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Section 2-1 Samples, Good and Bad

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Remember: We select a sample in order to get information about some population (entire group of individuals about which we want information) Read Pg. 63 Town Talk: Why isn’t this a good way to get a sample?

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Bad Samples Bias in sampling is bad The design of a statistical study is biased if it systematically favors certain outcomes Biased sampling generally results in samples that are not representative of their corresponding populations

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Voluntary Response Sample People choose whether to respond. Attracts people who feel strongly about an issue in question. It may not represent the opinions of the entire population. Bias refers to the tendency of a sample statistic to systematically over- or under-estimate a population

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Voluntary Response - Example Write in or call in opinion polls—only about 15% of the public has ever responded to a call-in poll which is not a representation of the population as a whole Talk Town –allowed people to call in rather than actively selecting its own sample therefore the result was biased - the sample was over weighted with people favoring the ambulance monopoly.

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Convenience Sample The selection of whichever individuals are easiest to reach Interviewer chooses sample People tend to pick neat, safe-looking individuals to select Sometimes a convenience sample may be drawn from telephone directories and car registration lists. In 1936, people who owned cars and telephones tended to be more affluent. Undercoverage is often a problem with convenience samples.

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Convenience Sample - Example Interviewing your friends to find out what school lunch entre is preferred, mall interviews may only target the rich/teenagers/retired people, people tend to pick neat, safe-looking individuals from the stream of customers

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Nonresponse Bias Sometimes individuals chosen for the sample are unwilling or unable to participate in the survey. The bias that results when respondents differ in meaningful ways from nonrespondents. Since only 25% of the sampled voters actually completed the mail-in survey, survey results overestimated voter support for….

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Good Samples Random sampling is a procedure for sampling from a population in which: The selection of a sample unit is based on chance. Every element of the population has a known, non-zero probability of being selected. Random sampling helps produce representative samples by eliminating voluntary response bias and guarding against undercoverage bias. All probability sampling methods rely on random sampling.

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Simple Random Sample (SRS) Consists of a group individuals from the population chosen in such a way that every individual and every mixture group has an equal chance to be in the sample actually chosen. It is a sample chosen by chance which avoiding bias.

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Example – SRS It is like putting names in a hat (population) and drawing out a handful (sample) Write 100 names and put in a hat and pick 10…this is an SRS because any ten slips have the same chance of being chosen. However, using a hat is often impractical so we use computer generated random digits to choose samples.

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Random Digits Table A table of random digits is a long string of the digits 0,1…9 Each entry is equally likely to be any of the 10 digits. Entries are independent of one another. Knowledge of 1 part of the table gives no information about any other part

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How to Choose an SRS LABEL - assign a numerical label to every individual Your goal is to use the shortest possible labels 1 digit for population up to 10 members(1-9) 2 digits for population for 11-100 members(01-99) 3 digits for population for 101-1000 members etc… (001-999) Recommend starting with 1, 01, or 001 (but can start with 0, 00 or 000)

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Select 5 Students from Statistics Class to be part of a sample survey Step 1: Label 18 students in alphabetical order. Then use 2 digits 01, 02,…19 (can use 00,…18) Will depend upon the size of the population Step 2: Use Table - can enter the table anywhere Use line 104 52, 71, 13, 88, 89, 93, 07, 46, 02, 27, 40, 01, 18 Answer: Sample is composed of students numbered 13, 07, 02, 01 and 18.

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Is this an SRS? Assume there are 10 boys and 10 girls Flip a coin: heads gives all girls, tails gives all boys Is this an SRS? No, because we can never get a mix of both girls and boys, so there is a 0% chance of ever getting a mixture of boys and girls.

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Classwork/Homework 1. Pg. 67-68 #1-4 3. Pg. 74-75 # 7-11

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