Producing Data: Sampling

Transcription

1 Producing Data: Sampling Math 667 Al Nosedal Department of Mathematics Indiana University of Pennsylvania Producing Data: Sampling p. 1/1

2 Observation vs Experiment An observational study observes individuals and measures variables of interest but does not attempt to influence the responses. Producing Data: Sampling p. 2/1

3 Observation vs Experiment An observational study observes individuals and measures variables of interest but does not attempt to influence the responses. An experiment, on the other hand, deliberately imposes some treatment on individuals in order to observe their responses. Producing Data: Sampling p. 2/1

4 Population and Sample The entire group of individuals that we want information about is called the population. Producing Data: Sampling p. 3/1

5 Population and Sample The entire group of individuals that we want information about is called the population. A sample is a part of the population that we actually examine in order to gather information. Producing Data: Sampling p. 3/1

6 Population and Sample The entire group of individuals that we want information about is called the population. A sample is a part of the population that we actually examine in order to gather information. Producing Data: Sampling p. 3/1

7 Voluntary Response Sample A voluntary response sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples are biased because people with strong opinions, especially negative opinions, are most likely to respond. Producing Data: Sampling p. 4/1

8 Voluntary Response Sample A voluntary response sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples are biased because people with strong opinions, especially negative opinions, are most likely to respond. Voluntary response is one common type of bad sample design. Another is convenience sampling which chooses the individuals easiest to reach. Producing Data: Sampling p. 4/1

9 Voluntary Response Sample A voluntary response sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples are biased because people with strong opinions, especially negative opinions, are most likely to respond. Voluntary response is one common type of bad sample design. Another is convenience sampling which chooses the individuals easiest to reach. Producing Data: Sampling p. 4/1

10 Interviewing at the mall Manufacturers and advertising agencies often use interviews at shopping malls to gather information about the habits of consumers and the effectiveness of ads. A sample of mall shoppers is fast and cheap. But people contacted at shopping malls are not representative of the entire U.S. population. They are richer, for example, and more likely to be teenagers or retired. Moreover, mall interviewers tend to select neat, safe-looking individuals from the stream of customers. Decisions based on mall interviews may not reflect the preferences of all consumers. Producing Data: Sampling p. 5/1

11 Bias Samples chosen by either voluntary response or convenience sampling are almost guaranteed not to represent the entire population. These sampling methods display bias, or systematic error, in favoring some parts of the population over others. Producing Data: Sampling p. 6/1

12 Bias Samples chosen by either voluntary response or convenience sampling are almost guaranteed not to represent the entire population. These sampling methods display bias, or systematic error, in favoring some parts of the population over others. Bias. The design of a study is biased if it systematically favors certain outcomes. Producing Data: Sampling p. 6/1

13 Bias Samples chosen by either voluntary response or convenience sampling are almost guaranteed not to represent the entire population. These sampling methods display bias, or systematic error, in favoring some parts of the population over others. Bias. The design of a study is biased if it systematically favors certain outcomes. Producing Data: Sampling p. 6/1

14 Simple Random Sample A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. Producing Data: Sampling p. 7/1

15 Choosing an SRS Step 1. Label. Assign a numerical label to every individual in the population. Producing Data: Sampling p. 8/1

16 Choosing an SRS Step 1. Label. Assign a numerical label to every individual in the population. Step 2. Table or Computer. Use a table of random digits or a computer program to select labels at random. Producing Data: Sampling p. 8/1

17 Choosing an SRS Step 1. Label. Assign a numerical label to every individual in the population. Step 2. Table or Computer. Use a table of random digits or a computer program to select labels at random. Producing Data: Sampling p. 8/1

18 Stratified Random Sample To select a stratified random sample, first divide the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRS s to form the full sample. Producing Data: Sampling p. 9/1

19 Cautions about sample surveys Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Producing Data: Sampling p. 10/1

20 Cautions about sample surveys Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Nonresponse occurs when an individual chosen for the sample can t be contacted or refuses to cooperate. Producing Data: Sampling p. 10/1

21 Cautions about sample surveys Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Nonresponse occurs when an individual chosen for the sample can t be contacted or refuses to cooperate. Producing Data: Sampling p. 10/1

22 Cautions about sample surveys Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Nonresponse occurs when an individual chosen for the sample can t be contacted or refuses to cooperate. Producing Data: Sampling p. 10/1

23 Cautions about sample surveys Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Nonresponse occurs when an individual chosen for the sample can t be contacted or refuses to cooperate. Producing Data: Sampling p. 10/1

24 Cautions about sample surveys In addition, the behavior of the respondent or of the interviewer can cause response bias in sample results. Respondents may lie, especially if asked about illegal or unpopular behavior. The sample then underestimates the presence of such behavior in the population. Producing Data: Sampling p. 11/1

25 Cautions about sample surveys In addition, the behavior of the respondent or of the interviewer can cause response bias in sample results. Respondents may lie, especially if asked about illegal or unpopular behavior. The sample then underestimates the presence of such behavior in the population. An interviewer whose attitudes suggests that some answers are more desirable than others will get these answers more often. Producing Data: Sampling p. 11/1

26 Cautions about sample surveys In addition, the behavior of the respondent or of the interviewer can cause response bias in sample results. Respondents may lie, especially if asked about illegal or unpopular behavior. The sample then underestimates the presence of such behavior in the population. An interviewer whose attitudes suggests that some answers are more desirable than others will get these answers more often. Producing Data: Sampling p. 11/1

27 Cautions about sample surveys The race or sex of the interviewer can influence responses to questions about race relations or attitudes toward feminism. Producing Data: Sampling p. 12/1

28 Cautions about sample surveys The race or sex of the interviewer can influence responses to questions about race relations or attitudes toward feminism. Careful training of interviewers and careful supervision to avoid variation among the interviewers can greatly reduce response bias. Producing Data: Sampling p. 12/1

29 Cautions about sample surveys The race or sex of the interviewer can influence responses to questions about race relations or attitudes toward feminism. Careful training of interviewers and careful supervision to avoid variation among the interviewers can greatly reduce response bias. Producing Data: Sampling p. 12/1

30 Wording effects The wording of questions is the most important influence on the answers given to a sample survey. Confusing or leading questions can introduce strong bias, and even minor changes in wording can change a survey s outcome. Producing Data: Sampling p. 13/1

31 Example: Help the poor? How do Americans feel about government help for the poor? Only 13% think we are spending too much on "assistance to the poor", but 44% think we are spending too much on "welfare". Producing Data: Sampling p. 14/1

32 THANK YOU!!! Producing Data: Sampling p. 15/1