater owner reports ticket
sales every weekend.

32. Page 220, D1 e. Sampling. With thousands of teachers in the
Los Angeles area, it would be too
time-consuming and expensive to do
in-depth interviews with all of them.
Sampling also makes it possible to collect
more or better information from teachers
interviewed.

33. Samples Trustworthy?
Recall, we use samples to learn something about a population

34. Samples Trustworthy?
Recall, we use samples to learn something about a population
Good sample is representative, that is, it looks like a small version of the population

35. Samples Trustworthy?
Recall, we use samples to learn something about a population
Good sample is representative, that is, it looks like a small version of the population
Some samples are more trustworthy (representative of the population) than others.

36. 2 ways to get untrustworthy sample
(1) bias in way sample is selected

37. 2 ways to get untrustworthy sample
(1) bias in way sample is selected
(2) bias in way you get a response from units in your sample

38. Bias
A biased person unreasonably favors one point of view over another
Biased opinion is not objective, or not balanced
In statistics, a biased sampling method is unbalanced

39. Danger of Biased Sampling
Biased sampling method produces samples such that the estimate from the sample, or statistic, is larger or smaller on average than the population parameter being estimated

40. Biased vs Nonrepresentative
Bias is a property of sampling method
Nonrepresentative is a property of a specific sample

41. Biased vs Nonrepresentative
Bias is a property of sampling method
Nonrepresentative is a property of a specific sample
You can not tell if a sample is nonrepresentative, but you can tell if a sampling method is biased

42. Page 223, D3

43. Page 223, D3
All are possible.
An unbiased sample-selection method will result in
some samples that are representative and some
that are not.
A biased selection method produces samples
where the estimate from the sample is too large or
too small on average.
But some samples are likely to have estimates that
are about right.

44. Sample selection bias is present in a sampling method if samples tend to result in estimates of population parameters that systematically are too high or too low

45. Types of Bias
Size bias: method that gives larger units a greater chance of being in the sample
Using map to select farms to sample
Different sizes of slips of paper

47. Types of Bias
Volunteer sample: those who care about the issue will be overrepresented, those who don’t care as much may not be represented at all
Polling radio station listeners
Town Hall meeting on recycling

48. Types of Bias
Convenience sample: units chosen are those that are easy to include
“ask your friends”
Your 1st quarter project

49. Types of Bias
Judgment sample: rely on judgment of an expert to choose a sample that he or she considers representative
Experts may overlook important feature of a population
Example: presidential election: Truman vs Dewey

50. Unbiased Sampling Method
Requires all units in population have a known chance of being selected

51. Unbiased Sampling Method
Requires all units in population have a known chance of being selected
Notice this says a known chance of being selected, not necessarily an equal chance of being selected

52. Unbiased Sampling Method
Requires all units in population have a known chance of being selected
You must prepare a “list” of population units called a sampling frame or frame, from which you select the sample

53. More Bias - - Not just from Method
Bias can also occur in the responses from the sample

54. Nonresponse bias: not uncommon for 40% of the people contacted to refuse to answer a survey

55. Questionnaire bias: arises from how the question is asked
Bias can result from tone of voice of interviewer, appearance of interviewer, the order in which questions are asked, and other factors
Most important source of questionnaire bias is _______?

56. Most important source of questionnaire bias is the wording of the question.
Those who report the results of a survey should always include the exact wording of the question.

57. Incorrect responses:
(a) people lying or responding in a way they think the interviewer wants them to respond

58. Incorrect responses:
(a) people lying or responding in a way they think the interviewer wants them to respond
(b) more likely to come from inaccurate measuring devices including inaccurate memories of people interviewed in self- reported data

59. Questions?