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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
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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.
