Introduction to Sampling (Dr. Monticino)

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

Overview  Language of statistics  Obtaining a sample

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

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

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

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

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

Other Sampling Techniques  Multi-stage cluster sampling

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

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

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

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

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)