Stats: Modeling the World. Chapter 11: Sample Surveys

Transcription

1 Stats: Modeling the World Chapter 11: Sample Surveys

2 Sampling Methods: Sample Surveys Sample Surveys: A study that asks questions of a small group of people in the hope of learning something about the entire population. Ex: Opinion Polls

3 Bias Bias: Any systematic failure of a sampling method to represent its population. Biased sampling methods tend to over- or underestimate parameters. Relying on voluntary response Under coverage of the population Nonresponse bias

4 What went wrong? The magazine used the phone book to find 10 million names to mail survey s too. But in 1936, at the height of the great depression, telephones were a real luxury, so they sampled more rich than poor voters.

5 Bias There is usually no way to fix a biased sample and no way to salvage useful information from it. The best option to deal with bias is to avoid it as much as possible by using a random selection process. Which is why understanding randomness is important..

6 Sample Size The fraction of the population that you ve sampled doesn t matter. It s the sample size itself that s important. A random sample of 100 students in a college represents the student body just about as well as a random sample of 100 voters represents the entire electorate of the United States.

7 Sampling Method: Census Census: A sample that consists of the entire population is called a census. Why bother determining the right sample size? Isn t it easier to just include everyone?

8 Census Taking Problems with taking a census: It can be hard (or expensive) to locate or measure or may be impractical Populations rarely stand still. The population often changes while you work, so it s never possible to get a perfect measure. Taking a census may be more complex than sampling.

9 Populations and Parameters Models use mathematics to represent reality. Parameters are the key numbers in those models. Population Parameter: A parameter that is part of a model for the population Ex: Population Average Statistic: Any summary found from the data Sample Statistics: The statistics that estimate population parameters

10 Parameter Notation:

11 Simple Random Samples Simple Random Sample(SRS): A sample of size n in which a set of n elements in the population has an equal chance of selection. Is our standard. Every possible group of n individuals has an equal chance of being our sample. That s what makes it simple. Let s Look at an example from the text.

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13 Representative Sample Representative: A sample is said to be representative if the statistics computed from it accurately reflect the corresponding population parameters. We want the statistics we compute to reflect the corresponding parameters accurately

14 SRS: Sampling Frame Sampling Frame: Is a list of individuals from which the sample is drawn Once we have our sampling frame, the easiest way to choose an SRS is to assign a random number to each individual in the sampling frame. Back to the dorm room example our sampling frame would be the list of 57 students applying for the room.

15 SRS: Sampling Variability Sample Variability: The natural tendency of randomly drawn samples to differ one from another. Each draw of random # s Selects different people

16 Stratified Sampling Stratified Sampling: A sampling design in which the population is divided into several subpopulations, or strata and random samples are then drawn from each stratum. Stratified samples can reduce sampling variability by identifying homogeneous subgroups. Let s look at an example from the text

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18 Cluster Sampling Cluster Sample: A sampling design in which entire groups, or clusters are chosen at random. Cluster sampling is usually selected as a matter of convenience, practicality, or cost. Cluster samples randomly select among heterogeneous subgroups that each resemble the population at large, making our samples more manageable. Let s look at an example from the text.

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20 Stratified vs. Cluster Sampling Boston Cream Pie consists of a layer or yellow cake, a layer of pastry crème, and chocolate frosting. Suppose a taster wants to check your company s pies for quality. They d need to eat small samples of randomly selected pies, tasting all three components: the cakes, the crème, and the frosting.

21 Stratified Sampling Method for Pie Tasting: One approach is to sample in strata (cake, chocolate frosting, crème) being homogeneous subgroups of your population. Select some tastes of the cake at random, some tastes of crème at random, and some bits of frosting at random. You ll end up with a reliable judgment of the pie s quality.

22 Cluster Sampling Method for Pie Tasting: Another approach is to cut a vertical slice out of each pie. The slice will be a lot like the entire pie, so by eating that slice you ll learn about the whole pie. This vertical slice containing all the different ingredients in the pie would be a cluster sample.

23 Stratified vs. Cluster Strata are internally homogeneous, but differ from one another. We select clusters to make sampling more practical or affordable.

24 Systematic Sampling Systematic sample: A sample drawn by selecting individuals systematically from a sampling frame starting at a random individual. When order of the list is not associated with responses sought, systematic sampling can give a representative sample. Systematic samples can work in some situations and are often the least expensive method of sampling. Let s look at an example from the text

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26 Multi-stage Sampling Sometimes we use a variety of sampling methods together. Multi-stage Samples: A sampling schemes that combine several sampling methods. Most surveys conducted by professional polling organizations use combinations of stratified, and cluster sampling as well as simple random sampling.

27 (Recall)Simple Random Sample(SRS): A sample of size n in which a set of n elements in the population has an equal chance of selection a) Roper is not using a simple random sample. The samples are designed to get 500 males and 500 females. This would be very unlikely to happen in a simple random sample b) They are using stratified sample, with two strata, males and females.

28 a) Population Unclear, but probably all U.S adults b) Parameter Proportion who have used and have benefitted from alternative medical treatments c) Sample Frame All Consumer Union Subscribers d) Sample Those subscribers who responded e) Method Not Specified, but probably questionnaire mailed. There doesn t appear to be any randomization f) Bias Voluntary response bias. Those who respond may have strong feeling one way or another.