Chapter 2: Samples, Good and Bad
This chapter explores the implications of biased sampling designs, including convenience and voluntary response samples, which can skew results. It emphasizes the importance of using Simple Random Sampling (SRS), ensuring that every individual has an equal chance of selection to produce unbiased estimates of population parameters. The chapter outlines steps for conducting an SRS, highlights the concept of parameters vs. statistics, and discusses errors in estimation, including bias and variability. Adopting good sampling methods minimizes bias and variability, resulting in more reliable data.
Chapter 2: Samples, Good and Bad
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Presentation Transcript
Chapter 2: Samples, Good and Bad • Biased design: Systematically favors certain outcomes. (p. 20) • Sampling designs that are often biased: Convenience sample: Selects whichever individuals are easiest to reach. (p. 20) Example: Interviewing people going into the library Voluntary response sample: Chooses itself by responding to a general appeal. (p. 20) Examples: Write-in, call-in, Internet opinion polls
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 the same chance of being selected. • A SRS may be selected using random digits • Random digits (p. 22): A long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with these two properties: • Each entry is equally likely to be any of the digits 0 through 9. • The entries are independent of each other. That is, knowledge of one part of the table gives no information about any other part.
Choosing an SRS • Step 1: Label. Assign a numerical label to every individual in the population (sampling frame). All labels must have the same number of digits. • Step 2: Table. Use the random number table to select labels at random. Table A, pp. 545-546 • Example: Consider this class as a population. There are N = 128 students. We wish to select a sample of 5 students. Everyone has a three-digit number from my alphabetized class roll (001to 128). Start at Line 113 and select a sample of 5 students.
Chapter 3: What Do Samples Tell Us? • Parameter: A number that describes a population; it is a fixed number, but we usually do not know its value. (31) • Statistic: A number that describes a sample; its value is computed from sample information, but it can change from sample to sample. (31)
Errors in Estimation • We wish to estimate a parameter from a statistic. • Bias: Consistent, repeated deviation of the sample statistic from the population parameter in the same direction when we take many samples. (34) • Variability: Describes how spread out the values of the sample statistic are when we take many samples. (34) • A good sampling method has both small bias and small variability. • To reduce bias: Use random sampling. Produces unbiased estimates of the parameter. • To reduce variability of an SRS: Use a larger sample.
