Unit 8: Sample Surveys

Transcription

1 Unit 8: Sample Surveys Marius Ionescu 10/27/2011 Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

2 Chapter 19: Surveys Why take a survey? Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

3 Chapter 19: Surveys Why take a survey? The investigators want to estimate a trait of some population. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

4 Surveys Denition Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

5 Surveys Denition A parameter is a numerical fact about a population; usually it can only be estimated! Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

6 Surveys Denition A parameter is a numerical fact about a population; usually it can only be estimated! A sample is part of a population. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

7 Surveys Denition A parameter is a numerical fact about a population; usually it can only be estimated! A sample is part of a population. A statistic can be computed from a sample and is used to estimate a parameter. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

8 Example Example With a sample of 500 people who live in Hamilton, one could calculate the following statistics: The average age of all people The percentage of students among all people living in Hamilton The percentage of all eligible voters The percentage of all eligible voters who are currently registered to vote. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

9 Estimated parameter ` Estimated parameter (statistic) = actual parameter + bias in measurement + chance error Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

10 Example Example (Polls) Important examples: taking a poll to predict election results. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

11 Example Example (Polls) Important examples: taking a poll to predict election results. the population is the people who vote on election day Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

12 Example Example (Polls) Important examples: taking a poll to predict election results. the population is the people who vote on election day the parameter is the % of people voting for each candidate Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

13 Example Example (Polls) Important examples: taking a poll to predict election results. the population is the people who vote on election day the parameter is the % of people voting for each candidate Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

14 Example Example (Polls) Important examples: taking a poll to predict election results. the population is the people who vote on election day the parameter is the % of people voting for each candidate Gallup takes a sample of the population and estimates the parameter. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

15 Potential Problems Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

16 Potential Problems Selection bias: a systematic tendency on the part of the sampling procedure to exclude one kid of person or another from the sample. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

17 Potential Problems Selection bias: a systematic tendency on the part of the sampling procedure to exclude one kid of person or another from the sample. Non-response bias: Non-respondents can be very dierent from respondents. When there is a high non-response rate, look out for non-response bias. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

18 Potential Problems Selection bias: a systematic tendency on the part of the sampling procedure to exclude one kid of person or another from the sample. Non-response bias: Non-respondents can be very dierent from respondents. When there is a high non-response rate, look out for non-response bias. Survey bias Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

19 Potential Problems Selection bias: a systematic tendency on the part of the sampling procedure to exclude one kid of person or another from the sample. Non-response bias: Non-respondents can be very dierent from respondents. When there is a high non-response rate, look out for non-response bias. Survey bias Wording of questions Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

20 Reducing the error Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

21 Reducing the error Large samples can reduce the spread of the error; Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

22 Reducing the error Large samples can reduce the spread of the error; They will not reduce, however, the bias! Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

23 Reducing the error Large samples can reduce the spread of the error; They will not reduce, however, the bias! When a selection procedure is biased, taking a large sample does not help. This just repeats the basic mistake on a larger scale. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

24 How do we select? 1 Quota sampling Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

25 How do we select? 1 Quota sampling 2 Probability methods Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

26 Quota sampling Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

27 Quota sampling In quota sampling, the sample is hand-picked to resemble the population with respect to some key characteristics. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

28 Quota sampling In quota sampling, the sample is hand-picked to resemble the population with respect to some key characteristics. The method seems reasonable, but does not work very well. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

29 Quota sampling In quota sampling, the sample is hand-picked to resemble the population with respect to some key characteristics. The method seems reasonable, but does not work very well. The reason is unintentional bias on the part of the interviewers. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

30 Using chance in survey work Simple random sampling means drawing at random without replacement. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

31 Probabilistic methods The interviewers have no discretion at all as to whom they interview There is a denite procedure for selecting the sample, and it involves the planned use of chance. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

32 Questions Example Polls are often taken by telephone. Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

33 Questions Example Polls are often taken by telephone. Could this bias the result? How? Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13

34 Questions Example Polls are often taken by telephone. Could this bias the result? How? What if the sample is drawn from the telephone book? Marius Ionescu () Unit 8: Sample Surveys 10/27/ / 13