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Chapter 4 Gathering Data

Chapter 4 Gathering Data. Section 4.2 Good and Poor Ways to Sample. Sampling Frame and Sampling Design. The sampling frame is the list of subjects in the population from which the sample is taken, ideally it lists the entire population of interest.

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Chapter 4 Gathering Data

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  1. Chapter 4Gathering Data Section 4.2 Good and Poor Ways to Sample

  2. Sampling Frame and Sampling Design • The sampling frame is the list of subjects in the population from which the sample is taken, ideally it lists the entire population of interest. • The sampling design determines how the sample is selected.

  3. Simple Random Sampling, (SRS) • Random Sampling is the best way of obtaining a sample that is representative of the population. • A simple random sample of ‘n’ subjects from a population is one in which each possible sample of that size has the same chance of being selected. • A simple random sample is often just called a random sample. The “simple” adjective distinguishes this type of sampling from more complex random sampling designs presented in Section 4.4.

  4. SRS Example: Drawing Prize Winners • A campus club decides to raise money for a local charity by selling tickets. • * The Athletic Department has donated 2 pairs of football season tickets as • prizes. • * The group of 60 individuals who purchased tickets to the banquet • comprises the population. • Partial List of Possible Samples: • (1,2), (1,3), (1,4), . . . , (1,58), (1,59), (1,60) • (2,3), (2,4), . . . , (2,58), (2,59), (2,60) • Etc… • Questions: • What is the chance that a particular sample of size 2 will be drawn? • Professor Shaffer is in attendance at the banquet and holds entry number 1. What is the chance that her entry will be chosen?

  5. SRS: Table of Random Numbers Table 4.1 A Portion of a Table of Random Numbers

  6. SUMMARY: Using Random Numbers to select a SRS • To select a simple random sample: • number the subjects in the sampling frame using numbers of the same length (number of digits). • select numbers of that length from a table of random numbers or using a random number generator. • include in the sample those subjects having numbers equal to the random numbers selected.

  7. Accuracy of the Results from Surveys with Random Sampling • Sample surveys are commonly used to estimate population percentages. • These estimates include a Margin of Error which tells us how well the sample estimate predicts the population percentage. • When a SRS of n subjects is used, the margin of error is approximately equal to

  8. Accuracy of the Results from Surveys with Random Sampling • A survey result states: “The margin of error is plus or minus 3 percentage points”. • This means: “It is very likely that the reported sample percentage is no more than 3% lower or 3% higher than the population percentage”.

  9. SUMMARY: Types of Bias in Sample Surveys • Bias: When certain outcomes will occur more often in the sample than they do in the population. • Sampling bias occurs from using nonrandom samples or • having undercoverage. • Nonresponse bias occurs when some sampled subjects • cannot be reached or refuse to participate or fail to answer • some questions. • Response bias occurs when the subject gives an incorrect • response (perhaps lying) or the way the interviewer asks the • questions (or wording of a question in print) is confusing or • misleading. • A Large Sample Does Not Guarantee An Unbiased Sample!

  10. Poor Ways to Sample • Convenience Sample: a type of survey sample that is easy to obtain. • Unlikely to be representative of the population. • Often severe biases result from such a sample. • Results apply ONLY to the observed subjects.

  11. Poor Ways to Sample • Volunteer Sample: most common form of convenience sample. • Subjects volunteer for the sample. • Volunteers do not tend to be representative of the entire population.

  12. SUMMARY: Key Parts of a Sample Survey • Identify the population of all subjects of interest. • Construct a sampling frame which attempts to list all subjects in the population. • Use a random sampling design to select n subjects from the sampling frame. • Be cautious of sampling bias due to nonrandom samples (such as volunteer samples) and sample undercoverage, response bias from subjects not giving their true response or from poorly worded questions, and nonresponse bias from refusal of subjects to participate. • We can make inferences about the population of interest when • sample surveys that use random sampling are employed.

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