Introduction to Sampling

1. Introduction to Sampling (Dr. Monticino)

2. Assignment Sheet • Read Chapter 19 carefully • Quiz # 10 over Chapter 19 • Assignment # 12 (Due Monday April 25th) • Chapter 19 • Exercise Set A: 1-6,8,11

3. Overview • Language of statistics • Obtaining a sample

4. Statistical Terms • Population • The whole class of individuals of interest • Voters • Customers • Marbles in a box • Parameter • Numerical facts about the population • Percentage who will vote for candidate A • Average income • Proportion of white marbles

5. Statistical Terms • Sample • Part of a population • 1000 eligible voters called at random • First 400 customers on Tuesday morning • 5 marbles drawn from the box with replacement • Statistic • Numerical value obtained from sample used to estimate population parameter

6. Sampling • Generally, determining population parameters by studying the whole population is impractical • Thus, inferences about population parameters are made from sample statistics • This requires that the sample represent the population

7. Sampling • To obtain a representative sample, probability methods are used • Employ an objective chance process to pick the sample • No discretion is left to the interviewer • The probability of any particular individual in the population being selected in the sample can be computed

8. Simple Random Sampling • Most straightforward sampling method is simple random sampling • Individuals in the sample are drawn at random from the population without replacement • Each individual is equally likely to be selected and each possible subset of individuals is equally likely to be selected • Care must be taken to ensure that the selection process is not biased

9. Other Sampling Techniques • Multi-stage cluster sampling

10. Other Sampling Techniques • Quota sampling • Sample is hand-picked to resemble the population with respect to selected key characteristics • Selection bias • Response/Non-response bias

11. Good and Bad Samples • Samples obtained by probability methods give a good representation of the population • In theory, simple random sampling gives best representation • Cluster samples, properly weighted, provide reasonable compromise between representing population and practical issues

12. Good and Bad Samples • Quota samples typically introduce selection and response/non-response bias • Samples of convenience rarely represent the population. Avoid these • When a sampling procedure is biased, taking a larger sample does not help

13. Good and Bad Samples • When examining a sample survey, ask: • What is the population? • What is the parameter being estimated? • How was the sample chosen? • What was the response rate? • Address these same questions when designing a sampling procedure

14. Sampling Error • Even a well designed sampling procedure may result in an estimate which differs from the true value of the population parameter • Bias • Chance error • It is important to have a measure of the sampling error of the parameter estimate (Dr. Monticino)