Chapter 12: Sample Surveys
Key Vocabulary:
population- A large group of individuals usually impractical to measure.
sample- A smaller group of individuals selected from a population.
sample survey- a study that asks questions of a sample drawn from some population in the hope of learning something about the entire population.
biased- a sample that does not represent the population in some way, it overlooks an important group.
randomization- Each individual is given a fair, random chance of selection. The best defense against bias is randomization.
census-a sample that consists of the entire population.
parameter- The numbers in the model that have to be chosen to explicitly determine the value of the model.
statistic-any summary found from the data
Simple Random Sample (SRS)- each combination of people has an equal chance of being selected. This is what we measure all other sampling methods against and what we hope every sampling method is achieving.
sampling frame - A list of individuals from whom the sample is drawn; individuals who may be in the population of interest but who are not in the sampling frame cannot be included in any sample.
sampling variability-the differences between each sample that we draw at random "sample-to-sample differences*
homogeneous groups-population that is split up into groups that are alike; for example (men, women).
heterogeneous groups-
strata-homogenous groups that are used to split up the population before a sample is chosen.
stratified random sample- a sampling design where the population is divided into subpopulations (strata) and then random samples are taken from each stratum.
cluster sampling- sampling method where an entire group (cluster) is chosen at random. Used for convenience, practicality, or cost.
multistage sampling- sampling method that uses and combines several other sampling methods to make more randomization.
systematic sampling- a sample drawn by selecting individuals systematically from a sampling frame. When there is no relationship between the order of the sampling frame and the variables of interest, a systematic sample can be representative.
respondents-
voluntary response bias- Bias introduced to a sample when individuals can choose on their own whether to participate in the sample. Samples based on voluntary response are always invalid and cannot be recovered, no matter how large the sample size.
convenience sampling- Simply include the individuals who are at hand. An unreliable method of sampling.
undercoverage- a sampling scheme that does not inclue some part of the population and/or makes them have less representation than it does have in the population. A bias is a result from undercoverage
nonresponse bias- Bias introduced to a sample when a large fraction of those sampled fail to respond. those who do respond are likely to not represent the entire group. Voluntary response is a form of nonresponse bias...but it may occur for many other reasons. Nonresponse is a problem in many surveys...think of it as the examplethey gave in the book "I know its dinnertime, but i'm sure yu wouldnt mind answering a few questions, it'll only take about twenty minutes...oh youre busy?" another example inculdes those who are at work durting the day won't respond to a telephone survey only conducted during the workday.
response bias- bias that is caused by a survery design that influences responses. Such examples are the words that are used to persuade people to answer questions more favorable to the cause, or if there is something that could be gained if you answer the survey (the employee discount that was used in the chapter 12 quiz)
1. Explain the difference between a population, a sampling frame, and a sample.
a population is an entire group of individuals in question.
a sampling frame is the list of individuals from whom the sample is drawn.
a sample represents a population, and is examined in hope of learning about that population. The subjects that actually gave us data.
2. What does it mean for a sample to be representative of a population?
This means that the small sample basically covers what the entire population thinks or does. The best way to get a sample to represent the population is by picking the sample at random.
3. What is meant by a biased sample?
A sample that is bias fails to represent its population accurately. ( like the election example on page 227- The names they used were from phone books, and only the wealthy owned phones during the Great Depression, and the wealthy tended to support Landon, so they predicted a win for Landon. But if you were to represent the population during the Depression correctly, the poor would need to be heavily represented, and the simulation would probably have correctly predicted a win for Roosevelt.)
Common errors include (that result in bias):
1.) relying on voluntary response
2.) undercoverage of the population
3.) nonresponse bias
4.) response bias
4. What is the role of randomization in selecting a sample?
Randomization protects us from influences of all the features of a population, even effects we weren't aware of. It makes sure that on the average the sample looks like the rest of the population.
5. What is meant by a census? Why is a census often impractical?
A census is a special sample where everyone is included and responses to surveys are received from the whole population.
A census is often impractical because:
1) it can be difficult to complete~ there will always be some individuals too hard to locate and the cost of locating them may exceed your budget.
2) populations rarely stand still~ babies are born and people die or move, a population changes while you work so it is never possible to get a perfect measure.
3) taking a census can be more complex that sampling~ they require the cooperation of the population members, many people are accidentally counted twice, and many people are overlooked.
6. Explain the difference between a parameter and a statistic.
A parameter is something we hope to estimate from the data. (For example, from the mean salaries of the subjects in a sample (a statistic created from data) we hope to estimate the mean salaries of all workers in the U.S.--> we rarely will know the true parameter)
7. A Simple Random Sample (SRS) must satisfy what two conditions?
Every subject/unit/etc. must have an equal chance for being selected and each combination of subjects/units/etc. must have an equal chance of being selected.
8. What is meant by sampling variability?
sampling variability is simply the differences between each randomly chosen sample. It is "the price we must pay for working with a sample rather than the entire" set of data.
9. When is stratified random sampling useful?
This is useful when having two or more different groups may bias your results. It may be better to just split them and analyze them separately. (like the example about girls/boys and their opinions on funding of sports-page 232)
10. When is cluster sampling useful?
When the sample size is very large and it would be too tidious to pick out random samples. Then you would take one little part, or cluster, and look at those data very thoroughly.
Example- If we wanted to check the reading level off our Stats textbook. We wouldn't want to go through the whole book and pick out a random word on every page or every other page. Instead, we would pick one page and use every word on that page as our sample.
11. What is meant by a multistage sampling?
Multistage sampling is a sampling scheme that combines several sampling methods together. A general example of multistage sampling is the combination of the cluster sampling and simple random samples, which is used by polling organizations.
12. When is systematic sampling appropriate?
Systematic sampling is appropriate when there is no relationship between the order of the sampling frame and the variables of interest.
13. In what way are voluntary response samples often biased?
they are usually biased towards those with strong opinions or who are strongly motivated. People with very negative opinions tend to respond more often than those with equally strong positive opinions.
14. Why is convenience sampling unreliable?
15. What is meant by undercoverage? Give an example.
Undercoverage is when a portion of the population is not sampled at all or has a smaller representation in the sample than it has in the population. An example is in a telephone survey, when a telephone survey is conducted and you often eat out, you are less likely to be surveyed (which is a source of undercoverage.)
16. Explain the difference between nonresponse bias and response bias.
17. How can the wording of questions cause bias in a survey?
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Name
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Statistic
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Parameter
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Mean
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y bar
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μ ( mu )
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Standard Deviation
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s
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Σ (sigma)
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Correlation
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r
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ρ (rho)
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Regression coefficient
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b
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β (beta)
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Proportion
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p
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ρ (pee)
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